# Von Mises Stress Calculator

URL: https://speedycalculator.com/calculators/physics/von-mises-stress/
Last updated: 2026-10-30

> The von Mises stress calculator finds the equivalent (von Mises) stress for a general 3D stress state, plane stress, principal stresses or pure shear, and the safety factor against yielding.

## Inputs

- Stress state
- σx (or σ₁) (MPa, kPa, Pa, GPa, psi, ksi)
- σy (or σ₂) (MPa, kPa, Pa, GPa, psi, ksi)
- σz (or σ₃) (MPa, kPa, Pa, GPa, psi, ksi)
- τxy (or τ for pure shear) (MPa, kPa, Pa, GPa, psi, ksi)
- τyz (MPa, kPa, Pa, GPa, psi, ksi)
- τzx (MPa, kPa, Pa, GPa, psi, ksi)
- Yield strength (optional) (MPa, kPa, Pa, GPa, psi, ksi)

## Results

- Von Mises stress σ_v
- Safety factor against yielding
- Yielding?

## Formula

```
σ_v = √(½[(σx − σy)² + (σy − σz)² + (σz − σx)²] + 3(τxy² + τyz² + τzx²))
Principal: σ_v = √(½[(σ₁ − σ₂)² + (σ₂ − σ₃)² + (σ₃ − σ₁)²]) · Pure shear: σ_v = √3·τ
```

## Explanation

Ductile metals yield when their distortion energy reaches a critical value. The von Mises stress condenses a complex stress state into one number you can compare directly with the yield strength from a tensile test.

### How to use the Von Mises Stress Calculator

- **Stress state**
- **σx (or σ₁)**
- **σy (or σ₂)**
- **σz (or σ₃)**
- **τxy (or τ for pure shear)**
- **τyz**
- **τzx**
- **Yield strength (optional)**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Choose the stress state, enter the components (with signs) and optionally the yield strength.

### Inputs explained

FieldWhat to enterStress stateChoose one: General 3D, Plane stress (2D), Principal stresses, Pure shearσx (or σ₁)Units: MPa, kPa, Pa, GPa, psi, ksiσy (or σ₂)Units: MPa, kPa, Pa, GPa, psi, ksiσz (or σ₃)Units: MPa, kPa, Pa, GPa, psi, ksiτxy (or τ for pure shear)Units: MPa, kPa, Pa, GPa, psi, ksiτyzUnits: MPa, kPa, Pa, GPa, psi, ksiτzxUnits: MPa, kPa, Pa, GPa, psi, ksiYield strength (optional)Units: MPa, kPa, Pa, GPa, psi, ksi

### Example values

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

σx (or σ₁) (MPa)Von Mises stress σ_v (MPa)6074.1629093.8083120117.8983150144.2221180171.7556240228.6919

## Worked example

Inputs — Stress state: Plane stress (2D); σx (or σ₁): 120 MPa; σy (or σ₂): 40 MPa; τxy (or τ for pure shear): 30 MPa; Yield strength (optional): 250 MPa.

Results — **Von Mises stress σ_v = 117.89826 MPa**; Safety factor against yielding = 2.1205; Yielding? = No – below yield.

## Key terms

- **Distortion energy**: Strain energy associated with change of shape.

## FAQ

**What does the von Mises criterion say?**
Yielding starts when σ_v reaches the uniaxial yield strength.

**Is it used for brittle materials?**
No – brittle materials use maximum normal stress or Mohr–Coulomb.

**How does it compare with Tresca?**
Tresca is slightly more conservative (up to 15%).

**Why √3 for pure shear?**
Shear yield strength is about 0.577 times the tensile yield strength.


## Sources

- [MIT OpenCourseWare – Mechanics of Materials](https://ocw.mit.edu/courses/2-001-mechanics-materials-i-fall-2006/)
- [The Engineering ToolBox](https://www.engineeringtoolbox.com/)