This angular deflection calculator finds how much a shaft twists under an applied torque, for solid or hollow circular shafts. Enter the torque, length, material, and diameters above.
Formulas
Twist θ = T × L ÷ (G × J) Hollow shaft J = π × (D⁴ − d⁴) ÷ 32
- G — shear modulus, J — polar moment of inertia
Example
T = 1000 N·m, L = 2 m, G = 79 GPa, D = 50 mm, d = 30 mm: θ = 0.047 rad (2.72°).
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Frequently Asked Questions
How do I calculate shaft angular deflection?
Use theta = T x L / (G x J). For a hollow shaft, J is pi times (D^4 minus d^4) over 32.
What is the polar moment of inertia?
It measures a section’s resistance to twisting. For a hollow round shaft it depends on the outer and inner diameters to the fourth power.
Does a hollow shaft twist more than a solid one?
For the same outer diameter, yes slightly, but hollow shafts save weight for nearly the same stiffness.