Mohr’s Circle Calculator

Written by Great Medico

Updated September 25, 2026 •2 min read

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A mohr’s circle result can look precise while still being wrong if one unit or convention is off. Solid-mechanics results are only useful when the geometry, loading convention, and material property match the physical part being modeled. This page keeps the calculation focused so the number is easy to trace back to the values you entered.

What this calculator does

The Mohr’s Circle Calculator turns Normal stress in the X direction (σxx), Normal stress in the Y direction (σyy), Shear stress (τxy) into the page’s maximum principal stress using the specific relationship described below. Supporting values appear only where this calculator derives them, which makes the headline easier to audit against the same model.

How to use it

Start with the fields that drive this result: Normal stress in the X direction (σxx), Normal stress in the Y direction (σyy), Shear stress (τxy), Shear stress (τyx). Use the unit menu beside each quantity instead of converting by eye; the page normalizes supported units before calculating. Then change one value at a time and watch whether the headline and supporting values move as the formula predicts.

How the calculation works

The page averages the two shear inputs, then forms mean normal stress (σx+σy)/2 and circle radius R = √[((σx−σy)/2)²+τ²]. Principal stresses are mean ± R, and the orientation is ½atan2(2τ, σx−σy). It also reports maximum shear and a plane-stress von Mises value.

Example

With the default plane-stress inputs (Normal stress in the X direction (σxx) = 100 MPa; Normal stress in the Y direction (σyy) = 50 MPa; Shear stress (τxy) = 25 MPa; Shear stress (τyx) = 25 MPa), the page returns a maximum principal stress of 110,355,339.059327 Pa. The paired minimum-principal and orientation values come from the same Mohr-circle radius, so they should be interpreted together rather than as unrelated outputs.

How to interpret the result

Treat the maximum principal stress as the value for the entered ideal geometry, loading state, and material constants. Compare it only with criteria that use the same stress, strain, hardness, or section-property definition and unit system.

Limitations and notes

Material properties can vary with alloy, processing, temperature, loading rate, direction, and test method; geometric idealizations also matter whenever the real part differs from the entered shape. An error in Normal stress in the X direction (σxx), Normal stress in the Y direction (σyy) can shift the answer far more than rounding does. The result is best used for estimation and comparison within the stated model; final engineering decisions should include the limits, factors, and checks required by the relevant standard.