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Shaft Torsion
Compute torsional stress and twist angle from torque and shaft size.
Calculator tabs
Inputs
Enter torque, shaft geometry, and the material property.
Results
Stress, polar moment, and elastic twist for a solid circular shaft.
Maximum shear stress τ
47.16 MPa
Twist angle θ (degrees)
1.801 deg
Safety factor based on shear stress
-
How it is calculated
Formulas used
tau = 16T / (pi * d^3)
theta = T * L / (J * G)
J = pi * d^4 / 32
Variables
- T
- Applied torque (N·mm).
- d
- Solid circular shaft diameter (mm).
- L
- Shaft length (mm).
- G
- Shear modulus (MPa).
- J
- Polar moment of area (mm⁴).
- τ
- Maximum shear stress (MPa).
- θ
- Elastic twist angle (radians).
Usage notes
- The section is treated as a uniform solid circular shaft.
- Linear-elastic material behavior and a small twist angle are assumed.
- The safety factor is shown only when allowable shear stress is greater than zero.
Show reports, charts, and comparison tools
After checking the basic result, open sharing, PDF, method notes, and comparison panels.
Tool-Specific Documentation
Shaft TorsionScope: What does this tool calculate?
Calculates torsional shear stress, polar moment, and twist angle for a circular homogeneous shaft from torque, diameter, length, and shear modulus.
Assumptions and Units
- Enter torque in N·m, diameter and length in mm, shear modulus in GPa, and optional allowable shear stress in MPa.
- The model assumes a solid circular section and elastic behavior; it uses τ=16T/(πd³) and θ=TL/(JG).
- Twist is converted to degrees; when an allowable stress is supplied, a simple stress ratio is shown.
Limits / Boundaries
- Notches, keyways, bending, combined loading, plastic behavior, and fatigue are outside this baseline torsion model.
- Verify shaft sizing against the real load spectrum, connection details, material data, and project safety criteria.
Applicable References
- Shigley, Mechanical Engineering Design (engineering reference for torsion and shaft design)
- Verification against project material data and applicable design requirements
Validation Example
Solid circular shaft check
| Input | Expected Output |
|---|---|
| T=250 N·m, d=30 mm, L=800 mm, G=80 GPa | τ≈47.16 MPa; θ≈1.801° |
Note: Evaluate the actual geometry, connection discontinuities, and combined loads separately.
Version and Update
- Version
- v1.0.0
- Last updated
- 2026-02-07
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