TPC (Tons per Centimeter)

TPC (Tons per Centimeter) is an important ship stability and cargo intake measurement used to calculate how much weight is required to change a ship's draft by one centimeter. In practical shipping, TPC helps Shipowners, Ship Managers, Shipbrokers, Charterers, Port Agents, Ship Masters, and cargo planners estimate how much cargo can safely be loaded without exceeding the permitted draft, load-line limit, port restriction, canal restriction, or water-density allowance.

In dry bulk and general cargo operations, the central commercial question is often simple: how much cargo can the ship lift? The answer is rarely based only on the ship’s summer deadweight. Cargo intake depends on available hold space, cargo density, stowage factor, bunkers remaining on board, freshwater, stores, constants, load-line zone, port draft, water density, trim, stability, and voyage requirements. TPC (Tons per Centimeter) is one of the tools used to convert draft difference into weight and weight difference into draft effect.

The cargo quantity stated in the Bill of Lading (B/L) is the quantity that the ship is expected to carry and deliver, subject to the contract and measurement method. Before that quantity can be finalized, the operator must check whether the ship has enough deadweight, enough cubic space, and enough draft allowance to carry the cargo safely. A ship may have sufficient deadweight but not enough hold volume for light cargo. Another ship may have enough cubic capacity but may be unable to load fully because of a shallow berth or seasonal load-line restriction.

Summer Deadweight (DWT) and Cargo Intake

Summer Deadweight (DWT) indicates the total weight the ship can carry when loaded to the summer load line. This includes cargo, bunkers, freshwater, lubricating oil, stores, provisions, crew, spare parts, ballast where applicable, and other weights on board. It is not the same as the cargo quantity that can be loaded. The cargo quantity available for commercial carriage is known as DWCC (Deadweight Cargo Capacity).

When a ship is loaded to her summer marks, she has reached the maximum draft permitted under the summer load-line condition. However, a ship cannot always load to summer marks. If the voyage passes through a winter zone, a shallow port, a canal, a river, a tidal berth, or a waterway with restricted depth, the permitted cargo intake must be reduced. The ship may also need to sail with enough bunkers to reach the next bunker port safely, and those bunkers reduce the cargo capacity available.

Therefore, cargo intake calculation starts with deadweight but does not end there. The operator must deduct all non-cargo weights and adjust for any draft limitation that applies during the voyage. The purpose of TPC is to help calculate how much weight must be removed or may be added when the permitted draft differs from the ship’s draft at the relevant load line.

Stowage Factor (SF) and Hold Capacity

One of the first cargo-intake questions is whether the ship has enough space for the cargo. This depends on the Stowage Factor (SF) of the commodity. Stowage Factor (SF) shows how many cubic meters are occupied by one metric ton of cargo in the ship's hold. It is a relationship between cargo volume and cargo weight.

Heavy cargoes have a low Stowage Factor (SF) because each metric ton occupies relatively little space. Iron ore is a typical example. It may have a Stowage Factor (SF) of about 0.40 m3/mt. Heavy grain may have a Stowage Factor (SF) around 1.30 m3/mt, while woodchips may have a much higher Stowage Factor (SF), such as about 2.50 m3/mt. These figures show why two cargoes of the same weight can require very different hold volumes.

If the cargo is dense, the ship may become draft-limited before the holds are full. If the cargo is light, the ship may become space-limited before the ship reaches her permitted draft. This distinction is essential in voyage estimation. A Shipowner should not assume that the full summer deadweight can be lifted unless both deadweight capacity and cubic capacity support the calculation.

For bulk cargoes, the operator normally uses the ship’s grain capacity. For bagged, palletized, baled, or packaged cargo, the operator uses bale capacity. Grain Capacity is larger because free-flowing bulk cargo can occupy recesses and spaces that packaged cargo cannot use. Bale Capacity is lower because cargo in bags, bales, units, or pallets cannot fill every frame space or irregular corner of the hold.

The maximum cargo by space is calculated by dividing the relevant capacity by the cargo’s Stowage Factor (SF):

Maximum cargo by space = Available hold capacity / Stowage Factor (SF)

If the result is lower than the ship’s draft-based cargo intake, the ship is space-limited. If the draft-based intake is lower than the space result, the ship is deadweight or draft-limited.

Deductions from Deadweight

After checking cargo volume, the operator must calculate the available weight capacity. The ship's Deadweight All Told (DWAT) includes all weights carried by the ship, not only cargo. Therefore, deductions must be made before identifying DWCC (Deadweight Cargo Capacity).

Common deductions include:

  • Constants, including crew, provisions, stores, spare parts, lubricating oils, slops, operational liquids, unpumpable residues, and other shipboard weights.
  • Freshwater carried for crew, machinery, and shipboard use.
  • Bunkers Remaining on Board (ROB), including fuel for the Main Engine (ME), Auxiliary Engines (AE), boilers, generators, and safety margin.
  • Ballast water, if any ballast must be retained for stability, trim, stress, or operational reasons.
  • Any additional weights required for the particular voyage, such as dunnage, lashing materials, cargo gear, grabs, special equipment, or security stores.
Constants vary according to ship type, size, age, trading pattern, management practice, and calculation method. A small dry cargo ship may have constants near the lower end of the range, while a very large bulk carrier may have substantially higher constants. A practical working assumption may place constants between about 250 tons and 500 tons, but the operator should use the ship's actual declared constants where available. Incorrect constants can distort cargo-intake calculations and lead to draft problems at the loading port.

