Mechanical & Civil Engineering
Shaft Angle of Twist Calculator
Calculate the angle of twist in a circular shaft under torque using theta = TL/JG.
Your inputs
Change any value to update the result instantly.
Angle of twist
0.5836 deg
Angle of twist (radians)
0.0102 rad
Polar moment of inertia
6,13,592.32 mm⁴
Shaft length
1,000 mm
What this calculator does
Shaft Angle of Twist Calculator: Applies the standard mechanics-of-materials relationship for this load case so a student can see how the stress, strain or deflection follows from the geometry and the load.
What your result means
The headline figure tells you how hard the material is being worked, or how much it moves, under the load you entered. Compare it with the allowable value for your material and required factor of safety.
Formula and working
θ = T·L / (J·G)
- 1
Collect the inputs
Applied torque = 500 N·m; Shaft length = 1,000 mm; Shaft diameter = 50 mm; Shear modulus = 80,000 MPa
- 2
Apply the formula
θ = T·L / (J·G)
- 3
Result
Angle of twist = 0.5836 deg
Frequently asked questions
Symbols and assumptions
- T
- Applied torque (N·m)
- L
- Shaft length (mm)
- d
- Shaft diameter (mm)
- G
- Shear modulus (MPa)
- • The material is homogeneous, isotropic and loaded within its linear-elastic range.
- • Inputs are entered in a consistent unit system, as labelled on each field.
Sources and review
Reviewed 2026-09-22 · Next review 2027-09-22
- • This is an educational estimate for learning and checking, not a design deliverable.
- • Real design must follow the governing code or standard for your jurisdiction and be reviewed and signed off by a qualified engineer.
- • Safety factors, load combinations and material certification are the responsibility of the designer, not of this page.
Important limitation
This is an educational estimate based only on the values and formula shown. Verify current rates, rules, units, and professional standards before relying on the result. It is not personalized financial or investment advice.
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