Section moment of inertia calculator
Pick the section shape and enter its dimensions. The result is given in cm⁴ so you can enter it straight into the beam deflection calculators.
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How to use it
- Enter section shape, width b or outer diameter d and height h or inner diameter d.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
Rectangle: I = b h³ ÷ 12 about the horizontal axis, Z = b h² ÷ 6. Circle: I = π D⁴ ÷ 64. Tube: I = π (D⁴ − d⁴) ÷ 64. Section modulus Z = I ÷ (half the height or half the outer diameter).
Example
Inputs: Section shape = Rectangle, Width b or outer diameter D = 100 mm, Height h or inner diameter d = 200 mm. Result: Moment of inertia: 6,666.6667 cm⁴; Moment of inertia in mm⁴: 66,666,666.7 mm⁴; Section modulus: 666,666.67 mm³.
Limits and caveats
- About the horizontal centroidal axis only; for a rectangle the height runs in the load direction.
- For rolled I and C sections use the maker tables.
Questions about this tool
Why does height matter more than width?
I grows with the cube of the height, so doubling the height makes the section 8 times stiffer while doubling the width only doubles it.
What is the difference between moment of inertia and section modulus?
Moment of inertia governs deflection; section modulus governs bending stress: σ = M ÷ Z.
How do I turn mm⁴ into cm⁴?
Divide by 10000, because 1 cm⁴ = 10⁴ mm⁴.