What is TPC (Tons per Centimeter)?

TPC (Tons per Centimeter) is the number of tons required to change the ship's mean draft by one centimeter. If a ship has a TPC of 60 tons, adding 60 tons will increase the mean draft by approximately one centimeter. Removing 60 tons will reduce the mean draft by approximately one centimeter. The same principle applies to fuel consumption during a voyage. If the ship burns 30 tons of fuel and water per day and her TPC is 60 tons, her mean draft will reduce by about half a centimeter per day, assuming other factors remain unchanged.

TPC is not a fixed universal value for the ship in all loading conditions. It changes according to draft because the shape of the ship’s underwater body changes as the ship sinks deeper or rises. For operational calculations, the TPC figure should be taken from the ship’s hydrostatic tables at the relevant draft. Using an approximate TPC may be acceptable for quick estimates, but final cargo-intake calculations should use the ship’s official stability and hydrostatic data.

TPC is especially useful when a draft restriction is lower than the ship’s summer draft. The difference between the permitted draft and the summer draft is converted into centimeters and multiplied by TPC. The result is the amount of deadweight that must be deducted from the summer deadweight to keep the ship within the lower permitted draft.

TPC Formula for Draft Restriction

The basic formula is:

Deadweight reduction = Draft difference in centimeters x TPC

If the ship’s summer draft is 12.50 meters and the available port draft is 12.20 meters, the difference is 0.30 meters, or 30 centimeters. If the ship’s TPC at that draft is 55 tons, the deadweight reduction is:

30 cm x 55 tons = 1,650 tons

This means the ship must load about 1,650 tons less than the summer deadweight condition, before considering any further allowances, trim, freshwater, bunkers, or safety margins. After this draft-based deadweight is calculated, the operator must deduct constants, bunkers, freshwater, and any other non-cargo weights to obtain the available DWCC.

Load Lines and Seasonal Draft Restrictions

A ship cannot safely enter a winter load-line zone loaded down to her summer marks if that would submerge the winter freeboard. Load-line regulations exist to preserve reserve buoyancy and safety in different seasonal sea conditions. Winter zones generally require more freeboard than summer zones because weather and sea conditions are more severe. Tropical zones may allow a deeper loading condition where conditions are less severe.

When a voyage crosses more than one load-line zone, the operator must ensure that the ship complies with the applicable load-line mark at each stage of the voyage. This may require calculating expected bunker consumption before entering the restricted zone. A ship may sail from a summer zone with a draft that would be too deep for a later winter zone only if bunker consumption and other weight changes reduce the draft sufficiently before entering that zone. This must be calculated carefully and supported by the ship’s stability information.

Load-line planning is therefore connected with bunker planning. Carrying more bunkers improves endurance and safety margin but reduces cargo intake and increases draft. Carrying fewer bunkers improves cargo capacity but may create bunker risk. TPC helps quantify these choices by showing how weight changes affect draft.

DWCC (Deadweight Cargo Capacity)

DWCC (Deadweight Cargo Capacity) is the commercial cargo weight the ship can carry after deducting all non-cargo weights from the applicable deadweight. It is one of the most important figures in dry bulk voyage estimation. Freight is often earned on cargo quantity, so every ton of DWCC can affect voyage revenue.

The simplified calculation is:

DWCC = Applicable deadweight - constants - freshwater - bunkers - other non-cargo weights

The applicable deadweight may be summer deadweight if the ship can load to summer marks and no later draft restriction applies. If a lower draft applies because of port limits, canal limits, river limits, seasonal load line, air draft, or water density, the applicable deadweight must be reduced first. TPC is used to calculate that reduction.

For example, if a ship has a summer deadweight of 50,000 tons but must reduce deadweight by 1,650 tons because of a draft restriction, the applicable deadweight becomes 48,350 tons. If constants are 400 tons, freshwater is 150 tons, bunkers are 1,200 tons, and other voyage weights are 100 tons, then:

DWCC = 48,350 - 400 - 150 - 1,200 - 100 = 46,500 tons

This is the cargo quantity available by weight, subject to hold capacity and stability confirmation.

FWA (Fresh Water Allowance)

FWA (Fresh Water Allowance) is the amount by which a ship may increase her draft when moving from salt water to fresh water while maintaining the same displacement. Fresh water is less dense than seawater. Because fresh water provides less buoyancy, a ship floats deeper in fresh water than in salt water for the same weight.

Standard seawater density is commonly taken as 1.025 gr/cm3, while freshwater density is taken as 1.000 gr/cm3. If a ship loads in fresh water and later sails into salt water, the ship will rise. If a ship loads in salt water and enters fresh water, the ship will sink deeper. This is why water density must be considered in ports, docks, rivers, estuaries, and inland waterways where the water may not be full seawater.

FWA is shown in the ship’s stability booklet and load-line information. It should not be guessed. It varies with ship size, form, and loading condition. Operators use FWA to calculate how much extra draft may be allowed when loading in dock water of lower density, provided the ship will be within the permitted load line when she reaches seawater.

