Free · Rotational and periodic motion calculators 🌎

Torque, Angular Deflection & Rotational Stiffness

Find rotational stiffness from positive torque and angular deflection in radians, including per-turn stiffness units.

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Calculator inputs

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How to use this calculator

  1. Enter the known values in the units shown. Results update as you type.
  2. Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
  3. Use the worked example to check the method. Reset restores the starting fields.

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Inputs and results stay in this browser tab. Bookify does not upload or store the values you enter.

Formula and method

A torque of 10 N·m causing 0.1 rad of angular deflection corresponds to rotational stiffness of 100 N·m/rad.

Rotational stiffness = torque / angular deflection in radians

Worked example

Enter these known values and leave the other values blank.

Applied torque magnitude
10 N·m
Angular deflection in radians
0.1 rad
Rotational stiffness
100 N·m/rad

Assumptions and limitations

  • Torque, deflection and stiffness are positive. Enter the angular deflection in radians; changing the stiffness unit does not change the angle input convention.
  • The ratio is a secant stiffness at the entered operating point. A single constant stiffness predicts other points only when the torque-deflection relationship is suitably linear.
  • One turn is exactly 2π radians. The same physical stiffness has a numerical value 2π times larger in torque per turn than in torque per radian.

Common questions

Can I enter degrees in the angle box?

Convert degrees to radians first by multiplying by π/180. The angle box is explicitly in radians.

Does this determine the shaft diameter?

No. Shaft geometry, material shear modulus, length and boundary conditions require a separate torsion model.

References

Kilogram-force centimeters use standard gravity and exactly one centimeter. Pound-force feet use the exact international pound and foot with standard gravity. Pound-force inches use the exact international pound and inch with standard gravity. Rotational stiffness uses exactly two pi radians per turn and exact pound-force feet.

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