Pendulum Period Calculator
Pendulum period calculator: period of a simple pendulum from its length and gravity, or the length for a given period — on Earth, the Moon or anywhere.
T = 2π √Lg
How to use this calculator
- Choose the quantity you want under “Solve for”.
- Type the known values and pick their units: any combination works.
- The result updates as you type. Open “Show the steps” to see the substitution.
T = 2π√(L/g) holds for small swings (under about 15°). The period does not depend on the mass or, for small angles, on the amplitude.
Formula
T = 2π √Lg
| Symbol | Quantity | Units |
|---|---|---|
| L | Length | m, km, cm, mm, µm, nm, pm, Å, in, ft, yd, mi, nmi, au, ly |
| g | Gravitational acceleration | m/s², ft/s², g, Gal |
| T | Period | s, ms, µs, ns, min, h, d, wk, yr |
Constants used: Small angles (< 15°); g = 9.80665 m/s² on Earth, 1.62 on the Moon
Worked example
Given: L = 1 m · g = 9.80665 m/s²
T = 2π √Lg
Result: T = 2.00641 s
Period for different values of Length
| L · Length | T · Period |
|---|---|
| 0.5 m | 1.4187 s |
| 0.75 m | 1.7376 s |
| 0.9 m | 1.9034 s |
| 1 m | 2.0064 s |
| 1.1 m | 2.1043 s |
| 1.25 m | 2.2432 s |
| 1.5 m | 2.4573 s |
| 2 m | 2.8375 s |
Other values as in the worked example.
Frequently asked questions
Period of a 1 m pendulum on Earth?
About 2.006 s.
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