🕰️ Simple Pendulum Calculator
Enter the pendulum length (and pick a gravity) to get its period and frequency.
Period (one full swing)
2.01 s
Frequency
0.498 Hz
A simple pendulum\'s period is T = 2π·√(L/g) — it depends only on the length and gravity, not on the mass of the bob or (for small swings) the amplitude. To double the period you need four times the length. This small-angle formula is accurate to about 1% for swings under ~20°. 🔒 In your browser.
How the simple pendulum calculator works
A simple pendulum swings with a period T = 2π·√(L/g), where L is the length from the pivot to the centre of the bob and g is the local gravitational acceleration. Remarkably, the period doesn't depend on the mass of the bob or, for small swings, on how far it swings — only on length and gravity. The tool returns the period (time for one complete back-and-forth) and the frequency (swings per second), and lets you switch gravity to the Moon, Mars or Jupiter.
This is the small-angle approximation, accurate to about 1% for swings under roughly 20°; larger amplitudes swing slightly slower. Because the period grows with the square root of length, you need four times the length to double the period — which is how a grandfather clock's ~1 m pendulum keeps a 2-second beat.
Frequently asked questions
How do you calculate the period of a pendulum?
T = 2π·√(L/g), with L the length in metres and g ≈ 9.81 m/s². A 1-metre pendulum on Earth has a period of about 2.0 seconds. Longer pendulums swing more slowly.
Does a pendulum's period depend on mass?
No. The period depends only on length and gravity, not on the mass of the bob — a heavy and a light pendulum of the same length keep the same time. This is a classic and slightly surprising result.
Does amplitude affect the period?
For small swings, barely — the simple formula assumes it doesn't. For larger amplitudes the period increases a little (about 1% by 20°, more beyond), because the restoring force is no longer perfectly proportional to displacement.
How long is a pendulum with a 1-second swing?
A pendulum with a 1-second period is about 0.25 m long on Earth; a "seconds pendulum" that ticks each second (a 2-second full period) is about 0.994 m. Length scales with the square of the period.
How does gravity change the period?
Weaker gravity means a longer period. On the Moon (g ≈ 1.62) a pendulum swings much more slowly than on Earth, and on Jupiter (g ≈ 24.8) much faster. Switch the gravity setting to compare.