Angle of Twist Calculator

Applying torque to a shaft twists one end relative to the other.

How the Math Works

The Angle of Twist Calculator uses the fundamental torsion formula φ = T·L ÷ (G·J) to determine how much a shaft will rotate when subjected to torque. Here, φ represents the angle of twist in radians, T is the applied torque, L is the shaft's length, G is the material's shear modulus (a measure of rigidity), and J is the polar moment of inertia that depends on the shaft's cross-sectional geometry. This equation shows that twist increases with greater torque or longer shafts, but decreases with stiffer materials or larger cross-sections.

Practical Applications

Engineers use this calculation during the design phase of any rotating machinery with shafts, such as automotive drivetrains, aircraft propulsion systems, or industrial equipment. By calculating the expected twist, engineers can ensure shafts won't deform excessively under load, which could cause misalignment, vibration, or failure. The calculator helps determine appropriate shaft diameters, select suitable materials, or verify that existing designs meet safety requirements before components are manufactured or installed.

Day-to-Day Use

While you may not calculate shaft twist daily, this principle affects many things you interact with regularly. The cars you drive, the power tools in your garage, and even the motors in household appliances all rely on properly designed shafts that don't twist dangerously under load. Understanding this calculation helps explain why certain machinery feels more robust or why maintenance professionals need to check for excessive play or wear in rotating components during routine inspections.

Worked example

200 N·m, 500 mm, G 79 GPa, J 250,000 mm⁴ → about 0.0051 rad (0.29°).

FAQ