Our Mohr’s Circle calculator will help you easily determine the principal stresses and absolute maximum shear stress for given normal and shear stresses on a plane.

# Mohr’s Circle Calculator

## How to Use the Calculator

Enter the values of the normal stresses (σx and σy) and the shear stress (τxy) into the respective fields and click “Calculate”. The result will provide you with the center coordinates and the radii of Mohr’s circle, which represent the principal stresses and the maximum shear stress.

## How it Calculates

The calculator computes the center (C) of Mohr’s circle using the formula C = (σx + σy) / 2, and the radius (R) using the formula R = √[(σx – σy)² / 4 + τxy²]. The principal stresses σ1 and σ2 are then C + R and C – R, respectively. The maximum shear stress τmax is equal to the radius R.

## Limitations

This calculator assumes that the plane stress conditions are met, that is, the stresses perpendicular to the plane are negligible. It is also presumed the material behavior is elastic and obeys Hooke’s law. The results may not be accurate for materials with non-linear or complex stress-strain behavior.