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Oscillations · Mechanics

Simple Pendulum Period Calculator

Calculate a simple pendulum’s period, frequency, length, or local gravitational acceleration using the small-angle approximation.

Formula shown Runs locally Reviewed Aug 11, 2026
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Equation guide

Ideal pendulum under the small-angle approximation

Period

T = 2π√(L/g)

Frequency

f = 1/T

Useful rearrangements

L = g(T/2π)²g = 4π²L/T²
Oscillations

Model an ideal simple pendulum

Preset values are approximate reference gravities; for giant planets they refer to a conventional atmospheric level, not a solid surface. The period formula assumes a point mass, massless rigid string, no damping, and a small angle. Inputs and displayed results use at most three decimal places.

T = 2π√(L/g)

Choose the unknown and enter the required positive quantities.

Using the model

Symbols, assumptions and limitations

Interpretation notes

The model treats the bob as a point mass on a massless, inextensible string with no damping. The period is approximately amplitude-independent only for small release angles; above about 10°, the true period becomes noticeably longer.

Worked examples

See the method in practice

01

One-metre pendulum

At g = 9.80665 m/s², a 1 m pendulum has a period of about 2.006 s and a frequency of about 0.498 Hz.

02

Finding length

A 2 s period near Earth’s surface requires a length of approximately 0.994 m in the small-angle model.

Questions

Frequently asked

Does the bob’s mass affect the period?

Not in the ideal simple-pendulum model; mass cancels from the equation.

Why enter the initial angle?

It checks whether the small-angle approximation is appropriate. The calculator does not use amplitude to correct the period.

Can this measure gravity?

Yes in principle, by rearranging g = 4π²L/T², but real experiments also require careful length and timing measurements.

Sources & review

Equations and examples are checked against the references below. Results are educational and should be independently verified for safety-critical work.

OpenStax University Physics — Pendulums

Written by the STEM Hub editorial team · Reviewed August 11, 2026 · Review methodology