DWA (Dock Water Allowance) and BWA (Brackish Water Allowance)

DWA (Dock Water Allowance) or BWA (Brackish Water Allowance) is the draft allowance used when the water density is between freshwater and seawater. Dock water or brackish water may be a mixture of seawater and freshwater. This commonly occurs in rivers, estuaries, enclosed docks, tidal basins, inland waterways, and ports influenced by rainfall, river discharge, or tidal mixing.

The formula is:

DWA = FWA x (1025 - density of dock water) / 25

In this formula, density is expressed as a figure such as 1020 rather than 1.020, and 1025 represents standard seawater. The number 25 is the difference between seawater density 1025 and freshwater density 1000.

Brackish Water Allowance (BWA) or Dock Water Allowance (DWA) Example

Assume:
  • Dock water density = 1.020, expressed as 1020 in the formula.
  • FWA = 300 mm.
The calculation is:

DWA = 300 mm x (1025 - 1020) / 25

DWA = 300 mm x 5 / 25

DWA = 60 mm

The ship may therefore load to an additional 60 mm draft in that brackish water condition, provided all other safety, load-line, stability, trim, and port requirements are satisfied. This does not mean the ship may ignore her load line. It means the operator may account for the fact that the ship will rise when moving from lower-density dock water into standard seawater.

Using TPC with DWA and FWA

TPC and water-density allowances are often used together. DWA gives the extra draft allowance in millimeters or centimeters. TPC then converts that draft allowance into an approximate weight allowance. If the DWA is 60 mm, this equals 6 cm. If the ship's TPC is 60 tons per centimeter, the weight represented by the DWA is approximately:

6 cm x 60 tons = 360 tons

This means the water-density allowance may permit approximately 360 additional tons of loading in that condition, subject to the ship’s official hydrostatic data, load-line marks, trim, and stability. The operator should avoid treating this as a casual bonus cargo. It must be verified carefully because overloading can lead to detention, fines, cargo short loading, unsafe departure, or insurance problems.

Practical Cargo Intake Calculation

A professional cargo intake calculation should follow a logical sequence:
  1. Identify the ship's summer deadweight, summer draft, TPC, FWA, capacities, and hydrostatic data.
  2. Confirm the cargo type, Stowage Factor (SF), moisture, trimming requirement, angle of repose, cargo hazards, and whether grain or bale capacity applies.
  3. Calculate the maximum cargo by space using grain or bale capacity divided by Stowage Factor (SF).
  4. Identify all draft limits at loading port, discharging port, canals, rivers, intermediate ports, and seasonal load-line zones.
  5. Convert draft differences into weight differences using TPC at the relevant draft.
  6. Apply FWA, DWA, or BWA if water density affects loading draft.
  7. Deduct constants, freshwater, bunkers, ballast retained, stores, and other non-cargo weights.
  8. Check trim, stability, longitudinal strength, hold loading limits, hatch cover loads, and stress restrictions.
  9. Compare the space-limited cargo figure with the draft-limited cargo figure and use the lower safe figure.
  10. Allow a prudent safety margin to avoid overloading, especially where draft readings, density, or cargo weights may vary.
The final cargo quantity should not be based only on one formula. It must be checked against the ship's loading manual, stability program, draft survey, terminal restrictions, Charterparty quantity, and the Ship Master's judgment. The Ship Master remains responsible for the safety of the ship and should not be pressured to load beyond safe limits.

TPC and Draft Surveys

TPC is also relevant to draft surveys. A draft survey estimates cargo weight by comparing the ship's displacement before and after loading or discharge. Surveyors read the ship's drafts, correct for trim, list, water density, and other factors, then calculate displacement using hydrostatic tables. The difference between light and loaded displacement, after adjusting for bunkers, ballast, freshwater, stores, and constants, gives the cargo quantity.

Because small draft-reading errors can produce significant weight differences, TPC gives a useful sense of sensitivity. If the ship’s TPC is 60 tons per centimeter, an error of just 2 cm in mean draft may represent about 120 tons. This is why draft marks, sea conditions, swell, list, trim, density measurement, and careful survey procedure matter. In high-value cargoes, a small draft error can create a large commercial dispute.

TPC and Bunker Consumption during the Voyage

As the ship burns fuel and consumes freshwater during the voyage, her draft decreases. This may be important where the ship leaves a loading port near the maximum permitted draft but must enter a later restricted zone or shallow discharging port. The operator can estimate the expected draft reduction by dividing expected weight consumption by TPC.

For example, if the ship consumes 36 tons of fuel and water per day and the relevant TPC is 60 tons per centimeter, the draft reduction is approximately 0.6 cm per day. Over 10 days, this represents about 6 cm. Such calculations help determine whether the ship will be within the required draft when reaching the next port or load-line zone.

However, fuel consumption is not perfectly predictable. Weather, speed, currents, route changes, port delays, cargo heating, generator load, and crane use can all change consumption. Therefore, draft planning should include a safety margin rather than relying on exact daily consumption.

