Midship Section Coefficient Calculator

Calculate the midship section coefficient (Cm) using two common methods: direct midship sectional area, or the relationship between block coefficient and prismatic coefficient.

Method 1: Midship Sectional Area

Area of the underwater midship section.
The coefficient compares the actual immersed midship section with the enclosing rectangle defined by beam × draft.

Calculation Result

Midship Section Coefficient
0.000
Cm
Midship Area
—
Beam
—
Draft
—
Enclosing Area
—
Result status
Method: —
Midship coefficient: 0.000
Check: —

What is the midship section coefficient?

The midship section coefficient, Cm, describes how full the underwater midship section is compared with the rectangle formed by the vessel's maximum beam and draft.

$$C_m = \frac{A_m}{B \times T}$$

Where Am is the immersed midship sectional area, B is beam, and T is draft.

What is the second way to calculate Cm?

Cm can also be obtained from the block coefficient and prismatic coefficient:

$$C_b = C_p \times C_m$$

$$C_m = \frac{C_b}{C_p}$$

This method is useful when the principal coefficients are already known from a hydrostatics or hull-form calculation.

What does Cm mean?

A value closer to 1.0 means the underwater midship section is fuller and occupies more of the enclosing beam × draft rectangle. A lower value indicates a more rounded or finer section.

Example: If Cm = 0.90, the immersed midship area is about 90% of the beam × draft rectangle.

Midship section coefficient example

Suppose the midship sectional area is 45 ft², beam is 8 ft, and draft is 6.5 ft.

$$C_m = \frac{45}{8 \times 6.5} = 0.865$$

Using the second method, if Cb = 0.55 and Cp = 0.75:

$$C_m = \frac{0.55}{0.75} = 0.733$$

What is the relationship between Cb, Cp, and Cm?

$$C_b = C_p \times C_m$$

This relationship connects the three principal hull-form coefficients used in many naval architecture calculations.

Note: Use the immersed midship sectional area corresponding to the same draft and condition as the beam and draft values. Mixing load conditions can produce an incorrect coefficient.

Midship section coefficient FAQ

What is the formula for midship section coefficient?

Cm = Am ÷ (B × T), where Am is immersed midship sectional area, B is beam, and T is draft.

How do you calculate Cm from Cb and Cp?

Divide the block coefficient by the prismatic coefficient: Cm = Cb ÷ Cp.

What is a typical midship section coefficient?

Values depend strongly on hull type and operating condition. Ship and boat hulls can have substantially different coefficients, so the coefficient should be calculated from the actual hull form rather than assumed from one generic value.

Can Cm be greater than 1?

For the standard definition based on immersed area divided by beam × draft, Cm should not exceed 1 because the actual section cannot be larger than its enclosing rectangle.