By Zencalcy Editorial TeamLast reviewed About us
A simple pendulum's period depends on its length and on gravity, not on the mass of the bob. For swings under about 15°, the period is 2π√(L/g): quadrupling the length doubles the period.
Period from length, or length from period.
T = 2π √(L / g)
T is the period in seconds, L the length from pivot to the bob's centre in metres and g standard gravity. The small-angle approximation is accurate to about 0.2% at 15°.
| Symbol | Meaning |
|---|---|
| T | Period of one full swing, in seconds. |
| L | Pendulum length, in metres. |
| g | Standard gravity, 9.80665 m/s². |
T = 2π√(1 / 9.80665) = 2.006 s. A clock pendulum with a one-second half-swing (two-second period) is about 0.994 m long.
Continue with the Spring Period Calculator, Angular Acceleration Calculator, or the Angular Momentum Calculator — or browse more rotational and periodic motion tools and all physics calculators.
The restoring force is proportional to mass, and so is the inertia being accelerated. The mass cancels out, leaving only length and gravity.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
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Content updated: September 2026