Common Mistakes in TPC Calculations

Many cargo-intake errors occur because operators use simplified figures without checking the ship's official data. Common mistakes include:
  • Using summer deadweight as cargo capacity without deducting bunkers, constants, freshwater, and other weights.
  • Ignoring port, canal, berth, river, or seasonal draft restrictions.
  • Using deadweight capacity without checking grain or bale capacity against Stowage Factor (SF).
  • Applying one TPC value at all drafts even though TPC changes with draft.
  • Forgetting water-density allowances in brackish water or dock water.
  • Assuming DWA allows extra cargo without checking whether the ship will be legal in seawater.
  • Failing to allow for trim, stability, longitudinal strength, or hold loading limits.
  • Using estimated constants that do not match the ship's real condition.
  • Ignoring bunker safety margin and later discovering that additional bunkers reduce cargo intake.
These mistakes can lead to overloading, short loading, detention, fines, charterparty disputes, deadfreight claims, cargo shortage disputes, unsafe sailing condition, and loss of commercial credibility. A professional operator treats TPC as part of a complete calculation rather than a standalone shortcut.

Commercial Importance of TPC in Chartering

TPC directly affects chartering economics because even a small draft difference can represent a significant cargo quantity. In a tight market, an additional few hundred tons of cargo may improve voyage revenue. In a restricted port, a few centimeters of lost draft may reduce earnings. The Shipbroker and operator must therefore understand TPC when calculating intake, offering cargo quantity, declaring MOLOO (More or Less in Owner's Option), estimating freight, or assessing deadfreight risk.

For Charterers, TPC matters because it affects whether the nominated ship can lift the contractual cargo. For Shipowners, it affects whether the ship can maximize earnings without violating draft limits. For Ship Masters, it supports safe loading decisions. For surveyors, it helps assess the impact of draft readings. For Port Agents, it helps explain loading restrictions and port limitations. TPC is therefore both a technical and commercial measurement.

Why TPC Matters in Daily Ship Operations

TPC (Tons per Centimeter) is not only a theoretical figure from the ship's hydrostatic tables. It is used in daily operational decisions whenever the ship's draft, cargo quantity, bunker quantity, or water density must be converted into a commercial loading decision. In dry bulk shipping, a difference of only a few centimeters can represent several hundred tons of cargo. That difference may decide whether the Shipowner earns additional freight, whether the Charterer has enough cargo space, whether the ship can pass a shallow berth safely, or whether a deadfreight claim may arise.

For a small coastal ship, one centimeter of draft may represent a modest cargo quantity. For a large bulk carrier, one centimeter can represent a very substantial amount of cargo. This is why cargo intake calculations should not be left until the ship reaches the loading berth. The Shipowner, Ship Manager, Shipbroker, Charterer, and Ship Master should all understand the expected intake before the fixture is concluded and before cargo is delivered to the terminal.

TPC also helps operators understand the effect of daily consumption. As the ship burns fuel and uses water, the ship becomes lighter and rises in the water. This may allow the ship to comply with a later draft restriction. However, relying on future consumption without a margin is risky. Weather, delays, speed changes, auxiliary engine use, cargo heating, crane operations, or route changes may alter actual consumption. Therefore, TPC should be used with practical caution and not as a mechanical shortcut.

TPC and the Difference Between Cargo Intake and Deadweight

A frequent commercial mistake is to treat the ship's deadweight as the cargo quantity that can be loaded. Deadweight is the total weight that can be carried in addition to the ship's lightweight. Cargo is only one part of that weight. Bunkers, freshwater, lubricants, stores, crew, provisions, spare parts, ballast retained on board, slops, residues, and operational equipment all consume part of the deadweight.

TPC becomes important when the applicable draft is lower than the draft linked to the full deadweight. The operator first calculates how much deadweight must be deducted because of the draft restriction. Only after that deduction should the operator subtract non-cargo weights to find DWCC (Deadweight Cargo Capacity). If the operator deducts constants and bunkers from summer deadweight without first applying the draft restriction, the calculation may overstate the safe cargo quantity.

The correct order is important. First, identify the maximum draft allowed. Second, compare that draft with the ship’s relevant load-line draft. Third, convert the draft difference into weight by using TPC. Fourth, reduce the available deadweight accordingly. Fifth, deduct all non-cargo weights. Sixth, compare the result with cargo-space capacity and stability limitations. The cargo that can be loaded is the lowest safe figure produced by these checks.

Example 1: Draft Restriction at the Loading Port

Assume a bulk carrier has a summer deadweight of 55,000 tons and a summer draft of 12.80 meters. The loading berth can safely accept the ship only up to a sailing draft of 12.45 meters. The ship's TPC at the relevant draft is 58 tons per centimeter. The draft difference is:

12.80 m - 12.45 m = 0.35 m = 35 cm

The deadweight reduction is:

35 cm x 58 tons = 2,030 tons

The ship cannot use her full summer deadweight. The applicable deadweight becomes:

55,000 tons - 2,030 tons = 52,970 tons

If the ship has constants of 420 tons, freshwater of 180 tons, bunkers of 1,050 tons, and other voyage weights of 70 tons, the DWCC calculation is:

52,970 - 420 - 180 - 1,050 - 70 = 51,250 tons

The ship’s safe cargo intake by weight is therefore about 51,250 tons, subject to hold capacity, trim, stability, and strength checks. If the Charterer expected 53,000 tons because the ship was described as 55,000 DWT, the difference is not a failure of the ship. It is the commercial consequence of the draft restriction.

