Principal Stresses Calculator (Mohr’s Circle)

About this calculator

This calculator finds the principal stresses of a 2D stress state (σx, σy, τxy) using the closed-form equivalent of Mohr's circle: σ₁,₂ = (σx + σy)/2 ± √[((σx − σy)/2)² + τxy²], and the maximum in-plane shear stress equals the radius of that circle, √[((σx − σy)/2)² + τxy²].

The principal stresses are the normal stresses acting on the planes where shear stress drops to zero — the orientation an engineer actually cares about, since materials typically fail along planes of maximum normal or shear stress. Structural, mechanical and civil engineers use this transformation constantly when checking whether a loaded beam, pressure vessel or machine part will yield or fracture.