Compute ship displacement from volume and density, from principal dimensions and block coefficient, from weight components, or adjust displacement using TPC.
∇ = — m³
Δ = — t
Δ = — t
ΔT = — cm, TPCused = — t/cm
Δ = — t
Ship displacement is the mass of the vessel in a stated loading condition. For a vessel floating freely in static equilibrium, that mass equals the mass of the water displaced by the immersed hull.
The displacement includes the vessel's lightweight together with cargo, ballast, fuel, fresh water, stores, crew, passengers and any other weight carried on board. It changes whenever weight is loaded, discharged, consumed or transferred off the vessel.
Ship practice often refers to displacement as the vessel's total weight. The numerical result produced by this calculator is expressed in metric tonnes, which is a unit of mass. A force value would additionally require multiplication by gravitational acceleration.
Displacement mass is related to underwater volume through water density:
Δ = ρ × ∇
| Symbol | Meaning | Usual unit |
|---|---|---|
| Δ | Ship displacement mass at the stated condition | t |
| ρ | Density of the water in which the vessel is floating | t/m3 |
| ∇ | Volume of water displaced by the immersed hull | m3 |
With density in t/m3 and underwater volume in m3, the result is obtained directly in metric tonnes.
Mass and volume are different quantities: displacement in tonnes must not be entered into a field asking for displaced volume in cubic metres. Convert between them using the water density belonging to the stated condition.
Consider a vessel at the following loading condition:
∇ = L × B × T × CB
∇ = 180 × 30 × 10 × 0.720 = 38,880 m3
Δ = ρ × ∇ = 1.025 × 38,880 = 39,852 t
The estimated displacement at the stated dimensions, coefficient and water density is 39,852 metric tonnes.
The calculator provides three methods. The correct method depends on whether the available information describes underwater geometry, onboard weight or a small change in draft.
| Method | Main inputs | Intended use |
|---|---|---|
| Direct from volume | ∇ and ρ | Known hydrostatic underwater volume |
| Direct from dimensions | L, B, T, CB and ρ | Geometric displacement estimate |
| Weight breakdown | Lightweight and all onboard weight components | Current total vessel mass |
| TPC adjustment | Reference draft, reference displacement, TPC and target draft | Small local draft change |
Use the volume mode when ∇ is available from hydrostatic tables, a hull model or another reliable source. Select the appropriate water-density preset or enter a measured custom density.
For example, an underwater volume of 30,000 m3 in seawater with ρ = 1.025 t/m3 gives:
Δ = 1.025 × 30,000 = 30,750 t
When underwater volume is not entered directly, the calculator first obtains it from:
∇ = L × B × T × CB
The result is then multiplied by water density. The length, beam and draft definitions must be the same definitions used to establish CB.
A block coefficient based on LPP should not be combined with LWL or LOA without recalculating the coefficient. The draft and coefficient must also belong to the same loading condition.
For a trimmed vessel, using a simple mean draft provides only a geometric estimate. Accurate displacement at trim requires hydrostatic data or integration of the actual immersed hull.
The vessel's total displacement can also be obtained by adding its lightweight and every weight carried on board:
Δ = Lightweight + Cargo + Ballast + Fuel + Fresh water + Stores + Crew and effects + Other weights
Empty fields in the calculator are treated as zero. Include every weight present in the loading condition and avoid entering the same item in more than one category.
| Component | Typical contents |
|---|---|
| Lightweight / lightship mass | Hull, machinery, permanent equipment and other fixed items |
| Cargo | Cargo carried in holds, tanks, containers or on deck |
| Ballast | Water or other ballast carried for the stated condition |
| Fuel | Fuel oils and other fuels included in the loading condition |
| Fresh water | Potable, technical and other fresh-water quantities |
| Stores | Provisions, consumables and operating stores |
| Crew and effects | Crew, passengers where applicable, baggage and personal effects |
| Other | Weights not represented by another listed category |
As a simple check, the following entries:
produce:
Δ = 12,000 + 9,000 + 1,500 + 800 + 200 + 50 + 30 + 20 = 23,600 t
TPC is the approximate change in displacement corresponding to a one-centimetre change in mean draft at the stated waterline.
The calculator converts the draft difference from metres to centimetres:
ΔTcm = (T1 − T0) × 100
It then adjusts the reference displacement:
Δ1 = Δ0 + TPCused × ΔTcm
A deeper target draft gives a positive draft difference. A shallower target draft gives a negative difference and reduces the estimated displacement.
For example:
ΔT = (12.10 − 11.80) × 100 = 30 cm
Δ1 = 30,500 + 56 × 30 = 32,180 t
Local approximation: TPC changes with draft because the waterplane area changes. This method is intended for a relatively small draft interval around the reference condition. For a large draft change, use hydrostatic displacement data across the relevant range.
When density scaling is enabled, the calculator assumes that the entered TPC corresponds to seawater with a density of 1.025 t/m3. It scales that value to the selected water density:
TPCused = TPC × (ρ ÷ 1.025)
This reflects the approximate proportional relationship between TPC and water density at an unchanged waterplane.
Reference-condition requirement: T0 and Δ0 must remain a valid draft and displacement pair for the starting condition. The optional correction changes the TPC slope used over the draft interval; it does not replace a full fresh-water or dock-water allowance calculation.
These terms describe different quantities and should not be used interchangeably.
| Term | Meaning | Typical unit |
|---|---|---|
| Displacement | Total vessel mass at a stated loading condition | t |
| Lightweight | Vessel mass without cargo and the listed variable consumable loads | t |
| Deadweight | Difference between displacement and lightweight | t |
| Gross tonnage | Regulatory index related to enclosed volume, not vessel mass | Dimensionless tonnage value |
| Net tonnage | Regulatory index related to the vessel's earning spaces, not vessel mass | Dimensionless tonnage value |
Deadweight = Displacement − Lightweight
Deadweight is carrying capacity rather than the total mass of the ship. Gross tonnage and net tonnage are not weight measurements and cannot be substituted for displacement.
At the same immersed volume, denser water produces a larger mass of displaced water. A vessel of fixed mass therefore floats at a shallower draft in denser water and at a deeper draft in less dense water.
Nominal values of 1.025 t/m3 for seawater and 1.000 t/m3 for fresh water are useful for basic calculations. When measured dock-water density is available, use the measured value for the stated condition.
Water density, draft, displaced volume and displacement must always be interpreted as one consistent hydrostatic condition.
Displacement changes whenever weight is loaded, discharged or consumed. Internal transfers between tanks or cargo spaces do not normally change total displacement, but they can change trim, heel and stability.
A displacement value should be associated with its loading condition, draft, trim and water density. Mean draft alone may not identify an accurate displacement when trim is substantial.
For operational calculations, use the vessel's approved hydrostatic tables, loading computer or stability information for the actual condition.
Displacement is required in hydrostatic, stability, resistance, powering and structural calculations. It establishes the vessel's total mass at a stated condition.
Displacement alone does not show how that mass is distributed. Two loading conditions can have the same displacement but different centres of gravity, trim, heel, shear forces, bending moments and stability.
Displacement by itself cannot determine:
Operational limitation: dimensional and TPC methods are estimates based on the entered assumptions. Approved vessel hydrostatics should take precedence when an operational, contractual or statutory displacement is required.
The terminology and calculation relationships used on this page follow established naval architecture sources:
NauticalSolver calculators are intended for preliminary engineering, study and independent checking. Use approved hydrostatic particulars, loading information and vessel-specific documentation for operational, contractual or statutory work.