Torsional Stress Calculator
Enter torque, shaft dimensions, length, and shear modulus to instantly compute shear stress and angle of twist for solid or hollow circular shafts.
Use the Torsional Stress Calculator
Fill in the inputs and click Calculate to see results.
Max Shear Stress (τ)
—
MPa
Angle of Twist (φ)
—
degrees
Intermediate Values
Outer radius (r)
—
Inner radius (ri)
—
Polar moment J
—
Torsional rigidity (G·J)
—
Angle of twist (radians)
—
Formulas Applied
J = π·D⁴ / 32
τ = T · r / J
φ = T · L / (G · J)
Summary
This tool applies the classical torsion equations to circular cross-sections. Given an applied torque, shaft geometry, length, and material shear modulus, it returns the maximum shear stress at the outer surface and the total angle of twist. Both solid and hollow shaft profiles are supported.
How it works
- Select shaft type: solid circle or hollow circle (tube).
- Enter the outer diameter (and inner diameter for hollow shafts).
- Input the applied torque, shaft length, and shear modulus of the material.
- The polar moment of inertia J is computed from the geometry.
- Maximum shear stress τ = T · r / J is evaluated at the outer radius.
- Angle of twist φ = T · L / (G · J) gives the rotation in degrees.
Use cases
- Sizing drive shafts in mechanical transmissions.
- Checking whether a propeller shaft meets allowable stress limits.
- Verifying torsion bar spring designs in suspension systems.
- Teaching the torsion formula in undergraduate mechanics of materials courses.
- Comparing solid vs. hollow shaft performance for a given weight budget.
- Quick feasibility checks before running FEA on a shaft assembly.
Frequently Asked Questions
Last updated: 2026-06-11 · Reviewed by Nham Vu