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Mohr’s Circle Calculator

Calculate principal stresses, maximum shear stress and orientation angle from plane stress state (σ_x, σ_y, τ_xy). Interactive Mohr’s circle visualisation.

Principal Stresses
σ₁ = 120 MPa, σ₂ = -20 MPa
σ_x=80, σ_y=20, τ_xy=50 MPa

Mohr’s Circle

Featured: Principal Stresses, Max Shear, Rotation Angle

Positive τ_xy = clockwise

Mohr’s Circle

Normal stress (σ) vs Shear stress (τ)

Principal Stresses
σ_{1,2} = (σ_x + σ_y)/2 ± √[((σ_x - σ_y)/2)² + τ_xy²]
τ_max = √[((σ_x - σ_y)/2)² + τ_xy²]
Principal Angle
tan(2θ_p) = 2τ_xy / (σ_x - σ_y)

Enter stresses to see results

Mohr’s Circle Guidelines

Sign Convention

Normal stress: +ve = tension, -ve = compression

Shear stress: +ve = clockwise on element

Key Points

Centre: (σ_avg, 0)

Radius: √[((σ_x-σ_y)/2)² + τ_xy²]

Principal planes: no shear

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