Rotational (moment) stiffness describes how much torque is needed per radian of rotation. Engineers use it for beam supports, bolted joints, couplings and torsion springs: a stiffer connection rotates less under the same moment.
How to use the Rotational Stiffness Calculator
- Applied moment
- Rotation angle θ
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Enter the applied moment and the measured rotation angle.
Inputs explained
| Field | What to enter |
|---|---|
| Applied moment | Units: N·m, kN·m, lbf·ft, lbf·in, kgf·m |
| Rotation angle θ | Units: rad, °, mrad |
What each result means
- Rotational stiffness k = [Applied moment]÷[Rotation angle θ]
- Per degree = [Applied moment]÷deg([Rotation angle θ])
Example values
How the main result changes when Applied moment changes and everything else stays at the example values above:
| Applied moment (N·m) | Rotational stiffness k (N·m/rad) |
|---|---|
| 50 | 1,000 |
| 75 | 1,500 |
| 100 | 2,000 |
| 125 | 2,500 |
| 150 | 3,000 |
| 200 | 4,000 |
Formula
k = M / θ
Worked example
Inputs — Applied moment: 100 N·m; Rotation angle θ: 0.05 rad.
Results — Rotational stiffness k = 2,000 N·m/rad; Per degree = 34.90659 N·m/°.
Key terms
- Rotational stiffness
- Moment per unit rotation.
Frequently asked questions
What is a pinned support?
One with zero rotational stiffness.
What is a fixed support?
One with (ideally) infinite rotational stiffness.
How is it related to torsional stiffness?
For shafts, k = G·J/L.
What units are used?
N·m/rad.