Mohr’s Circle Calculator

Mohr’s Circle for Plane Stress

Mohr’s circle is a graphical way to represent the state of stress at a point and find principal stresses without repeating trigonometric calculations for every angle. Given the normal stresses σx and σy and shear stress τxy, the circle’s center is at C = (σx + σy)/2 and its radius is R = √(((σx−σy)/2)² + τxy²).

The principal stresses, where shear is zero, are σ1 = C + R and σ2 = C − R, and the radius R itself equals the maximum in-plane shear stress. The orientation of the principal plane is θp = ½atan2(2τxy, σx−σy).

This is a standard mechanics-of-materials calculation used for general structural and mechanical engineering reference.