# Mohrs Circle Calculator

Calculate Mohr’s Circle stress and strain parameters in seconds with this easy-to-use calculator. Get accurate results fast!

Mohrs circle is a 2D graphical representation of the Cauchy stress tensor, used to analyze and identify the stresses acting on a given point. The magnitudes of normal and shear stresses are represented by the abscissa (σ_{n}) and ordinate (τ_{n}) respectively. With the help of this Mohrs circle calculator, it is possible to calculate the mean, maximum, principal and Von Mises stresses.

C = \sigma_x + \sigma_y / 2

\sigma_1 = \left(\left(\sigma_x + \sigma_y\right) / 2\right) + \sqrt{\left(\left(\sigma_x - \sigma_y\right) / 2\right)^2 + \tau_{xy}^2}

\sigma_2 = \left(\left(\sigma_x + \sigma_y\right) / 2\right) - \sqrt{\left(\left(\sigma_x - \sigma_y\right) / 2\right)^2 + \tau_{xy}^2}

\tau_{max} = \sqrt{\left(\left(\sigma_x - \sigma_y\right) / 2\right)^2 + \tau_{xy}^2}

\sigma_{VM} = \sqrt{\left(\sigma_x^2 + \sigma_y^2\right) - \left(\sigma_x \sigma_y\right) + \left(3 \tau_{xy}^2\right)}

\tau_{yx} = -\tau_{xy}

**Where:**

- C = Mean Stress
- σ
_{1}= Principal Stress I - σ
_{2}= Principal Stress II - τ
_{max}= Maximum Shear Stress - σ
_{VM}= Von Mises Stress - τ
_{yx}= Shear Stress

Mohr’s circle calculator is a tool used in mechanics and materials science to calculate stresses and strains on a material under different loading conditions. It takes in the values of normal and shear stresses on a material in two perpendicular directions and produces a graphical representation of the stress state of the material in the form of a circle. The circle’s center represents the average stress, while its radius represents the difference between the maximum and minimum stresses. Mohr’s circle is a useful tool for visualizing stress state and determining the maximum shear stress on a material.