Zerdly

Section Modulus Calculator

Computes the elastic section modulus (Z) of rectangles, solid rounds and round tubes, with the formula and a worked example.

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How to use this calculator

Enter Values

Enter your values and press Calculate to see results.

Before you rely on this: First-pass guide only. Verify safety-critical or regulated work against the relevant standards, your project requirements and a qualified professional.

How to use this calculator

  1. Choose your cross-section and enter its dimensions in millimetres — rectangle (b, h), solid circle (d), or tube (outer D, inner d).
  2. You can fill more than one shape to compare.
  3. 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.
  • For an I-beam, channel or RHS, get the second moment of area I first, then use Z = I ÷ c (c = half the section depth for symmetric sections).

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.

What about an I-beam, channel or rectangular hollow section (RHS)?

This tool covers rectangles, solid rounds and round tubes (circular hollow sections) directly. For an I-beam (UB/UC), channel (PFC) or rectangular hollow section, first find the second moment of area I for that shape with the Second Moment of Area calculator — for an RHS, I = (B·H³ − b·h³)/12 — then divide by the distance to the extreme fibre: Z = I ÷ c. Published steel section tables also list the elastic section modulus Z directly for standard rolled sections.

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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Cite this tool

Zerdly. (2026). Section Modulus Calculator. Retrieved from https://www.zerdly.com/tools/section-modulus-calculator/

Tip: Enter any known values to calculate the remaining results.

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