# Kinetic Energy of a Pendulum Calculator

URL: https://speedycalculator.com/calculators/physics/pendulum-kinectic-energy/
Last updated: 2026-10-30

> The pendulum kinetic energy calculator finds a simple pendulum's period and frequency from its length, and its maximum kinetic energy and speed at the bottom from the mass and release height.

## Inputs

- Length L (m, cm, mm, km, in, ft, yd, mi)
- Gravitational acceleration g (m/s², ft/s², g, cm/s²)
- Mass m (kg, g, mg, t, lb, oz)
- Release height h (m, cm, mm, km, in, ft, yd, mi)

## Results

- Period T
- Frequency f
- Maximum kinetic energy
- Maximum speed
- Release angle

## Formula

```
T = 2π√(L/g),  KE_max = m·g·h,  v_max = √(2gh)
```

## Explanation

As a pendulum swings, its energy changes from potential at the highest points to kinetic at the bottom. The release height sets the energy available; the length sets the period.

### How to use the Kinetic Energy of a Pendulum Calculator

- **Length L**
- **Gravitational acceleration g**
- **Mass m**
- **Release height h**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Enter the length, gravity, the bob's mass and the height of release above the lowest point (which must be less than twice the length).

### Inputs explained

FieldWhat to enterLength LUnits: m, cm, mm, km, in, ft …Gravitational acceleration gUnits: m/s², ft/s², g, cm/s²Mass mUnits: kg, g, mg, t, lb, ozRelease height hUnits: m, cm, mm, km, in, ft …

### What each result means

- **Period T** = 2×pi×sqrt([Length L]÷[Gravitational acceleration g])
- **Frequency f** = 1÷[Period T]
- **Maximum kinetic energy** = [Mass m]×[Gravitational acceleration g]×[Release height h]
- **Maximum speed** = sqrt(2×[Gravitational acceleration g]×[Release height h])
- **Release angle** = deg(acos(1 - [Release height h]÷[Length L]))

### Example values

How the main result changes when **Length L** changes and everything else stays at the example values above:

Length L (m)Maximum kinetic energy (J)0.50.49030.750.490310.49031.250.49031.50.490320.4903

## Worked example

Inputs — Length L: 1 m; Gravitational acceleration g: 9.80665 m/s²; Mass m: 0.5 kg; Release height h: 0.1 m.

Results — Period T = 2.00641 s; Frequency f = 0.4984 Hz; **Maximum kinetic energy = 0.49033 J**; Maximum speed = 1.40047 m/s; Release angle = 25.842 °.

## Key terms

- **Simple pendulum**: A point mass on a light string.

## FAQ

**Where is a pendulum fastest?**
At the bottom of its swing.

**Does the mass change the period?**
No – only the length and gravity.

**How is the release angle related to height?**
h = L(1 − cos θ).

**Is the period formula exact?**
Only for small angles; large swings are slightly slower.


## 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)