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Physics calculator

Bending Stress Calculator

Elastic bending stress from a moment and a section modulus. S can also be formed from Ix and c. Runs locally.

Instant result
Result
—

Enter values to calculate.

Inputs—
Mode—
Formula—
Trust summary Engine tested · Source checked · 6/6 tests · Production surface contract 6/6 · v1.0.0
Input interpretation
Enter values to calculate.
Result
—
Model
Elastic bending stress on one centroidal axis from M and S.
Scope
Calculation runs locally in the browser; values are not uploaded.
Verification
Engine tested · 6/6 tests · Production surface contract 6/6 · Source checked · v1.0.0
Named expert review
Optional · Not performed
Sources
  • Hibbeler, Mechanics of Materials — Bending — flexure formula
Sources
Evidence
3 golden · 3 boundary · Production surface contract 6/6 · Artifact integrity PASS
Production
Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (8 capabilities; 189 remain CURRENT) @ 2026-09-23T21:48:15.717Z
Semantic contract
PASS

Formulas

Core equations used by this calculator.

Flexureσ = M/S
Section modulus from IxS = Ix/c
iEnter S directly, or omit S and pass Ix with c. That second path calls the section-modulus engine. A rectangle built from b and h stays on the rectangular-section page.

How to use

1

Enter the moment and the modulus

M is the bending moment. S is the elastic section modulus at the fiber of interest. S must be positive.

2

Read the stress

σ = M/S. The sign of M is the sign of the stress at that fiber.

Example calculations

Common configurations with formula and result.

ϟ

Moment 12, modulus 4

M = 12, S = 4, in one consistent unit system. σ then has the unit of M/S.

σ = 12/4
σ = 3
ϟ

From Ix and c

M = 24, Ix = 36, c = 3, with S omitted. The page form can instead take S = Ix/c = 12 directly.

S = 36/3, σ = 24/12
σ = 2

Bending Stress calculator specification

Version 1.0.0 · Engine tested

Calculation status

Review policy · Evidence

Definition
On one centroidal axis, the elastic bending stress is σ = M/S. S is the elastic section modulus at the fiber. A positive moment keeps the stress sign of that fiber.
What it calculates
Elastic bending stress on one centroidal axis from M and S.
Inputs
  • M
  • S
Outputs
  • sigma
  • M
  • S
Formula
σ = M/S. If S is omitted, S = Ix/c from the section-modulus engine.
Assumptions
  • Calculation runs locally in the browser; values are not uploaded.
  • Keep units consistent with the labels on each field.
  • Enter S directly, or omit S and pass Ix with c. That second path calls the section-modulus engine. A rectangle built from b and h stays on the rectangular-section page.
Units
  • M and S set the stress unit. σ has the unit of M/S.
Boundary conditions
  • missing M → MISSING_REQUIRED_INPUT
  • missing S and missing Ix → MISSING_REQUIRED_INPUT
  • S ≤ 0 or c ≤ 0 → VALUE_MUST_BE_POSITIVE
  • Ix < 0 → INVALID_INPUT
Example
M=12 S=4 → σ=3
Validation cases

4 published on this page · 6/6 tests · Production surface contract 6/6 · View evidence

  • M=12 S=4 → σ=3
  • M=24 Ix=36 c=3 → S=12, σ=2
  • M=-12 S=4 → σ=-3
  • S=0 → VALUE_MUST_BE_POSITIVE
Sources
  • Hibbeler, Mechanics of Materials — Bending — flexure formula
    Supports: The elastic bending stress at a fiber is the moment divided by the elastic section modulus at that fiber.
Calculation version
1.0.0

Background

Interpretation and common distinctions.

Find the elastic bending stress on one centroidal axis.

Supported and not supported

Supported: σ = M/S. S can be typed in, or formed as Ix/c by the section-modulus engine. The sign of M is the sign of the stress at that fiber.

Not supported: a rectangle built from b and h, transverse shear, beam deflection, and the plastic modulus. /calc/mechanical is not open.

Agent / API notes

Capability id: mechanical.statics.bending_stress · tool id: bending-stress · pin 1.0.0.

{ "M": 12, "S": 4 }

Share the link with M and S. The result is not written into the link.

Other calculators in this family: Section modulus, Rectangular section, Hollow circular section .

S Section modulus › bh Rectangular section › R Hollow circular section ›
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Frequently asked questions

Key distinctions behind the calculation.

Does this build a rectangle from b and h?

No. Width and height stay on the rectangular-section page. Bring the section modulus here.

What if I have Ix and the distance to the fiber?

Omit S and pass Ix with c. S is Ix/c from the section-modulus engine, then σ = M/S.

Is this the plastic modulus?

No. This is elastic flexure. The plastic modulus of a rectangle is its own page.