Mohr's Circle Calculator

Visualize the 2D stress state and compute principal stresses, max shear, and the principal plane angle.

Enter σx, σy, and τxy to compute.

How to use

Enter the normal stresses σx and σy (in MPa) and the shear stress τxy (in MPa, sign matters — positive for counterclockwise couple). Press Compute to draw Mohr's circle: the circle's center sits at (σx+σy)/2 on the σ axis and its radius is √[((σx−σy)/2)² + τxy²]. The principal stresses σ1 and σ2 are the intersections with the σ axis (center ± radius), the maximum shear stress equals the radius, and the principal plane angle θp = 0.5 × arctan(2τxy / (σx−σy)). Read every derived value from the trace and export it if needed.

Based on 2D stress transformation theory (Mohr's circle method).