Free tool

Mohr circle calculator for geology

Normal and shear stress on a plane from σ1, σ3 and the angle to the plane, drawn on a Mohr circle, with an optional Coulomb failure envelope and tensile strength.

Open the mohr circle calculator

Formulas

With θ the angle between σ1 and the normal to the plane:

• σn = ½(σ1 + σ3) + ½(σ1 − σ3)·cos 2θ
• τ = ½(σ1 − σ3)·sin 2θ

The circle is centered at ½(σ1 + σ3) with radius ½(σ1 − σ3), and the plane plots at 2θ. Geologists count compression as positive.

Failure

The failure envelope is a line with intercept equal to the cohesion and slope angle equal to the friction angle φ. Shear fractures form where 2θ measured from σ3 equals 90° − φ.