Prismatic Coefficient Calculator
The prismatic coefficient (Cp) measures how a hull's volume is distributed between fine ends and full ends. It compares the actual displaced volume to a prism that has the midship cross-section running the full waterline length. A low Cp means fine ends; a high Cp means fuller ends. Enter the displaced volume, the midship section area, and the waterline length in consistent units to get Cp, always a value between 0 and 1.
Prismatic coefficient formula
Reference prism volume = midship area * waterline length
Cp = displaced volume / (midship area * waterline length)
Use consistent units throughout. The result is a fraction between 0 and 1.
Worked example
- Displaced volume 350, midship area 20, waterline length 32.
- Prism volume = 20 * 32 = 640.00.
- Cp = 350 / 640 = 0.55, a typical cruising-yacht value.
Prismatic coefficient: frequently asked questions
What is the prismatic coefficient?
The prismatic coefficient (Cp) describes how fullness is distributed along a hull. It is the displaced volume divided by the product of the maximum (midship) cross-section area and the waterline length: Cp = volume / (midship area * waterline length). A low Cp has fine ends; a high Cp carries fullness toward the bow and stern.
What is a typical prismatic coefficient?
For displacement sailing yachts, Cp commonly falls in the range of about 0.50 to 0.58, with an optimum that depends on speed-to-length ratio. Faster hulls and motor vessels tend toward higher values. Cp is always between 0 and 1.
Why does the prismatic coefficient matter?
Cp influences wave-making resistance at a given speed. A hull with too fine ends (low Cp) for its intended speed, or too full ends (high Cp), makes more drag than the optimum. Designers choose Cp to suit the boat's typical speed-to-length ratio.
How do I get the displaced volume?
Displaced volume equals the boat's weight divided by the water density, or it comes from the hull lines. Enter the volume, the midship section area, and the waterline length in consistent units (all in feet and cubic feet, or all in metres and cubic metres).
Official sources
- U.S. Navy, Naval Sea Systems Command: naval architecture and ship design.
- NIST: unit conversions (length, area, volume).
Reviewed by the CalculatorHub team, edited by James Graham, 19 June 2026. See our methodology.