# Bending Stress Calculator

> Calculate bending stress step by step: σ = M × c ÷ I = M ÷ S.

Page: https://freecalculator.tech/tools/bending-stress-calculator
Last reviewed: 2026-11-03

## Formula

σ = M × c ÷ I = M ÷ S.

- c in mm and I in cm⁴ are converted to SI.
- Gives stress at the outermost fibre; it is zero at the neutral axis.
- Assumes linear elastic bending of a straight beam.
- σ = M × c ÷ I = M ÷ S.
- Inputs used: Bending moment, Distance from neutral axis to outer fibre, Second moment of area I.

## Inputs

- Bending moment
- Distance from neutral axis to outer fibre
- Second moment of area I

## Worked example: 3.75 kN·m on I = 1,000 cm⁴, c = 100 mm

Centre moment from the beam deflection example (PL/4).
1. σ = 3,750 × 0.1 ÷ 1 × 10⁻⁵.
2. σ = 37.5 MPa.

## Common questions

### How do I find the bending moment?

For a simply supported beam with a centre load, M = PL/4; with uniform load, M = wL²/8. Other cases need beam tables.

### Is the stress tension or compression?

One face is in tension and the other in compression, both with this magnitude for a symmetric section.

### What is section modulus?

S = I ÷ c; it lets you compute stress as M ÷ S. It is listed in steel section tables.

### How do I use the Bending Stress Calculator?

Enter the required values for Bending moment, Distance from neutral axis to outer fibre, Second moment of area I. The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.

### What formula does the Bending Stress Calculator use?

σ = M × c ÷ I = M ÷ S. The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone.

### Can the Bending Stress Calculator be used for exact decisions?

Use it as a calculation aid, not as a substitute for checking the underlying rule, contract, policy, or professional advice that applies to your situation. When a result depends on local rules, personal details, prices, or dates, enter those values yourself and confirm them before acting.

## Limitations and assumptions

- Elastic bending only.
- Symmetric sections assumed for equal top/bottom stress.
- Stress concentrations and lateral buckling not checked.
- Results are estimates for planning and learning. Real designs, installations and bids must be checked by a qualified, licensed professional against the codes that apply where you work.
- The result depends on the values you enter for this bending stress calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.

## Sources

- MIT OpenCourseWare — https://ocw.mit.edu/courses/3-11-mechanics-of-materials-fall-1999/

## Cite this page

- APA: Free Calculator. (2026, November 3). Bending Stress Calculator. https://freecalculator.tech/tools/bending-stress-calculator
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