Section Modulus Calculator
Work out section modulus instantly with clear inputs, formula shown and shareable results.
About Section Modulus Calculator
For a solid rectangle the second moment of area is bh^3/12 and the section modulus is bh^2/6, the value that converts a bending moment straight into peak stress. A 100 x 200 mm section gives Z = 666,667 mm3 and I = 66.7 million mm4. Because depth is squared in Z and cubed in I, orientation matters enormously.
Formulas
Second moment of area
I = b h^3 / 12
Section modulus
Z = b h^2 / 6 = I / (h/2)
Worked example
With the default values below, Section Modulus Calculator returns Section Modulus Z of 666,666.7. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Section width bminimum 0 mm
- 100 mm
- Section depth hminimum 0 mm
- 200 mm
Results
- Section Modulus Z
- 666,666.7 mm3
- Second Moment Of Area I
- 66,666,666.7 mm4
- Section Modulus In SI
- 6.6667 × 10⁻⁴ m3
- Radius Of Gyration
- 57.735 mm
Step by step
- 1Values used
- 2Second moment of area
- 3Section modulus
- 4Section Modulus Z= 666,666.7 mm3
- 5Second Moment Of Area I= 66,666,666.7 mm4
- 6Section Modulus In SI= 0.0007 m3
- 7Radius Of Gyration= 57.735 mm
Assumptions and limits
- The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 4 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What is the difference between I and Z?
I governs deflection and buckling; Z governs bending stress. Z is simply I divided by the distance to the extreme fibre.
Why are I-beams shaped that way?
Because material far from the neutral axis contributes most to I. Concentrating it in flanges gives the same strength for much less weight.