Failure Theories Calculator
von Mises, Tresca, Rankine and Coulomb–Mohr — principal stresses, factor of safety and your stress point on the failure envelope.
What it does
Enter a plane-stress state and a material. The calculator finds the principal stresses and principal angle, the von Mises equivalent stress, and the factor of safety under each failure theory, then plots your stress point on the failure envelopes in the σ₁–σ₂ plane with Mohr's circle alongside.
How to use it
- Enter σx, σy and τxy in MPa (tension positive, compression negative).
- Choose ductile (enter yield strength Sy) or brittle (enter Sut and Suc).
- Read the principal stresses, the factor of safety under each theory and the safe / marginal / fails verdict.
- Check the envelope plot and the step-by-step hand calculation.
Solve by hand first, then validate
Every result comes with the working, so you can follow the formulas instead of trusting a black box — the same method we teach in our ANSYS Workbench course. Browse more free calculators and references in Resources.
Frequently asked questions
Which failure theory should I use?
For ductile metals use von Mises (distortion energy) — it matches test data best and is the equivalent stress FEA tools show by default; Tresca is slightly more conservative. For brittle materials like cast iron use Coulomb–Mohr, which accounts for different tensile and compressive strengths.
Does it handle 3D stress?
It assumes plane stress (σz = τxz = τyz = 0), which covers most thin parts and surface points where failure starts.
Is it free? Do I need to sign in?
Yes, it's free and needs no sign-in.