What Is a Prismatic Coefficient Calculator?
The prismatic coefficient (Cp) is a naval architecture ratio that describes how "full" or "fine" a hull's ends are relative to its largest underwater cross-section. This calculator divides your hull's displacement volume by the volume of an equivalent prism (waterline length times maximum cross-sectional area) to give you that ratio directly.
Designers use Cp alongside other hull coefficients to predict how a hull shape will behave across a range of speeds, particularly around the transition toward and past hull speed.
How to Read Your Results
Prismatic Coefficient (Cp)
A number typically between about 0.45 and 0.70 for most displacement and semi-displacement hulls. Lower values mean finer, more tapered ends; higher values mean fuller ends with volume distributed more evenly along the length.
Interpretation
A general-guidance label based on common naval architecture bands for Cp, helping translate the raw number into what it typically means for hull behavior.
Displacement Volume & Max Section Area Used
Your entered figures echoed back for confirmation — a quick way to check for a typo before trusting the result.
Real-World Example
A hull with 157 cubic feet of displacement volume, a 28-foot waterline length, and a maximum cross-sectional area of 10 square feet:
| Item | Value |
|---|---|
| LWL × max area | 280 cu ft |
| Displacement volume | 157 cu ft |
| Prismatic coefficient | ≈0.561 |
| Interpretation | Moderate — typical displacement sailing hull |
That Cp of about 0.56 sits comfortably in the typical range for a moderate-displacement cruising sailboat. A racier hull with finer ends might come in closer to 0.50, while a motor-sailer or trawler-type hull with fuller ends could run closer to 0.62 or higher — a useful check whenever you're comparing two hull designs of similar length and displacement.
Tips for Accurate Results
- Keep units consistent — volume in cubic feet, length in feet and area in square feet (or the metric equivalents together).
- Convert displacement weight to volume if that's all you have: divide weight in lbs by 64 for seawater or 62.4 for fresh water to get cubic feet.
- Use the true maximum section, not an average — Cp specifically compares to the largest cross-section, usually near midships.
- Sanity-check against typical ranges — most cruising sailboats fall roughly between 0.52 and 0.58.
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Last updated: August 2026 · Reviewed by: Simple Calculator Tools Editorial Team