Section Modulus Calculator

About the Section Modulus Calculator

Calculates the elastic section modulus of a solid rectangular cross-section from its width and height, a key property for bending strength.

How to use this calculator

1. Enter the rectangle width as \(b\).
2. Enter the rectangle height as \(h\).
3. Use the calculator to compute \(S = \\frac{b h^2}{6}\).
4. Check that your units are consistent, then read the result in cubic units.

The formula explained

The formula \(S = \\frac{b h^2}{6}\) computes the section modulus of a rectangular cross section about its centroidal axis. It combines the width and the square of the height, so height has a much bigger effect than width.

• b = the width of the rectangular section
• h = the height of the rectangular section
• S = the section modulus of the rectangle

Step by step method

1. Measure or choose the rectangle width \(b\) and height \(h\).
2. Square the height, so calculate \(h^2\).
3. Multiply \(b\) by \(h^2\), then divide by \(6\) to get \(S\).

Worked example

Problem. Find the section modulus for a rectangular section with width \(b = 8\) in and height \(h = 12\) in.

1. Substitute the values into \(S = \\frac{b h^2}{6}\), so \(S = \\frac{8(12^2)}{6}\).
2. Compute \(12^2 = 144\), so \(S = \\frac{8 \\times 144}{6}\).
3. Calculate \(8 \\times 144 = 1152\), then \(1152 \\div 6 = 192\).

Tips and common mistakes

• Make sure \(b\) and \(h\) use the same length unit, because the result depends on consistent units.
• For a rectangle, increasing \(h\) has a stronger effect than increasing \(b\), since \(h\) is squared in the formula.

Frequently asked questions