Von Mises Stress Calculator — Yield Criterion & Safety Factor
Compute the von Mises equivalent stress (σ_vm) from a 3-D stress state — six stress components — and compare it to the material yield strength to determine the factor of safety. Works for plane stress (2-D) by setting σ₃ = 0 and shear stresses to 0.
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Equivalent stress for yield prediction (same unit as inputs)
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Normal stress difference terms
(σ₁−σ₂)² + (σ₂−σ₃)² + (σ₃−σ₁)² = 60,000 - 2
Shear stress term
3 × (τ₁₂² + τ₂₃² + τ₁₃²) = 0 - 3
Expression under √
½ × 60,000 + 0 = 30,000 - 4
Von Mises stress σ_vm = √(…)
√(30,000) = 173.21Yielding is predicted when σ_vm reaches the material yield strength.
How does this calculator work?
σ_vm = √[½·((σ₁−σ₂)²+(σ₂−σ₃)²+(σ₃−σ₁)²) + 3·(τ₁₂²+τ₂₃²+τ₁₃²)]. Yielding occurs when σ_vm ≥ Sy. Enter six stress components and the material yield strength; the calculator returns the von Mises stress, Tresca shear stress and the safety factor. Assumes static loading of a ductile isotropic material.
Formula
How this is calculated
The von Mises criterion (distortion energy theory) predicts yielding when the elastic strain energy due to shape distortion equals the energy in a uniaxial tension test at yield. In practical terms, it combines all six stress components (three normal: σ₁, σ₂, σ₃; three shear: τ₁₂, τ₂₃, τ₁₃) into a single scalar equivalent stress σ_vm. Yielding is predicted when σ_vm ≥ Sy, where Sy is the uniaxial yield strength from a standard tensile test.
For a 2-D (plane-stress) case — a thin plate or surface where stresses through the thickness are negligible — set σ₃ = 0 and shear stresses to 0, reducing the formula to σ_vm = √(σ₁² − σ₁σ₂ + σ₂²). The calculator also reports the Tresca (maximum shear stress) criterion as a second reference: it is more conservative than von Mises and easier to apply by hand.
The safety factor is defined as Sy / σ_vm. A value below 1 means yielding is predicted; values below 1.5–2 are considered marginal for many engineering designs, depending on load uncertainty, material variability and consequences of failure. This tool assumes a ductile, isotropic material under static loading — it does not account for fatigue, stress concentrations, temperature effects or fracture.
Frequently asked questions
Both predict yielding of ductile metals under complex loading. Tresca uses the maximum shear stress (τ_max = (σ_max − σ_min) / 2) and is more conservative. Von Mises uses the distortion energy and better matches experimental data for most metals. In plane stress the two criteria agree at uniaxial and equal-biaxial stress but diverge at shear-dominated states.
Use a Mohr's circle construction or solve the characteristic equation det(σ_ij − σ·δ_ij) = 0 for the three eigenvalues. Many FEA packages report principal stresses directly. For a 2-D state, σ₁,₂ = (σ_x + σ_y)/2 ± √[((σ_x − σ_y)/2)² + τ_xy²].
Yes, as long as every input uses the same unit. The calculator is unit-agnostic — it applies the formula numerically. If you enter stresses in kPa, your safety factor and von Mises output are also in kPa compared to a yield strength in kPa.
Also known as
TG we-Calculate Editorial Team. (2026). Von Mises Stress Calculator — Yield Criterion & Safety Factor [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/von-mises-stress-calculator
TG we-Calculate Editorial Team. "Von Mises Stress Calculator — Yield Criterion & Safety Factor." TG we-Calculate. 2026. https://we-calculate.com/calculator/von-mises-stress-calculator.
TG we-Calculate Editorial Team, "Von Mises Stress Calculator — Yield Criterion & Safety Factor," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/von-mises-stress-calculator
@misc{wecalculate_von_mises_stress_calculator, title = {Von Mises Stress Calculator — Yield Criterion & Safety Factor}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/von-mises-stress-calculator}}, year = {2026}, note = {TG we-Calculate} }
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