Angle of Twist Calculator

Free calculate the angular displacement in a shaft subjected to torsional loading. Get instant, accurate results with our easy-to-use calculator.

Input Parameters

For solid circular shaft: J = πd⁴/32

Steel: ~80 GPa, Aluminum: ~26 GPa

Results

Enter parameters to calculate angle of twist

Angle of Twist Formula

Formula

θ = (T × L) / (G × J)

Where:

  • • θ = angle of twist (radians)
  • • T = applied torque (N⋅m)
  • • L = shaft length (m)
  • • G = shear modulus (Pa)
  • • J = polar moment of inertia (m⁴)

Polar Moment of Inertia

Solid circular shaft:

J = πd⁴/32

Hollow circular shaft:

J = π(d₀⁴ - dᵢ⁴)/32

Where d = diameter, d₀ = outer, dᵢ = inner

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