Example 2: Discharging Port Draft Restriction

A ship may be able to load deeply at the loading port but may be restricted by the discharging port. Assume a ship loads in a deep-water export terminal and will discharge at a river port with a maximum arrival draft of 11.20 meters. The ship's sailing draft after loading would be 11.55 meters if the full cargo were loaded. The sea passage to the discharging port will take 12 days. The ship expects to consume 32 tons of fuel and water per day. The relevant TPC is 64 tons per centimeter.

The total expected consumption before arrival is:

12 days x 32 tons = 384 tons

The expected draft reduction from consumption is:

384 tons / 64 tons per cm = 6 cm

If the ship sails at 11.55 meters, expected arrival draft will be approximately:

11.55 m - 0.06 m = 11.49 m

This is still above the permitted arrival draft of 11.20 meters. The operator must therefore reduce the loading quantity further. The remaining draft excess is:

11.49 m - 11.20 m = 0.29 m = 29 cm

The extra cargo reduction needed is:

29 cm x 64 tons = 1,856 tons

This example shows why it is not enough to check the loading port only. The discharge port, river passage, tidal window, canal, or berth restriction may govern the entire cargo intake even if the loading terminal can accept a deeper draft.

Example 3: Extra Cargo Allowed by Dock Water Allowance

Assume a ship is loading in dock water with a density of 1.015. The ship's FWA (Fresh Water Allowance) is 280 mm. The ship's TPC at the relevant draft is 52 tons per centimeter. The Dock Water Allowance is calculated as:

DWA = FWA x (1025 - dock water density) / 25

In this formula, 1.015 is used as 1015:

DWA = 280 mm x (1025 - 1015) / 25

DWA = 280 mm x 10 / 25

DWA = 112 mm

112 mm is equal to 11.2 cm. The approximate additional weight represented by this allowance is:

11.2 cm x 52 tons = 582.4 tons

In principle, the ship may load about 582 tons more in that dock-water condition than she could load at the same apparent draft in standard seawater, provided the ship will not be overloaded when she reaches seawater and provided stability, trim, and load-line requirements are satisfied. In practice, the Ship Master and surveyor should apply a prudent margin because dock-water density can vary during loading, especially in tidal ports and river berths.

Example 4: Cargo Intake Limited by Hold Space Instead of Draft

Assume a ship has grain capacity of 62,000 m3 and a draft-based DWCC of 48,000 tons. The nominated cargo is woodchips with a Stowage Factor (SF) of 2.50 m3/mt. The maximum cargo by space is:

62,000 m3 / 2.50 m3/mt = 24,800 mt

Although the ship may have enough draft-based capacity for 48,000 tons, the ship can carry only about 24,800 tons of this cargo because the holds will be full. TPC is not the limiting factor here. The cargo is space-limited. This is common with very light bulk cargoes such as woodchips, certain biomass cargoes, some agricultural products, and cargoes with high Stowage Factor (SF).

If the Shipowner had fixed the ship assuming full deadweight cargo without checking the Stowage Factor (SF), the voyage estimate would be completely wrong. Freight earnings based on weight would be much lower than expected. This example shows why TPC must be used together with Stowage Factor (SF), grain capacity, and bale capacity.

Example 5: Cargo Intake Limited by Deadweight Instead of Space

Assume another ship has grain capacity of 58,000 m3 and an available DWCC of 45,500 tons. The cargo is iron ore with a Stowage Factor (SF) of 0.40 m3/mt. The theoretical cargo by space is:

58,000 m3 / 0.40 m3/mt = 145,000 mt

Obviously, the ship cannot carry 145,000 tons because the ship’s deadweight is far lower. In this case, the ship is deadweight-limited. The cargo will occupy only part of the hold volume, but the ship may already be at her permitted draft. Heavy cargoes require careful loading distribution because excessive weight concentration in particular holds can exceed tank-top strength or create unacceptable bending moments and shear forces.

For dense cargoes, TPC helps estimate the draft effect of weight, but the loading manual, hold-loading limits, stability computer, and structural restrictions are equally important. A ship may have enough total deadweight but still be unable to place all cargo in the desired holds because of local strength limits.

Example 6: Bunker Consumption and Arrival Draft

Assume a ship departs with an arrival restriction ahead. The ship's draft on sailing is 10.90 meters. The next port permits only 10.75 meters on arrival. The voyage will take 8 days. The ship expects to consume 28 tons of fuel and water per day. The TPC is 56 tons per centimeter.

Total expected consumption is:

8 days x 28 tons = 224 tons

Expected draft reduction is:

224 tons / 56 tons per cm = 4 cm

Expected arrival draft is:

10.90 m - 0.04 m = 10.86 m

The ship is still expected to arrive 11 cm deeper than the permitted draft. The additional cargo or weight that must be removed before sailing is:

11 cm x 56 tons = 616 tons

Therefore, the ship should not sail at 10.90 meters if the 10.75-meter arrival restriction is firm, unless a tidal allowance, lightering arrangement, density correction, or other lawful draft solution exists. This type of calculation is common when planning voyages to river ports, lake ports, tidal berths, and shallow terminals.

