# Mohrs circle

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 (σn) and ordinate (τn) respectively. With the help of this Mohrs circle calculator, it is possible to calculate the mean, maximum, principal and Von Mises stresses.

Normal Stress σ xx
MPa
Shear Stress τ xy
MPa
Normal Stress σ yy
MPa
°
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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
• σ1 = Principal Stress I
• σ2 = Principal Stress II
• τmax = Maximum Shear Stress
• σVM = Von Mises Stress
• τyx = 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.