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Ship Propulsive Power by the Admiralty Coefficient

Also known as Admiralty coefficient · Admiralty constant · ship power from displacement and speed · power needed by a ship at a speed · Admiralty formula · ship horsepower estimate · ship power from a similar ship · displacement to the two thirds speed cubed over power · vessel power at service speed · speed-power estimate for a ship · shaft power from speed

P=Δ2/3 V3CP = \frac{\Delta^{2/3}\,V^{3}}{C}
sig figs

Worked example: 20 000 t, 15 kn, C 450 → 5 526 kW. Press Try an example to run it live, then adjust anything.

Enter your known values, leave one input blank, and solves for the missing one. Tap a variable’s symbol to see what it means, with a typical value. Change any unit and the answer follows.

Where Ship Propulsive Power by the Admiralty Coefficient fits

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See also

Ship Fuel Burn by the Cubic Speed Law: The same cube of the speed applied to the fuel: the burn per day at one speed from the burn at another.Wind Turbine Power Output: Another power that rises with the cube of a speed, the wind through a rotor.API Gravity to Specific Gravity (Crude Oil and Condensate): The other end of the fuel chain: the density of the oil a ship burns, which turns tonnes into barrels.
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Ship Propulsive Power by the Admiralty Coefficient explained

PVΔ2/3wetted areaC from a similar ship

The Admiralty coefficient is a way to estimate the power a ship needs from the power of a similar ship that is known. It is defined as C=Δ2/3 V3PC = \frac{\Delta^{2/3}\,V^{3}}{P}, with the displacement Δ\Delta in tonnes, the speed VV in knots and the shaft power PP in kilowatts. Take CC from a ship of the same type and a similar hull, and the power at another size or speed follows as P=Δ2/3 V3CP = \frac{\Delta^{2/3}\,V^{3}}{C}. The Wärtsilä Encyclopedia of Marine and Energy Technology describes it as a coefficient for the preliminary estimation of the power a new design needs to reach its speed.

This is a scaling rule of thumb, not a derived law, though its two exponents have physical reasons. The cube of the speed comes from resistance that rises with the square of the speed, times the speed it acts through. The two-thirds power of the displacement is the wetted area of a hull of fixed shape. The International Maritime Organization's Fourth Greenhouse Gas Study (2020) gives an Admiralty formula written as ratios, with the speed ratio raised to a power it assumes to be 3 and the draught ratio to the power 0.66.

Values of CC run from 400 to 600, with the higher values for the more economical vessels. In the worked example a 20 000 tonne ship at 15 knots with C=450C = 450 needs 20 0002/3×153/450=736.806×3 375/450=5 52620\,000^{2/3} \times 15^3 / 450 = 736.806 \times 3\,375 / 450 = 5\,526 kW. The cube of the speed is steep: doubling the speed to 30 knots multiplies the power by eight, to 44 208 kW. Run backward, the same 5 526 kW gives 15 knots, or 20 000 tonnes.

A coefficient is only as good as the ship it came from. The estimate assumes the same hull form, the same loading and trim, the same state of the hull and a speed in the range where the resistance still follows the square of the speed. Check which kind of power and which units a coefficient was worked in before using it, since coefficients in horsepower are smaller than those in kilowatts. The same cube of the speed applies to a ship's fuel burn, and to the wind through a rotor.

Ship Propulsive Power by the Admiralty Coefficient formula

P=Δ2/3 V3CP = \frac{\Delta^{2/3}\,V^{3}}{C}
Where
  • PP= Shaft power (kW)
  • Δ\Delta= Displacement (t)
  • VV= Speed (kn)
  • CC= Admiralty coefficient
Where this comes from
  • Wärtsilä Encyclopedia of Marine and Energy Technology, 'Admiralty coefficient, Admiralty constant', read 23 Oct 2026 (the equation is an image on the page, which was fetched and read): 'C = D^(2/3) V^3 / P', 'where: D = displacement in tons, V = speed in knots, P = shaft power in kW. Values range from 400 to 600, the higher the value the more economic the vessel', for 'the preliminary estimations of the power required in a new design to attain the desired speed'. Read it
  • Molland, A. F., Turnock, S. R., & Hudson, D. A. (2011). Ship Resistance and Propulsion: Practical Estimation of Ship Propulsive Power. Cambridge University Press (the wanted list's source, a book; its DOI is the book's and the text was not opened here). Read it
  • International Maritime Organization (2020). Fourth IMO Greenhouse Gas Study 2020, section on the ship's propulsive power demand, equation 8 (the 'Admiralty formula'), read 23 Oct 2026 in the full report: power scales with the ratio of the speed to the reference speed raised to a power n that 'is assumed to be 3' and the ratio of the draughts to the power 0.66 (the equation itself is an image in the pdf; the two exponents are given in the text under it). Read it
Revised 30 October 2026
Cite this page

formula.expert. (2026, October 30). Ship Propulsive Power by the Admiralty Coefficient Calculator. https://formula.expert/solvers/ship-admiralty-power

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