Last updated October 5, 2026 · Report an error
A simple pendulum's swing period depends only on its length and the local gravitational acceleration — not on its mass or how far it swings (for small angles).
This calculator finds the period of a simple pendulum, with a choice of Earth, Moon, Mars, or custom gravity.
How it works
Enter the pendulum's length and choose a gravity value. The calculator applies the simple pendulum period formula \(T = 2\pi\sqrt{L/g}\) to find the period, and also reports the frequency (swings per second).
- Enter pendulum length (m).
- Enter gravity.
- Enter custom gravity (m/s², if selected above).
- Click Calculate to see your results.
Examples
1 meter pendulum on Earth
A 1-meter pendulum on Earth has a period of about 2.01 seconds — meaning one full back-and-forth swing takes just over 2 seconds.
Who should use it
- Checking physics coursework involving simple harmonic motion and pendulums.
- Comparing how a pendulum's period would change on other planets or moons.
Industry applications
- Physics education
- Horology (pendulum clocks historically used this exact relationship for timekeeping)
Advantages
- Includes Moon and Mars gravity presets alongside Earth and a custom option.
- Reports both period and frequency in one calculation.
Limitations
- Assumes small swing angles — large-angle pendulums have a slightly longer true period than this formula predicts.
Common mistakes to avoid
- Assuming a heavier pendulum bob swings faster or slower — mass doesn't affect the period at all.
- Using this formula for large swing angles, where the small-angle assumption starts to break down.
Best practices
- For real-world timing experiments, keep swing angles small (under about 15°) to stay within this formula's valid approximation range.
Tips
- Historically, pendulum clocks used this exact formula — adjusting the pendulum's length was the standard way to fine-tune a clock's accuracy.
Frequently asked questions
Yes, with no signup and no limit on how many calculations you run.
No — for an ideal simple pendulum, the period depends only on length and gravity, not on the mass of the bob at the end.
It's a classic physics thought experiment — since gravity is weaker on the Moon and Mars, the same pendulum swings slower (has a longer period) there than on Earth.
This formula assumes small swing angles (a common simplifying assumption) — for very large swing angles, the true period is slightly longer than this formula predicts.