Prismatic Coefficient Calculator

Model hull volume distribution with practical design inputs. Review coefficient ranges across varied loading conditions. Improve fairing, speed planning, and displacement checks with confidence.

Enter Hull and Displacement Inputs

Use direct areas and volumes when known. Otherwise, estimate from common naval geometry inputs.

Vessel Name

Length on Waterline, LWL (m)

Beam at Waterline, BWL (m)

Draft, T (m)

Midship Immersed Area, Am (m²)

Midship Coefficient, Cm

Displacement Volume, ∇ (m³)

Displacement Mass (tonnes)

Water Density (kg/m³)

Optional Block Coefficient, Cb

Target Cp Minimum

Target Cp Maximum

Design Notes

Formula Used

Primary formula: Cp = ∇ / (Am × LWL)

Here, ∇ is displacement volume, Am is the immersed midship section area, and LWL is length on waterline.

Derived midship area: Am = Cm × BWL × T

Derived displacement volume from mass: ∇ = Displacement mass / Water density

Cross-check formula: Cp = Cb / Cm

The coefficient compares actual underwater volume with the volume of a prism having the same midship area and waterline length.

How to Use This Calculator

Enter the vessel name and the length on waterline.
Provide either direct midship area or estimate it from beam, draft, and midship coefficient.
Provide displacement volume directly, or enter displacement mass with water density.
Add optional block coefficient and target Cp limits for design checks.
Press the calculate button to display the result above the form.
Review the interpretation, compare with target range, and export the result as CSV or PDF.

Example Data Table

Vessel Type	LWL (m)	BWL (m)	Draft (m)	Am (m²)	Volume (m³)	Cp
Racing Sailboat	11.50	3.20	1.85	2.65	15.85	0.5200
Fast Motor Yacht	18.20	4.60	1.25	6.55	64.37	0.5400
Patrol Boat	24.00	5.20	1.55	10.80	155.52	0.6000
Coastal Trawler	22.00	5.80	2.05	11.90	175.27	0.6694

Frequently Asked Questions

1. What does the prismatic coefficient measure?

It measures how underwater volume is distributed along the hull length. Higher values indicate fuller ends, while lower values indicate finer entrance and run sections.

2. Why is Cp important in hull design?

Cp affects resistance, speed potential, load carrying, and wave-making behavior. Designers compare it with intended operating speeds and displacement requirements during fairing.

3. What is a normal Cp range?

Typical values often range from about 0.50 to 0.75, depending on vessel type. Fine craft use lower values, while fuller displacement vessels commonly use higher values.

4. Can I calculate Cp without direct displacement volume?

Yes. Enter displacement mass and water density, and the calculator converts mass into displacement volume before computing the prismatic coefficient.

5. What if I do not know midship area?

You can estimate immersed midship area from beam, draft, and midship coefficient. This is useful during concept design and early hull comparisons.

6. How is Cp different from block coefficient?

Block coefficient compares displacement volume with a full rectangular block. Prismatic coefficient instead compares displacement volume with a prism based on midship area.

7. Should Cp ever be greater than one?

In practical ship geometry, Cp is usually below one. Values above one normally suggest inconsistent units, incorrect areas, or an unrealistic displacement entry.

8. Can this tool replace detailed resistance analysis?

No. It is a screening and comparison tool. Final performance work still needs hydrostatics, resistance estimation, stability review, and model testing or simulation.