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
| Field | What to enter |
|---|---|
| Stress state | Choose one: General 3D, Plane stress (2D), Principal stresses, Pure shear |
| σx (or σ₁) | Units: MPa, kPa, Pa, GPa, psi, ksi |
| σy (or σ₂) | Units: MPa, kPa, Pa, GPa, psi, ksi |
| σz (or σ₃) | Units: MPa, kPa, Pa, GPa, psi, ksi |
| τxy (or τ for pure shear) | Units: MPa, kPa, Pa, GPa, psi, ksi |
| τyz | Units: MPa, kPa, Pa, GPa, psi, ksi |
| τzx | Units: MPa, kPa, Pa, GPa, psi, ksi |
| Yield 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) |
|---|---|
| 60 | 74.162 |
| 90 | 93.8083 |
| 120 | 117.8983 |
| 150 | 144.2221 |
| 180 | 171.7556 |
| 240 | 228.6919 |
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
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.
Frequently asked questions
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.