Torsional Deflection of a Shaft Calculator: Angle of Twist & Stress Analysis

The torsional deflection (θ) of a shaft is calculated using the formula:
θ = (T × L) / (G × J)
Where:

• θ: Torsional Deflection (radians)
• T: Applied Torque (N·m, lb·in)
• L: Length of Shaft (m, in)
• G: Shear Modulus of Elasticity (Pa, psi)
• J: Polar Moment of Inertia (m⁴, in⁴)

The Polar Moment of Inertia (J) depends on the shaft's cross-section:
For a solid circular shaft:
J = (π × Do4) / 32
For a hollow circular shaft:
J = (π × (Do4 - Di4)) / 32
Where:

• D_o: Outer Diameter (m, in)
• D_i: Inner Diameter (m, in)

Note: Ensure consistent units for accurate results (e.g., all SI units or all Imperial units). The calculator assumes SI units for input (N·m, m, GPa, m) for internal calculations.