Shear Modulus Calculator

About the Shear Modulus Calculator

The Shear Modulus Calculator determines the Shear Modulus (G), also known as the modulus of rigidity. This key mechanical property measures a material’s resistance to shape deformation under shear stress. It defines how a material responds when subjected to opposing forces acting parallel to its surface — an essential concept in mechanics of materials, elasticity theory, and structural engineering.

What You Can Calculate

• Shear Modulus (G): The ratio of shear stress (τ) to shear strain (γ), indicating material stiffness under shear loads.
• Material Rigidity: Assess the ability of metals, composites, and polymers to resist torsional and shearing forces.

Formula Used in the Calculator

The Shear Modulus is calculated using the following relationship:

• G = τ / γ

Where:

• G = Shear Modulus (Pa, MPa, or GPa)
• τ = Shear Stress
• γ = Shear Strain (dimensionless)

How to Use the Shear Modulus Calculator

1. Enter the shear stress (τ) — the force applied parallel to the surface of the material.
2. Enter the shear strain (γ) — the angular deformation or displacement per unit thickness.
3. Select the appropriate stress unit (Pa, MPa, or GPa).
4. The calculator will automatically compute the Shear Modulus (G) in Pascals.

Applications of Shear Modulus in Engineering

• Structural Engineering: Used in the design of beams, shafts, and columns to evaluate torsional stiffness and deflection under loads.
• Elasticity and Solid Mechanics: Essential for determining material deformation behavior under combined stresses.
• Vibration Analysis: Helps estimate stiffness for dynamic and frequency response modeling.
• Material Science: Used in evaluating rigidity and comparing the elastic properties of metals, ceramics, and polymers.
• Mechanical Design: Supports safe and efficient design of rotating or shear-loaded components like couplings, rods, and drive shafts.