Calculate the Von Mises equivalent stress for any loading condition. Enter your normal stresses (σx, σy, σz) and shear stresses (τxy, τyz, τxz) to get the Von Mises stress — a single equivalent value you can compare directly against your material's yield strength to assess failure risk.
Von Mises Stress (σv)
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Safety Factor
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Yield Status
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Principal Stress σ1
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Principal Stress σ2
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Maximum Shear Stress
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Von Mises stress is a scalar equivalent stress value used to predict yielding in ductile materials under complex loading. It combines normal and shear stress components into a single value that can be compared to the material's uniaxial yield strength. If the Von Mises stress exceeds the yield strength, the material is predicted to yield.
The Von Mises yield criterion states that a material begins to yield when the Von Mises stress reaches the material's yield strength. It is widely used for ductile metals and is considered more accurate than the Tresca criterion for most engineering applications because it accounts for the contribution of all stress components.
For 3D principal stresses σ1, σ2, σ3, the formula is: σv = √[0.5 × ((σ1−σ2)² + (σ2−σ3)² + (σ3−σ1)²)]. For a 2D plane stress state (σ3 = 0), this simplifies to: σv = √(σ1² − σ1·σ2 + σ2²). You can enter raw stress components into this calculator and it will compute the principal stresses and Von Mises stress automatically.
Von Mises stress is best used when analyzing ductile materials (such as steel or aluminium alloys) subjected to complex, multi-axial loading. It is the standard failure criterion in most structural, mechanical, and finite element analysis (FEA) workflows. For brittle materials, the maximum normal stress criterion is typically more appropriate.
Yes, the Von Mises stress can exceed individual principal stress magnitudes in certain stress states. However, for a uniaxial stress state (all other components zero), the Von Mises stress equals the applied normal stress. In combined loading scenarios involving significant shear, the Von Mises stress may be larger than any single principal stress component.
For a circular shaft subjected only to a torque T, the only non-zero stress is the shear stress τ. In this case, σx = σy = 0 and τxy = τ, so the Von Mises stress becomes σv = √3 × τ. This is derived directly from the 2D Von Mises formula.
In a 2D (plane stress) analysis, out-of-plane normal stress σz and shear stresses τyz and τxz are assumed to be zero. The 2D formula is: σv = √(σx² − σx·σy + σy² + 3τxy²). The full 3D formula includes all six stress components and is used when the loading is truly three-dimensional. This calculator supports both modes.
The safety factor (SF) is calculated by dividing the material's yield strength by the Von Mises stress: SF = Yield Strength / σv. A safety factor greater than 1.0 means the component is not expected to yield. Values below 1.0 indicate predicted yielding. Engineers typically design for safety factors of 1.5 or higher depending on the application.