# Rotational Stiffness Calculator

URL: https://speedycalculator.com/calculators/physics/rotational-stiffness/
Last updated: 2026-10-30

> The rotational stiffness calculator finds the stiffness of a joint, spring or support from the applied moment and the rotation it produces.

## Inputs

- Applied moment (N·m, kN·m, lbf·ft, lbf·in, kgf·m)
- Rotation angle θ (rad, °, mrad)

## Results

- Rotational stiffness k
- Per degree

## Formula

```
k = M / θ
```

## Explanation

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

FieldWhat to enterApplied momentUnits: N·m, kN·m, lbf·ft, lbf·in, kgf·mRotation angle θUnits: 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)501,000751,5001002,0001252,5001503,0002004,000

## 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.

## FAQ

**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.


## Sources

- [OpenStax – University Physics Volume 1](https://openstax.org/details/books/university-physics-volume-1)
- [HyperPhysics (Georgia State University)](http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html)