This tool calculates the torsional stress in a shaft based on the input load and material properties.

## How to Use the Torsion Calculator

Enter the following values into the calculator:

**Length (L):**The length of the object experiencing torsion in meters.**Radius (r):**The radius of the object in meters.**Shear Modulus (G):**The material’s shear modulus in Pascals.**Torque (T):**The applied torque in Newton-meters.

After entering the values, click “Calculate” to find the angle of twist (θ) in radians.

## Calculation Explanation

The angle of twist (θ) is calculated using the formula:

θ = (T * L) / (G * J)

Where:

**T:**Torque in Newton-meters**L:**Length in meters**G:**Shear modulus in Pascals**J:**Polar moment of inertia, which is calculated as (π * r^{4}) / 2

## Limitations

This calculator assumes a uniform circular cross-section and linear elastic behavior of the material. It is intended for initial estimates and educational purposes and may not be suitable for complex engineering designs.

## Use Cases for This Calculator

### Calculate Torsion Constant

Enter the dimensions of the cross-section and material properties to determine the torsion constant. The calculator will perform the required mathematical operations to give you the precise value.

### Find Shear Stress

Input the applied torque and the polar moment of inertia to calculate the shear stress in the material. Get an instant result for the maximum shear stress experienced by the cross-section.

### Determine Angle of Twist

Specify the length of the shaft, the material properties, and the applied torque to figure out the angle of twist. The calculator will provide you with the angle in radians or degrees.

### Compare Materials

Compare different materials by entering their respective properties to see how they affect the torsional behavior. Visualize the differences in torsion constants and shear stresses for better decision-making.

### Design Validation

Verify the suitability of the chosen material and dimensions by inputting the design parameters. Ensure your design meets the required safety margins and performance criteria.

### Optimize Cross-Section

Experiment with varying cross-section dimensions to find the optimal shape for minimal weight or maximum strength. Instantly see how changes affect the torsion constant and shear stress.

### Shaft Sizing

Input the maximum allowable shear stress and material properties to determine the minimum required shaft diameter for a given torque. Ensure your shaft can handle the applied loads effectively.

### Material Selection

Explore different materials by inputting your design requirements and constraints. Compare how different materials perform under torsional loading conditions to make an informed choice.

### Educational Tool

Use the calculator as an educational aid to understand the concepts of torsion and its effects on different materials. Experiment with various scenarios to grasp the principles effectively.

### Professional Engineering Tool

Utilize the calculator as a professional engineering tool for accurate torsion analysis in real-world projects. Save time on manual calculations and ensure precise results for your designs.