Example 7: TPC and a Small Draft Reading Error

Draft readings are not always perfect. Waves, swell, current, list, trim, poor lighting, inaccessible draft marks, marine growth, and human error may affect readings. Assume a draft survey is performed on a ship with a TPC of 70 tons per centimeter. If the mean draft is read 3 cm too deep, the displacement may be overstated by approximately:

3 cm x 70 tons = 210 tons

If the cargo is valued or freighted at a high rate, this error may have a meaningful financial effect. If the same error occurs in both opening and closing surveys, the effect may partly cancel. If it occurs only in one survey, the cargo quantity may be misstated. This is why professional draft surveys require careful draft reading, water-density measurement, correction for trim and list, and accurate accounting for ballast, fuel, freshwater, and constants.

TPC and Trim Considerations

TPC is based on the change in mean draft, but real ships do not always sink evenly. Cargo distribution affects trim. Adding cargo forward may increase forward draft more than aft draft. Adding cargo aft may increase aft draft more than forward draft. A ship may be within the mean draft limit but still exceed a forward or aft draft restriction at a lock, river passage, berth, or canal.

For this reason, TPC alone does not complete the loading calculation. The operator and Ship Master must check fore draft, aft draft, mean draft, trim, stability, bending moments, shear forces, propeller immersion, bridge visibility, and port-specific restrictions. Some ports restrict maximum arrival draft at the deepest point, not only mean draft. A ship trimmed by the stern may therefore violate a port limit even if the calculated mean draft appears acceptable.

Trim can also affect cargo operations. A small stern trim may be necessary for propeller immersion and steering performance. Excessive trim may create difficulties with hatch access, draft survey accuracy, crane outreach, cargo distribution, or port clearance. TPC helps with weight-to-draft conversion, but trim calculations require the ship’s hydrostatic and stability information.

TPC and Longitudinal Strength

Bulk carriers are subject to longitudinal stresses. Loading heavy cargo into selected holds while leaving others empty may create high bending moments and shear forces. This is especially important for alternate-hold loading with dense cargoes such as iron ore. The ship may be within deadweight and draft limits but still overstressed if the cargo distribution is unsuitable.

TPC cannot show whether the ship’s structure is within permissible bending and shear limits. It only helps estimate draft change from weight change. A complete loading plan must use the ship’s loading instrument or approved loading manual. The Ship Master and Chief Officer must ensure that hold distribution complies with class-approved limitations.

This is why a Charterer’s request to load maximum cargo into fewer holds for faster discharge may not be acceptable. Commercial efficiency cannot override structural safety. If the loading plan exceeds permissible limits, cargo must be redistributed even if this increases loading time or terminal work.

TPC and Safe Margin in Cargo Intake

A prudent cargo intake calculation should include a safety margin. The margin may be small or large depending on the reliability of the data. If the port draft is firm, water density is stable, the ship's constants are well known, and draft marks are easy to read, the margin may be modest. If the berth is tidal, water density changes, draft marks are difficult to read, cargo weight is estimated, or weather may delay sailing, the margin should be larger.

Overloading creates serious consequences. The ship may be stopped by port authorities, class, Flag State, Port State Control, pilots, terminal inspectors, or the Ship Master. Cargo may need to be discharged back ashore, causing delay, cost, cargo claims, demurrage disputes, and reputational damage. If the ship sails overloaded, safety, insurance, and legal consequences may be severe.

Underloading also has consequences. If the Shipowner declares too conservative an intake, freight revenue may be lost. If the Charterparty quantity is not loaded, the Charterer may face deadfreight or sale-contract issues. The goal is not simply to load less. The goal is to load the maximum safe and lawful quantity supported by the ship’s documents, port limits, cargo characteristics, and the Ship Master’s judgment.

TPC and MOLOO in Dry Bulk Chartering

Many dry bulk Charterparties state cargo quantity with a margin, such as 50,000 metric tons 10% more or less in Owner's option. This is commonly known as MOLOO (More or Less in Owner's Option). The Shipowner or Ship Master uses this margin to adjust final intake according to draft, bunkers, constants, stowage, load-line zone, and safety requirements.

TPC is directly relevant to MOLOO because it helps the Shipowner justify the final declared intake. If the ship is restricted by draft, the Shipowner can calculate the reduction from the advertised or expected cargo quantity. If water density allows additional loading, TPC helps estimate the extra weight that may be safely lifted. If bunker requirements increase because the next bunker port is farther away than expected, TPC helps show the draft consequence of additional bunkers.

However, MOLOO should not be abused. The option must be exercised in good faith and within the Charterparty terms. The Shipowner should not deliberately reduce cargo intake for convenience if the ship can safely and lawfully lift more. Likewise, the Charterer should not insist on a quantity that exceeds the ship’s safe draft or stability limits.

TPC and Deadfreight Risk

Deadfreight arises when the Charterer fails to provide the agreed cargo quantity and the Shipowner loses freight on unused cargo capacity. TPC can help determine whether missing cargo is due to Charterer default or genuine ship limitation. If the ship could safely load the full contractual quantity but the Charterer supplies less cargo, deadfreight may arise. If the ship cannot safely load the full quantity because of draft, density, load-line, or capacity limitations, the analysis is different.

