Mohr's Circle Generator

Type the stresses on an element — σₓ, σᵧ and τₓᵧ — and watch Mohr's circle draw itself. Get the principal stresses, the maximum in-plane shear, the plane orientations, and (optionally) the stresses on any rotated plane, with the working shown step by step.

🆓 Free interactive tool — build as many circles as you like · Balance … EP

① Element stresses

Use any consistent stress unit (MPa, ksi, psi…). Sign convention: tension is positive, compression negative. τₓᵧ is positive when it tends to rotate the element counter-clockwise on the +x face. Leave the angle blank to skip the rotated-plane stresses.

σₓ (normal, x)

σᵧ (normal, y)

τₓᵧ (shear)

θ — plane rotation (°, optional) CCW positive

② Mohr's circle

Circle (σ_avg, R) X face (σₓ, τₓᵧ) Y face (σᵧ, −τₓᵧ) Rotated plane (θ)

τ is plotted downward-positive (Hibbeler convention), so a physical rotation of θ counter-clockwise is a 2θ rotation in the same sense on the circle.

📐 Results

Average / centre σ_avg

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Radius R

—

σ₁ (max principal)

—

σ₂ (min principal)

—

τ_max (in-plane)

—

θ_p → σ₁

—

θ_s → τ_max

—

τ_abs,max (3D)

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Mohr's Circle Generator

① Element stresses

② Mohr's circle

📐 Results

Stresses on the plane rotated θ = —°

Worked solution