Pendulum Period Calculator — Length, Gravity & Oscillation
A simple pendulum swings back and forth with a period that depends only on its length and gravity — not on its mass, not on its amplitude (for small swings). The free pendulum calculator on PublicSoftTools computes period and frequency instantly, and lets you animate the swing on different planets.
The Pendulum Period Formula
For small oscillation angles (less than about 15°), the period of a simple pendulum is:
T = 2π √(L / g)
Where T is the period in seconds, L is the pendulum length in meters, and g is gravitational acceleration (9.81 m/s² on Earth). Frequency is simply f = 1/T.
Pendulum Period Across Planets
| Body | g (m/s²) | Period of 1 m pendulum | Length for 1 s period |
|---|---|---|---|
| Earth | 9.81 m/s² | 2.007 s | 0.248 m |
| Moon | 1.62 m/s² | 4.94 s | 0.041 m |
| Mars | 3.72 m/s² | 3.26 s | 0.094 m |
| Jupiter | 24.79 m/s² | 1.26 s | 0.624 m |
How to Use the Calculator
- Open the pendulum calculator.
- Enter the pendulum length in meters.
- Select a gravitational preset (Earth, Moon, Mars, Jupiter) or enter a custom g value.
- Read the period T and frequency f from the results panel.
- Click Animate to watch the pendulum swing in real time using the calculated period.
Why Mass Doesn't Matter
The gravitational force on the bob is F = mg, which causes acceleration a = g × sin(θ). Mass cancels out completely — a heavier bob experiences more gravitational force but has proportionally more inertia. The result is that period is entirely independent of mass, a fact Galileo first observed by watching a chandelier swing in the Pisa Cathedral.
Measuring g with a Pendulum
Rearranging the formula: g = 4π²L / T². To measure local gravity with a pendulum:
- Tie a weight to a string of measured length L.
- Count 20 complete swings and divide by 20 to get the period T.
- Calculate g = 4π²L / T².
With a 1-meter pendulum on Earth, you should get T ≈ 2.006 s, giving g ≈ 9.80 m/s² — accurate to within 0.1% of the actual value.
Common Questions
What is the small angle approximation?
The formula T = 2π√(L/g) assumes sin(θ) ≈ θ (in radians), which holds for θ < ~15°. At 20° the error is about 1%; at 45° the error grows to about 7%. For larger amplitudes, the true period is longer than the formula predicts.
Why do grandfather clocks use 1-meter pendulums?
A 1-meter pendulum on Earth has a period of almost exactly 2 seconds — one second per half-swing (tick-tock). This makes it trivial to convert pendulum oscillations to timekeeping. The precise length is 0.9940 m for a 2.000-second period at sea level.
Calculate Pendulum Period
Enter pendulum length and gravity to get period, frequency, and an animated swing.
Open Pendulum Calculator