Calculate hull efficiency and performance characteristics using prismatic coefficient analysis
Fine-lined racing hull
Balanced cruising hull
Full-bodied motor yacht
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Download NowThe prismatic coefficient tells you how a hull's volume is distributed along its length, and it is the single best clue to the speed range at which a boat will be efficient. Two hulls can displace the same weight yet plane or sail well at very different speeds purely because their volume is packed in different places.
A low Cp bunches volume amidships with fine ends, which suits slower displacement work. A high Cp carries fullness out toward the bow and stern, which pays off at higher speeds and when planing, because the hull has the buoyancy it needs forward to lift and run.
Enter displacement, waterline length, beam, draft and midship-area, and the calculator returns the prismatic coefficient alongside the block and midship coefficients, so you can see how your hull form trades volume between the middle and the ends.
Cp = ∇ ÷ (LWL × Am), where ∇ = Displacement ÷ 64 and Am = midship section area| Hull Purpose | Cp Range | Volume Emphasis |
|---|---|---|
| Slow displacement | 0.45 - 0.55 | Bunched amidships |
| Moderate cruiser | 0.55 - 0.62 | Balanced |
| Fast / racing | 0.62 - 0.70 | Fuller ends |
| High-speed planing | 0.70 - 0.85 | Fullness forward |
Typical prismatic-coefficient ranges by hull purpose.
Formula verified against standard naval-architecture references · Updated October 2026
The prismatic coefficient (Cp) is the ratio of a hull's underwater volume to the volume of a prism that is as long as the waterline and as full as the biggest midship section. It describes how the buoyancy is spread along the length. A low Cp means volume is concentrated amidships with fine ends; a high Cp means the hull keeps more fullness out toward bow and stern, which favours higher speeds.
It depends on your target speed. Slow displacement hulls do well around 0.45 to 0.55, moderate cruisers near 0.55 to 0.62, fast and racing hulls 0.62 to 0.70, and high-speed planing forms higher again. The right value is the one matched to the Froude number you sail at, because Cp is fundamentally about where the buoyancy needs to be for that speed.
The block coefficient (Cb) compares the hull volume to a single box of length, beam and draft, describing overall fullness. The prismatic coefficient compares the same volume to a prism based on the largest midship section, describing how that volume is distributed along the length. They are linked: Cp equals Cb divided by the midship coefficient Cm, so together the two tell you both how full and how evenly spread the hull is.
At higher speeds a hull trims and the important buoyancy shifts toward the ends, so a form with fuller ends and a higher Cp planes and runs more easily, while a fine-ended low-Cp hull digs in and stalls. At low speeds the reverse is true and finer ends waste less energy. Choosing Cp is, in effect, designing the hull to be efficient in the speed band it will live in.
Yes. Displacement fixes the total volume, but Cp is about where that volume sits. You can move fullness forward or aft, refining the bow and filling the run, or vice versa, without adding or removing a pound. Designers use this freedom to tune a hull to a speed range while holding weight and midship section constant.
The midship area is the true immersed cross-section at the point of maximum depth, not the simple beam times draft rectangle. Plan or offset the section, account for the bilge radius, chine or turn of the bilge, and integrate the wetted shape. Dividing that area by beam times draft gives the midship coefficient, which feeds straight into the prismatic calculation.
The prismatic coefficient tells you where the hull's volume sits along its length, and that placement shapes how the boat makes and sheds wave drag. A higher Cp carries fullness toward the ends, letting a hull rise onto and run along its own wave, so it suits fast planing and high-speed displacement forms; a lower Cp puts fullness amidships, easing low-speed resistance but burying the fine ends and steeper wave-making sooner as speed climbs. The classic rule ties Cp to the intended speed-length ratio: choose fuller ends for boats meant to run fast and finer, keel-centered sections for slow displacement hulls, so the shape is doing the least work at the speed you actually sail.