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