# Stress & Strain Calculator

Calculate engineering stress σ = F/A and engineering strain ε = ΔL/L₀ under uniaxial load. Choose what to solve: for stress, enter force F (N) and cross-section area A (mm²) → result in MPa; for strain, enter original length L₀ and elongation ΔL (negative for compression) → dimensionless ratio. Units are self-consistent (N, mm) so stress comes out directly in MPa.

> Canonical page: https://elysiatools.com/en/tools/stress-strain-calculator

- **Category:** Math & Numbers

- **Keywords:** stress, strain, sigma = F/A, epsilon = dL/L, uniaxial, tension, compression, engineering strain, normal stress, mechanics of materials, strength of materials

## Overview

Calculate engineering stress or strain for a uniaxial load using σ = F/A or ε = ΔL/L₀. Enter force and cross-section area for stress in MPa, or original length and elongation for a dimensionless strain result.

## Inputs

- **Solve for** (select)
- **Force F (N)** (number): Axial force in newtons. Required when solving for stress. Positive = tension.
- **Cross-section Area A (mm²)** (number): Cross-section area perpendicular to the load, in mm². Required when solving for stress.
- **Original Length L₀ (mm)** (number): Original (unstressed) gauge length in mm. Required when solving for strain.
- **Elongation ΔL (mm)** (number): Change in length in mm. Required when solving for strain. Positive = elongation, negative = compression.
- **Decimal Places** (number)

## When to use

- Calculate normal stress from an axial force and cross-section area.
- Calculate engineering strain from an original length and change in length.
- Check tensile or compressive loading using consistent N and mm inputs.

## How it works

- Choose whether to solve for stress or strain.
- For stress, enter force F in newtons and area A in mm²; the calculator applies σ = F/A.
- For strain, enter original length L₀ and elongation ΔL in mm; the calculator applies ε = ΔL/L₀.
- Set the number of decimal places and review the JSON result with the calculated value and loading type.

## Use cases

- Evaluate axial stress in a tensile specimen or structural member.
- Measure engineering compression strain from a change in gauge length.
- Verify mechanics of materials calculations before documenting results.

## Frequently asked questions

### What formula is used for stress?

The calculator uses engineering stress σ = F/A, where F is force in newtons and A is cross-section area in mm².

### What formula is used for strain?

The calculator uses engineering strain ε = ΔL/L₀, where ΔL is the change in length and L₀ is the original length.

### What units does the stress result use?

With force in N and area in mm², stress is returned directly in MPa.

### How do I enter compression?

Enter a negative elongation ΔL for compression. The resulting strain is negative and the loading is identified as compression.

### What inputs are needed for a stress calculation?

Select Stress and enter axial force F in N plus cross-section area A in mm².

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