What this calculator does
Von Mises stress reduces a combined state of stress, made up of normal stresses acting in two directions plus a shear stress, into a single equivalent number that can be compared directly against a material's yield strength. Real components are rarely loaded in one direction alone, and von Mises stress is the standard way engineers judge whether a combined loading will cause yielding.
It is not a stress that exists in a single physical direction; it is a calculated equivalent. When the combined stress state reduces to a single applied stress with no shear, such as simple tension or compression along one axis, von Mises stress correctly reduces to exactly that applied stress.
The formula
For a 2D plane-stress state, von Mises stress equals the square root of (σx squared, minus σx times σy, plus σy squared, plus three times τxy squared). All three input stresses can be positive, negative or zero; the formula always returns a non-negative equivalent stress.
| Term | Meaning |
|---|---|
| σx, σy | The normal stresses acting along two perpendicular in-plane directions. |
| τxy | The shear stress acting in the same plane. |
| σv | Von Mises equivalent stress, compared against yield strength to judge whether a material will yield under this combined loading. |
The inputs explained
| Field | What to enter |
|---|---|
| Normal stress σx (MPa) | The normal stress acting in the x-direction. Enter as negative for compression. |
| Normal stress σy (MPa) | The normal stress acting in the y-direction. Enter as negative for compression. |
| Shear stress τxy (MPa) | The in-plane shear stress. |
When to use it
Checking a component against yield strength
Comparing the calculated von Mises stress directly against a material's yield strength, using a chosen safety factor, is the standard check for whether a design will yield under a given combined load.
Combining stresses from separate load cases
A shaft or bracket often carries both a direct axial or bending stress and a separate torsional shear stress; von Mises stress combines both into one figure rather than checking each in isolation.
Comparing loading scenarios at a stress concentration
At features like holes or fillets where stress concentrates, working out von Mises stress for the local combined stress state shows whether that location, not just the nominal section, is the governing check.
Worked examples
Every figure in the tables below is produced by this page’s own calculator at build time, so the numbers and the tool always agree. Select any row to load that scenario.
How von Mises stress changes as shear stress increases, at fixed normal stresses
Fixed normal stresses of 100 MPa and 40 MPa, across a range of added shear stress.
| Shear stress τxy | Von Mises stress (σv) |
|---|---|
| 0 MPa | 87.178 MPa |
| 20 MPa | 93.808 MPa |
| 40 MPa | 111.355 MPa |
| 60 MPa | 135.647 MPa |
| 80 MPa | 163.707 MPa |
| 100 MPa | 193.907 MPa |
How von Mises stress changes as the second normal stress varies, at a fixed first normal stress
A fixed σx of 100 MPa with no shear, across a range of values for σy, including compression.
| Normal stress σy | Von Mises stress (σv) |
|---|---|
| -100 MPa | 173.205 MPa |
| -50 MPa | 132.288 MPa |
| 0 MPa | 100.000 MPa |
| 50 MPa | 86.603 MPa |
| 100 MPa | 100.000 MPa |
| 150 MPa | 132.288 MPa |
Questions
What does it mean if von Mises stress exceeds the yield strength?
It indicates the material is predicted to yield, that is, begin permanent plastic deformation, under that combined stress state, according to the von Mises (distortion energy) yield criterion, one of the most widely used yield criteria for ductile metals.
Why does pure uniaxial stress give a von Mises stress equal to the applied stress?
With σy and τxy both zero, the formula reduces to the square root of σx squared, which is simply the absolute value of σx. This is the expected result: a single applied stress with no other loading should be its own equivalent stress.
Does the sign of σx or σy matter?
Yes for the inputs, but the final von Mises stress is always reported as non-negative, since it represents a magnitude for comparison against yield strength rather than a directional stress. Compression is entered as a negative value and does affect the result through the σx·σy cross term.
Is von Mises stress the same as shear stress?
No. Shear stress (τxy) is one of the three inputs to this calculation, describing stress acting parallel to a surface. Von Mises stress is a separate, derived equivalent stress that combines shear together with the two normal stresses into one figure. See the shear strain calculator for shear-specific deformation instead.
For the deformation caused by shear loading rather than the equivalent stress from combined loading, see the shear strain calculator.