Prismatic Coefficient (Cp)
Compute a hull's prismatic coefficient (Cp), Cp = ∇/(Am·L), the ratio of the displaced volume to that of a prism with the midship section area (Am) along the whole length. It indicates how volume is distributed lengthwise: a low Cp concentrates volume amidships (good for low speeds), a high Cp pushes it to the ends (better at high speeds). It is decisive in resistance design. Enter the displaced volume, the midship section area and the length.
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Prismatic coefficient (Cp)
While the block coefficient measures overall 'fullness', the prismatic coefficient Cp = ∇/(Am·L) describes how the volume is distributed along the hull, comparing it with a prism whose midship section area stays constant from bow to stern. A low Cp (~0.55) concentrates volume amidships and fines out the ends — excellent at low speeds, with less wave-making resistance. A high Cp (~0.65+) pushes volume out toward the extremities — better at high speeds, where the fore and aft bodies need volume to support the wave train. It is a key parameter in optimizing resistance to forward motion. Enter the displaced volume, the midship section area and the length.
Related Tools
Block Coefficient (Cb)
Compute a ship's block coefficient (Cb), Cb = ∇/(L·B·T), the ratio of the displaced (carene) volume to the enclosing box (length × beam × draft). It measures how 'full' the hull is: slow cargo ships have a high Cb (~0.8); fast, fine vessels a low Cb (~0.5). It is one of the central parameters of naval architecture. Enter the displaced volume, the length, the beam and the draft.
Hull Wetted Surface
Estimate the hull's wetted surface area by Denny's formula, S = 1.7·L·T + ∇/T, from the length (L), the draft (T) and the displaced volume (∇). The wetted surface drives frictional resistance — the largest share of drag at low speeds — and underlies power calculation and the area to be coated with antifouling paint. Enter the length, the draft and the displaced volume.
Hull Speed
Compute the hull speed of a displacement vessel, V ≈ 2.43·√(LWL), in knots, from the waterline length (LWL, in meters). It is the theoretical limit of a hull's economical speed: as the boat approaches it, it gets trapped in its own bow wave and the required power soars. That is why sailboats and displacement craft rarely exceed it. Enter the waterline length.
Reserve Buoyancy
Compute a vessel's reserve buoyancy, R = (total_volume − submerged_volume)/submerged_volume·100%, the percentage of watertight volume above the waterline relative to the submerged volume. It is the safety margin against sinking: the larger it is, the more cargo or flooding the hull tolerates before submerging. It defines the freeboard and the damage survivability. Enter the total watertight volume and the submerged volume.
Power by Admiralty Coefficient
Estimate a ship's propulsive power by the Admiralty formula, P = (∆^(2/3)·V³)/C, from the displacement (∆, t), the speed (V, knots) and the Admiralty coefficient (C), characteristic of similar hulls. It is a classic, fast method to predict the required power in the preliminary design stage, based on similarity with existing ships. The V³ dependence shows the high cost of speed. Enter the displacement, the speed and the coefficient C.
Ship Roll Period (IMO IS Code)
Computes the natural roll period of a ship using the empirical formula of the IMO International Code on Intact Stability (IS Code 2008), used in the weather criterion and in the inclining experiment. The period is T = 2 × C × beam ÷ square root of GM, with the coefficient C = 0.373 + 0.023 × (beam ÷ draught) − 0.043 × (length ÷ 100), so that rolling gets faster as the metacentric height grows. The number indicates comfort and safety: short periods, below some 8 seconds, reveal a stiff ship that rolls with high acceleration and punishes cargo and crew; long periods indicate a tender ship, with little stability reserve. The IMO empirical form was adopted rather than the pendulum expression T = 2π × radius of gyration ÷ square root of (g × GM), because the roll radius of gyration is rarely known on board — which is exactly what the coefficient C estimates from hull geometry. Enter the beam, the draught, the waterline length and the metacentric height GM.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.