# Bending Stress Calculator

URL: https://speedycalculator.com/calculators/construction/bending-stress/
Last updated: 2026-10-25

> The bending stress calculator finds the maximum bending stress σ = M·c/I in rectangular, round, tubular and I-shaped beams from the bending moment and section dimensions, plus the moment of inertia and section modulus.

## Inputs

- Cross-section
- Width b / flange width (mm, in, cm)
- Height h (mm, in, cm)
- Outer diameter (mm, in, cm)
- Inner diameter (mm, in, cm)
- Wall thickness / flange thickness (mm, in, cm)
- Web thickness (mm, in, cm)
- Bending moment (N·m, kN·m, lbf·ft, lbf·in)

## Results

- Moment of inertia
- Distance to outer fibre
- Section modulus
- Maximum bending stress

## Formula

```
σ = M × c ÷ I = M ÷ S
Rectangle: I = b h³ ÷ 12; circle: I = π d⁴ ÷ 64; tube: I = π (D⁴ − d⁴) ÷ 64
Rectangular hollow: I = (B H³ − (B − 2t)(H − 2t)³) ÷ 12; I-beam: I = (b h³ − (b − t_w)(h − 2t_f)³) ÷ 12
```

## Explanation

When a beam bends, fibres on one side are stretched and on the other compressed. The stress is zero at the neutral axis and largest at the outer fibre, a distance c away. Comparing the maximum bending stress with the allowable or yield stress of the material tells you if the beam is strong enough.

### How to use the Bending Stress Calculator

- **Cross-section**
- **Width b / flange width**
- **Height h**
- **Outer diameter**
- **Inner diameter**
- **Wall thickness / flange thickness**
- **Web thickness**
- **Bending moment**
- Every result field is editable: type into **Maximum bending stress** and **Bending moment** plus every other field update to match.

Results update as you type, and every field accepts the units shown in its menu.

### How it works

Choose the cross-section, enter its dimensions and the bending moment. The calculator works out I, c and the section modulus S and the maximum stress. Type an allowable stress into the result to find the moment the section can carry.

### Tips for an accurate estimate

- Keep units consistent – the calculator handles conversions, but check every field's unit before reading a result.
- Use values from standards, data sheets or test pieces whenever you have them; typical values are only a starting point.
- Apply appropriate safety factors and have structural, electrical and pressure work checked by a qualified professional.
- Record the inputs you used so the calculation can be reviewed later.

### Common mistakes to avoid

- Confusing diameter and radius, or nominal and actual sizes.
- Using allowable stresses and ultimate strengths interchangeably.
- Treating rule-of-thumb results as a substitute for code tables or an engineered design.

### Inputs explained

FieldWhat to enterCross-sectionChoose one: Solid rectangle, Solid circle, Hollow circle (tube), Rectangular hollow section …Width b / flange widthUnits: mm, in, cmHeight hUnits: mm, in, cmOuter diameterUnits: mm, in, cmInner diameterUnits: mm, in, cmWall thickness / flange thicknessUnits: mm, in, cmWeb thicknessUnits: mm, in, cmBending momentUnits: N·m, kN·m, lbf·ft, lbf·in

### What each result means

- **Section modulus** = [Moment of inertia]÷[Distance to outer fibre]
- **Maximum bending stress** = [Bending moment]×[Distance to outer fibre]÷[Moment of inertia]

### Example values

How the main result changes when **Bending moment** changes and everything else stays at the example values above:

Bending moment (N·m)Maximum bending stress (MPa)1,000121,500182,000242,500303,000364,00048

## Worked example

Inputs — Cross-section: Solid rectangle; Width b / flange width: 50 mm; Height h: 100 mm; Outer diameter: 60 mm; Inner diameter: 50 mm; Wall thickness / flange thickness: 8 mm; Web thickness: 6 mm; Bending moment: 2,000 N·m.

Results — Moment of inertia = 416.67 cm⁴; Distance to outer fibre = 50 mm; Section modulus = 83.33 cm³; **Maximum bending stress = 24 MPa**.

## FAQ

**What is the bending stress formula?**
σ = M·c/I, where M is the bending moment, c the distance to the outer fibre and I the moment of inertia.

**What is the section modulus?**
S = I/c; the bending stress is simply M/S.

**How do I know if the stress is acceptable?**
Compare with the allowable stress – for structural steel often about 0.6 × yield (≈ 150–165 MPa for S235/A36).

**What formula does the Bending Stress Calculator use?**
σ = M × c ÷ I = M ÷ S.