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
| Field | What to enter |
|---|---|
| Length L | Units: m, cm, mm, km, in, ft … |
| Gravitational acceleration g | Units: m/s², ft/s², g, cm/s² |
| Mass m | Units: kg, g, mg, t, lb, oz |
| Release height h | Units: 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) |
|---|---|
| 0.5 | 0.4903 |
| 0.75 | 0.4903 |
| 1 | 0.4903 |
| 1.25 | 0.4903 |
| 1.5 | 0.4903 |
| 2 | 0.4903 |
Formula
T = 2π√(L/g), KE_max = m·g·h, v_max = √(2gh)
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.
Frequently asked questions
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.