Clear pre-fixture cargo-intake analysis reduces deadfreight disputes. The Shipbroker should check whether the cargo quantity is realistic. The Shipowner should avoid promising more than the ship can safely lift. The Charterer should understand that advertised DWT does not equal guaranteed cargo intake. The Charterparty should identify cargo quantity, margin, stowage factor assumptions, port restrictions, and any special loading limitations.

TPC and Port Restrictions

Port restrictions can be more important than the ship's design deadweight. A loading or discharging port may restrict draft because of berth depth, channel depth, tide, silting, river level, lock depth, bar conditions, under-keel clearance policy, or pilotage rules. Some ports provide a maximum draft only for a certain tidal window. Others apply a permanent all-tide draft limit.

TPC allows the operator to quantify the cargo loss caused by the restriction. If the port reduces permissible draft by 20 cm and the ship’s TPC is 65 tons, the commercial impact may be about 1,300 tons of deadweight. At a freight rate of USD 20 per ton, that draft restriction represents about USD 26,000 in gross freight impact before considering costs. This is why port restrictions must be checked before fixing.

Port Agents should provide the latest draft information because published port data may not reflect recent silting, dredging, seasonal river levels, berth damage, tidal restrictions, or local notices. The operator should not rely only on old port descriptions. Draft restrictions change, and a wrong assumption can damage the voyage result.

TPC and Water Density Measurement

Water density should be measured at the time and place of loading or draft survey. Density may vary between the surface and deeper water, between flood and ebb tide, and between rainy and dry periods. In river ports and estuaries, density can change during the same cargo operation. If a ship loads over several days, the density used at the start may not be the same as the density at completion.

Where density variation is material, the Ship Master and surveyor should take representative samples and apply correct corrections. A small density error may produce a meaningful draft or displacement error. If the ship is loading near maximum marks, density should be treated carefully. Overconfidence in a single density reading can lead to overloading or later disagreement about cargo quantity.

TPC and Freshwater Departure to Saltwater

Ships loading in freshwater can load deeper than the saltwater load-line mark by the Fresh Water Allowance because the ship will rise when entering seawater. However, this must be handled correctly. The ship must not be overloaded in terms of displacement. The deeper freshwater draft is allowed only because the same displacement will produce a shallower draft in seawater.

For example, if a ship has an FWA of 240 mm, the ship may float 24 cm deeper in freshwater than in seawater at the same displacement. If the TPC is 50 tons per centimeter, the draft allowance corresponds roughly to 1,200 tons of weight effect. But this does not mean the ship may simply load 1,200 tons above lawful displacement without calculation. The proper method is to apply the ship’s official FWA and hydrostatic data to confirm the lawful departure condition.

TPC and Cargo Moisture

Some bulk cargoes may contain moisture. Moisture changes both weight and safety characteristics. A cargo that becomes wetter may weigh more than expected. If cargo moisture increases before or during loading, the cargo weight delivered to the ship may rise even though the cargo volume appears unchanged. This can affect draft and cargo intake.

For certain cargoes, moisture also creates safety risk, including liquefaction. TPC can show the draft effect of extra water weight, but it cannot determine cargo safety. The Ship Master must rely on cargo declarations, test certificates, transportable moisture limit, moisture content, inspection, and applicable safety rules. If cargo condition is unsafe, the ship should not load merely because draft capacity appears available.

TPC and Bunker Strategy in Voyage Estimation

Bunkers are both cost and weight. Buying more bunkers at a cheaper port may reduce fuel cost but reduce cargo intake. Buying fewer bunkers may increase cargo intake but create higher bunker cost later or reduce safety margin. TPC allows the operator to calculate the cargo penalty of carrying extra bunkers.

Assume an operator can buy 600 extra tons of bunkers at a cheaper port before loading. The ship’s TPC is 60 tons per centimeter. Those extra bunkers increase draft by approximately:

600 tons / 60 tons per cm = 10 cm

If the loading port has enough draft and the freight rate is low, buying cheaper bunkers may be sensible. If the ship is draft-restricted and freight is high, the extra bunkers may reduce cargo revenue more than the bunker saving. A proper voyage estimate must compare bunker saving, freight loss, port cost, delay, and safety margin.

TPC and Time Charter Delivery and Redelivery

TPC may also be relevant during Time Charter delivery and redelivery. Bunkers remaining on board are measured and priced, and the ship's draft may be checked as part of delivery or redelivery condition. If bunker quantities are disputed, draft, soundings, density, tank tables, and consumption records may be examined. Although TPC is not the main tool for bunker surveys, it helps operators understand the relationship between significant bunker quantity differences and visible draft change.

If a Time Charterer redelivers the ship with substantially more or fewer bunkers than agreed, the financial settlement may be affected. Excess bunkers may be purchased by the Shipowner at the agreed price or market price, depending on the Charterparty. Insufficient bunkers may create a claim if the ship cannot safely proceed to the next employment. TPC helps quantify the operational effect of these weight differences.

