Section Modulus Calculator
A free, browser-based calculator. Runs entirely in your browser — no sign up, nothing stored.
Enter Values
How to use this calculator
- Choose your cross-section and enter its dimensions in millimetres — rectangle (b, h), solid circle (d), or tube (outer D, inner d).
- You can fill more than one shape to compare.
- Read the elastic section modulus Z in mm³ (and cm³).
How it works
The Section Modulus Calculator finds Z — the property that links bending moment to bending stress (stress = moment ÷ Z), so a larger Z means lower stress for the same load.
Z = I / c, where c is the distance from the centroid to the extreme fibre. Rectangle: Z = b·h²/6. Solid circle: Z = π·d³/32. Tube: Z = π·(D⁴ − d⁴)/(32·D).
Worked example
100 × 200 mm rectangle. Z = 100×200²/6 = 666,667 mm³ = 667 cm³. Under a 22.5 kN·m moment the bending stress is 22.5×10⁶ / 666,667 ≈ 33.8 MPa.
Tips
- Keep units consistent: a moment in N·mm divided by Z in mm³ gives stress in MPa (N/mm²).
- Section modulus grows with the square of depth — depth is the cheapest way to add bending strength.
Frequently asked questions
Elastic or plastic section modulus?
This tool gives the elastic section modulus (Z or Sₑ), used for stress at first yield. The plastic modulus (S or Z_p), used for ultimate moment capacity in steel design, is larger and calculated differently.
How do I use Z to check a beam?
Divide the maximum bending moment (from the Simply Supported or Cantilever calculator) by Z to get the peak bending stress, then compare it against the material's allowable or yield stress with an appropriate safety margin.
Can I use these results for final design?
No. These calculators are for first-pass sizing, checking and learning. They assume ideal supports, static loads and elastic behaviour, and they don't apply load factors, member capacity, buckling or connection checks. Always verify against the relevant design code (e.g. AS 4100, AS 1170, Eurocode) and have a qualified engineer sign off structural work.
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Tip: Enter any known values to calculate the remaining results.
All calculations run in your browser. Your inputs are never saved or transmitted.