# Tensile & Yield Strength Calculator

Compute engineering tensile strength σ_uts = F_max/A₀, yield strength σ_y = F_y/A₀ (optional), and the yield ratio σ_y/σ_uts from a uniaxial tension test. Forces in kN, area in mm² → stress in MPa. A₀ is the original cross-section. Yield ratio <0.55 high ductility, 0.55–0.85 moderate, >0.85 low ductility.

> Canonical page: https://elysiatools.com/en/tools/tensile-strength-calculator

- **Category:** Math & Numbers

- **Keywords:** tensile strength, ultimate tensile strength, yield strength, yield ratio, tension test, F_max/A, stress-strain, ductility, mechanical testing

## Overview

Calculate engineering tensile strength, optional yield strength, and yield ratio from uniaxial tension-test data. Enter the original cross-section area in mm², maximum force in kN, and optionally yield force in kN to receive stress values in MPa and a ductility classification.

## Inputs

- **Original Cross-section Area A₀ (mm²)** (number): Original (unstressed) cross-section area of the gauge section, in mm². Engineering convention uses A₀, not the necked area.
- **Maximum Force F_max (kN)** (number): Maximum force reached during the test (at onset of necking), in kN.
- **Yield Force F_y (kN, optional)** (number): Force at the yield point, in kN. Optional — when omitted, only σ_uts is reported (yield ratio needs F_y).
- **Decimal Places** (number)

## When to use

- You need the ultimate tensile strength from a maximum-force measurement.
- You want to calculate yield strength and yield ratio using a measured yield force.
- You need a quick ductility classification based on the calculated yield ratio.

## How it works

- Enter the original, unstressed cross-section area A₀ in mm².
- Enter the maximum test force F_max in kN and optionally the yield force F_y in kN.
- The calculator applies σ_uts = F_max/A₀ and, when provided, σ_y = F_y/A₀, converting the force values to produce stress in MPa.
- When yield force is included, it calculates σ_y/σ_uts and classifies ductility as high, moderate, or low.

## Use cases

- Evaluate tensile-test results for structural metals and engineering materials.
- Compare yield-to-ultimate strength ratios between material samples.
- Prepare concise strength calculations for laboratory notes or engineering reports.

## Frequently asked questions

### What inputs are required?

Original cross-section area A₀ and maximum force F_max are required. Yield force F_y is optional.

### What units should I use?

Enter area in mm² and forces in kN. The calculated stresses are reported in MPa.

### Which cross-section area should I enter?

Use the original, unstressed gauge-section area A₀, not the reduced necked area.

### What happens if I omit the yield force?

The calculator reports tensile strength only. Yield strength, yield ratio, and ductility class are not computed.

### How is ductility classified?

A yield ratio below 0.55 indicates high ductility, 0.55–0.85 indicates moderate ductility, and above 0.85 indicates low ductility.

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