TPC and Canal or Waterway Transit

Canals, locks, rivers, and restricted waterways may impose strict draft limits. These limits may be affected by water level, seasonal conditions, maintenance work, rainfall, drought, dredging, or authority notices. TPC helps calculate how much cargo must be reduced to meet a transit draft.

Assume a ship’s expected sailing draft is 13.05 meters, but a canal transit limit is 12.95 meters. The difference is 10 cm. If TPC is 72 tons per centimeter, the ship must reduce weight by about 720 tons before transit, unless consumption before reaching the canal reduces the draft sufficiently. If the canal is several days after loading, expected consumption may be credited, but only with a prudent margin. Any delay before canal arrival may reduce consumption assumptions if the ship spends time at anchor using less fuel than expected at sea.

TPC in Claims and Disputes

TPC can become important evidence in disputes about cargo quantity, overloading, short loading, deadfreight, draft restriction, draft survey figures, and voyage instructions. If a Charterer alleges that the ship failed to load the agreed quantity, the Shipowner may rely on TPC, hydrostatic data, draft limits, bunker quantities, and water density to show that the ship could not safely load more. If the Shipowner claims deadfreight, the Charterer may examine the same information to determine whether the ship actually had spare capacity.

Disputes may also arise when the Bill of Lading (B/L) quantity differs from draft survey quantity or shore scale quantity. TPC does not resolve the legal priority of measurement methods, but it helps identify whether the physical figures are plausible. If a claimed quantity would require a draft that the ship never reached, the claim may be questioned. If a draft difference corresponds broadly with the claimed weight difference, the figures may be more credible.

Practical Checklist for TPC-Based Cargo Intake

A practical checklist helps reduce mistakes:
  1. Use the ship's official hydrostatic tables and loading manual, not only rough figures.
  2. Confirm TPC at the relevant draft, not at an unrelated condition.
  3. Check whether the cargo is space-limited or draft-limited.
  4. Confirm Stowage Factor (SF), grain capacity, bale capacity, and hold restrictions.
  5. Identify all port, canal, river, seasonal, and berth draft limits.
  6. Apply FWA, DWA, or BWA only with reliable water-density information.
  7. Deduct constants, freshwater, bunkers, retained ballast, and other voyage weights.
  8. Calculate expected consumption before any later draft-restricted point.
  9. Check trim, stability, bending moments, shear forces, and hold loading limits.
  10. Keep a safety margin where data is uncertain or conditions may change.
  11. Document assumptions clearly so that the calculation can be explained later.
This checklist is useful for Shipowners, Ship Managers, Shipbrokers, Charterers, Port Agents, cargo surveyors, and Ship Masters. It also helps avoid the common problem of negotiating a cargo quantity that the ship cannot physically, legally, or safely carry.

How to Explain TPC to Charterers and Cargo Interests

Charterers and cargo interests may not always understand why a ship described as a certain DWT cannot load the same figure as cargo. The explanation should be simple and commercial. DWT is total carrying capacity. DWCC is cargo capacity after deducting non-cargo weights and applying draft limits. TPC converts draft differences into tons. Stowage Factor (SF) determines whether the cargo will fill the holds before the ship reaches her draft.

A clear explanation can prevent conflict. Instead of saying only “the ship cannot lift more,” the operator should show the calculation: draft limit, TPC, deadweight reduction, bunkers, constants, freshwater, and final DWCC. When the calculation is transparent, the Charterer is more likely to accept the intake limitation or adjust cargo planning before the ship arrives.

TPC, Safety, and Commercial Discipline

TPC demonstrates how closely safety and commercial calculation are connected. Every additional ton of cargo increases freight income, but every additional ton also affects draft, freeboard, stability, strength, and compliance. The commercial desire to maximize intake must never override the Ship Master's responsibility for safety. A safe ship is the basis of the voyage, and no freight benefit justifies overloading.

At the same time, excessive caution without calculation can reduce earnings unnecessarily. Professional operations requires a balanced approach: use the ship’s data, apply the formulas correctly, check the restrictions, consult the Ship Master, and keep evidence. The purpose of TPC is to support accurate decision-making, not to replace judgment.

Conclusion

TPC (Tons per Centimeter) is the number of tons required to change a ship's draft by one centimeter. It is a practical tool used to connect weight, draft, cargo intake, bunker consumption, load-line compliance, and water-density allowances. In dry bulk and cargo planning, TPC helps operators calculate how much cargo may be loaded when draft restrictions or water-density conditions apply.

A correct cargo-intake calculation requires more than knowing the ship’s Summer Deadweight (DWT). The operator must check Stowage Factor (SF), grain or bale capacity, constants, freshwater, bunkers, port draft, seasonal load lines, FWA, DWA, BWA, trim, stability, and strength limitations. TPC helps convert centimeters into tons, but it must be used with the ship’s official hydrostatic data and a sound operational judgment.

For Shipowners, Charterers, Shipbrokers, Ship Managers, Port Agents, Ship Masters, and surveyors, understanding TPC is essential. It reduces the risk of overloading, improves voyage estimation, supports safe cargo planning, assists draft surveys, and protects commercial earnings. In practical shipping, every centimeter can matter, and TPC explains what that centimeter is worth in tons.