What is the formula for a simple pendulum period?

T = 2π√(L/g), where L is the string length in meters and g is gravitational acceleration in m/s². This approximation holds for small amplitudes (below ~15°).

Does the mass of the bob affect the period?

No. For an ideal simple pendulum, the period is independent of the bob mass. Only length and gravity determine T.

What value of g should I use?

Earth standard is 9.81 m/s². It varies from about 9.78 m/s² at the equator to 9.83 m/s² at the poles. The Moon is roughly 1.62 m/s² and Mars is about 3.72 m/s².

Why is the small-angle approximation used?

For large angles the true period is longer and requires an elliptic integral. The formula T = 2π√(L/g) is accurate to within 1% for amplitudes up to about 15°, covering most practical pendulum applications.

What is angular frequency?

Angular frequency ω (omega) = 2π/T = 2πf. It expresses how many radians per second the pendulum cycles through and is useful in wave and oscillation equations.

How do I find the length needed for a 1-second half-swing?

A full period of 2 seconds (one swing each way takes 1 second) requires L = g·(T/2π)² = 9.81·(2/6.2832)² ≈ 0.993 m — about 99.3 cm. Enter T-target values by working backwards with the formula.

Simple Pendulum Calculator

Enter pendulum length and gravity to instantly get period, frequency, and angular frequency.

Pendulum Parameters

Pendulum Length

Gravitational Acceleration (m/s²)

Presets:

Results

Enter values and click Calculate

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Summary

A simple pendulum consists of a mass (bob) suspended from a fixed point by a string or rod. For small angles (under ~15°), its motion is approximately simple harmonic, and the period depends only on the string length and local gravity — not the mass. This calculator applies the standard formula T = 2π√(L/g) to give you period, frequency, and angular frequency in one step.

How it works

Enter the pendulum length in meters (or choose a preset unit).
Set the local gravitational acceleration — Earth standard is 9.81 m/s².
Click Calculate (or press Enter) to run the computation.
The tool applies T = 2π√(L/g) for period, f = 1/T for frequency, and ω = 2πf for angular frequency.
Results update instantly; adjust inputs to explore different scenarios.

Use cases

Verify pendulum clock designs for a given target period.
Determine pendulum length needed for a specific frequency.
Explore how gravity differences on other planets affect pendulum motion.
Assist physics students with simple harmonic motion assignments.
Calibrate escape mechanisms in mechanical clockmaking.
Compare pendulum behavior at different elevations where g varies slightly.

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu