Angle of Twist Calculator

Angle of twist (θ):

Torque (T):

Length of the shaft (L):

Shear modulus (G):

Polar moment of inertia (J):

How This Is Calculated

$$ \theta = \frac{T \cdot L}{G \cdot J} $$ where:

θ = Angle of twist (rad)

T = Torque (Nm)

L = Length of the shaft (m)

G = Shear modulus (Pa)

J = Polar moment of inertia (m⁴)

Assumptions

The cross-section remains uniform.
The material behaves elastically.
The shaft is in pure torsion without warping.
There are no stress concentrations.

Related Calculators

Bending Stress

Deflection Under Load

Natural Frequency for Torsional Vibration

Polar Moment of Inertia of a Circular Shaft

Power Transmitted Through a Shaft