The section modulus tells how well a beam shape resists bending: maximum bending stress equals bending moment divided by S. Deep sections with material far from the centre (like I-beams) give the most strength per kilogram.
How to use the Section Modulus Calculator
- Section
- Width b (flange / outer)
- Height h (outer)
- Wall / web thickness t
- Flange thickness t_f
- Outer diameter D
- Inner diameter d
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the section shape and enter its dimensions. Results are for bending about the horizontal (x) axis; for tees and angles the smaller (critical) section modulus is given.
Inputs explained
| Field | What to enter |
|---|---|
| Section | Choose one: Square, Rectangle, Hollow rectangle, Solid circle … |
| Width b (flange / outer) | Units: mm, cm, m, in, µm |
| Height h (outer) | Units: mm, cm, m, in, µm |
| Wall / web thickness t | Units: mm, cm, m, in, µm |
| Flange thickness t_f | Units: mm, cm, m, in, µm |
| Outer diameter D | Units: mm, cm, m, in, µm |
| Inner diameter d | Units: mm, cm, m, in, µm |
What each result means
- Elastic section modulus S = [I]÷[c]
- Area moment of inertia I = [I]
- Cross-section area = [A]
- Distance to the extreme fibre c = [c]
- Radius of gyration = sqrt([I]÷[A])
Example values
How the main result changes when Width b changes and everything else stays at the example values above:
| Width b (flange / outer) (mm) | Elastic section modulus S (mm³) |
|---|---|
| 50 | 333,333.3333 |
| 75 | 500,000 |
| 100 | 666,666.6667 |
| 125 | 833,333.3333 |
| 150 | 1,000,000 |
| 200 | 1,333,333.3333 |
Formula
S = I / c (c = distance from the neutral axis to the extreme fibre), σ_max = M / S
Worked example
Inputs — Section: Rectangle; Width b (flange / outer): 100 mm; Height h (outer): 200 mm.
Results — Elastic section modulus S = 666,666.66667 mm³; Area moment of inertia I = 66,666,666.66667 mm⁴; Cross-section area = 20,000 mm²; Distance to the extreme fibre c = 100 mm; Radius of gyration = 57.735 mm.
Key terms
- Neutral axis
- Line through the centroid where bending stress is zero.
Frequently asked questions
How do I get bending stress from S?
σ = M/S.
Why are I-beams efficient?
Most material is in the flanges, far from the neutral axis.
What is the difference between S and I?
I measures stiffness; S = I/c measures bending strength.
What about the plastic section modulus?
It is larger (by the shape factor, 1.5 for rectangles) and used in plastic design.