Prismatic Coefficient Calculator
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View ProfileCalculate Cp fast with our Prismatic Coefficient calculator. Find hull volume, length, or midship area with simple formulas and clear steps.
| Equation | Solves For | Notes |
|---|---|---|
| Cp = ∇ ÷ (L × A_M) | Prismatic coefficient | Main formula |
| Cp = C_B ÷ C_M | Prismatic coefficient | Alternative, from block & midship coefficients |
| ∇ = Δ ÷ ρ | Displacement volume | From displacement mass; seawater ρ ≈ 1.025 t/m³ |
| ∇ = Cp × L × A_M | Displacement volume | Rearranged |
| L = ∇ ÷ (Cp × A_M) | Reference length | Rearranged |
| A_M = ∇ ÷ (Cp × L) | Midship area | Rearranged |
A Prismatic Coefficient calculator helps you find Cp with ease. It uses ship hull data. You can enter volume, length, and midship area. The tool then finds Cp for you. You can also use mass and water density to find volume. A second mode uses CB and CM. A third mode can find volume, length, or area.
What is a prismatic coefficient?
The prismatic coefficient, or Cp, shows how hull volume spreads along its length. It compares the ship volume with a simple prism. That prism has the same length and the same midship area. Cp has no unit. A low value means the ends are fine. A high value means the ends are fuller.
Prismatic Coefficient Formula
The main Prismatic Coefficient formula is:
Cp = ∇ / (L × AM)
Here, ∇ is the ship displacement volume. L is the reference length. AM is the immersed midship area.
You can also use:
Cp = CB / CM
Here, CB is the block coefficient. CM is the midship section coefficient. These forms match when the same hull data and length rules apply.
How to use online Prismatic Coefficient calculator
- Pick the main mode. Enter displacement volume, length, and midship area. You may use metres, feet, m², ft², m³, or ft³.
- Choose mass if needed. Enter ship mass and water density. The tool changes mass to tonnes. It then finds volume.
- Enter the hull data. Add the reference length and immersed midship area. The tool changes each value to SI units.
- Get the result. The tool first finds prism volume. It uses L × AM. It then divides ship volume by prism volume. The result is Cp.
- Try the solve mode. Enter Cp and two known values. The tool can find ∇, L, or AM. It can also find Cp from CB and CM.
Example Prismatic Coefficient calculation
Suppose a ship has a volume of 12,000 m³. Its length is 150 m. Its midship area is 100 m².
First find prism volume:
Vprism = L × AM
Vprism = 150 × 100
Vprism = 15,000 m³
Now find Cp:
Cp = 12,000 / 15,000
Cp = 0.80
So, the Prismatic Coefficient is 0.80.
Think of the prism as a simple box-like shape. The ship fills 80% of that prism by volume.
How do I calculate the coefficient?
Use:
Cp = ∇ / (L × AM)
Keep all units in a matching system. If you use feet, area must use square feet. The calculator handles the unit change for you.
Final Verdict
The Prismatic Coefficient calculator makes hull form work fast and clear. It uses the standard Cp formula. It also supports CB and CM. You can solve for missing volume, length, or midship area. This makes the tool useful for ship design checks and study work.
FAQs
What is a prismatic coefficient?
It is a ratio that shows how ship volume spreads along its length. It has no unit.
How do I calculate the coefficient?
Divide displacement volume by length times midship area. You can also divide CB by CM.
Can I use mass instead of volume?
Yes. Enter mass and water density. The tool finds volume first.
What does Cp = 0.80 mean?
It means the ship volume is 80% of the matching prism volume.
Is this a Prismatic coefficient calculator free tool?
Yes. The online calculator lets you find Cp without doing the math by hand.