Free · Physics models
Shaft Torsional Stiffness
Compare stiffness from measured torque and twist with the ideal uniform-shaft modulus estimate.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
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Formula and method
2 N·m over 0.5 rad gives 4 N·m/rad. A shaft with G = 1 GPa, J = 10⁻⁸ m⁴ and L = 2 m gives 5 N·m/rad.
k = T/θ; kshaft = GJ/L.
Worked example
Enter these known values and leave the other values blank.
- Internal torque (T)
- 2 N·m
- Angle of twist (ϕ)
- .5 rad
- Shear modulus (G)
- 1 GPa
- Polar moment of inertia (J)
- .00000001 m⁴
- Beam length (L)
- 2 m
- Torsional stiffness (k)
- 4 N·m/rad
- Torsional stiffness (k)
- 5 N·m/rad
Assumptions and limitations
- The two stiffness estimates are separate comparisons and need not match.
- The uniform-shaft estimate assumes linear elasticity, a compatible polar moment and a suitable cross section.
- Signed torque and angle must have the same sign and neither can be zero.
- Enter known quantities and clear the unknown to use available inverse branches. Locks retain supplied values. Consistency messages cover fully visible equations; identities with hidden dependencies may require a manual consistency check. Preset values are illustrative approximations, and unit selectors preserve the underlying quantity.
Common questions
How do I solve for a different quantity?
Clear that quantity and supply enough independent known values. Some outputs are one-way or tied to a selected preset, so they cannot determine every input.
References
The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.