About the Pendulum Period Calculator
A pendulum takes the same time for each swing no matter how wide the swing is, as long as it is small. That time, called the period, depends only on the length of the pendulum and on gravity. This calculator gives the period for the length you enter, with a small correction for bigger swings, plus the frequency and the number of swings per minute. Type the length of the pendulum, the swing angle and the gravity and the pendulum period appears at once, with a few related figures underneath, and you can copy the result with one tap. The sums run in your browser, so nothing you enter is uploaded.
Updated October 2026
How to use the Pendulum Period Calculator
- 1Enter the length of the pendulum, the swing angle and the gravity.
- 2Pick the units or options from the menus if the pendulum period tool offers them.
- 3Read the pendulum period in the large result box.
- 4Look at the extra rows for related figures.
- 5Press Copy result to keep the answer.
When you need the pendulum period
Clockmakers use the formula to set the length of a pendulum so that a clock ticks at exactly one second per swing. Teachers use it in experiments to measure gravity, and hobbyists use it to build metronomes and swings.
Because the period depends on the square root of the length, to make a pendulum swing twice as slowly you need four times the length. On the Moon the same pendulum is about 2.5 times slower than on Earth.
How the pendulum period is worked out
For small swings, period = 2π × √(length ÷ g). For larger swings the period is multiplied by about 1 + θ²/16 + 11θ⁴/3072, with θ in radians. A 1 m pendulum on Earth has a period of 2.006 s for small swings, so it makes about 30 swings a minute. Swinging 10° from the vertical stretches the period very slightly to 2.010 s. A 0.25 m pendulum swings twice as fast, with a period of 1.003 s.
Every answer on this page comes from that one rule, so you can check any result by hand with a calculator. The figures shown underneath, such as other units, are conversions of the same answer.
- Length in m or ft
- Swing angle correction
- Five gravities
Mistakes to avoid with pendulum period
Length means the distance from the pivot to the centre of the weight, not to the bottom of it. The formula also assumes a small bob on a light string. A rod or a bob that is large compared with the length changes the answer.
On phone and computer
On a phone, type into the boxes one after another and read the pendulum period underneath; Copy result puts it on the clipboard for a message or a note. On a computer the inputs sit on the left and the answer on the right, so you can change one figure and watch the pendulum period move. The pendulum period calculator works the same on both. The frequency is the reciprocal of the period, so use Frequency Converter to move between hertz and seconds. Free Fall Calculator and Weight on Other Planets Calculator show how gravity changes things, and Unit Converter handles length.
Features
- Length is pivot to the centre of the bob
- Four times the length, twice the period
- Small swings are isochronous
- Clear messages when the pendulum period inputs make no sense
- Copy the result with one tap
- Private: nothing is uploaded
Frequently asked questions
How do I calculate pendulum period?
For small swings, period = 2π × √(length ÷ g). For larger swings the period is multiplied by about 1 + θ²/16 + 11θ⁴/3072, with θ in radians. A 1 m pendulum on Earth has a period of 2.006 s for small swings, so it makes about 30 swings a minute. Swinging 10° from the vertical stretches the period very slightly to 2.010 s. A 0.25 m pendulum swings twice as fast, with a period of 1.003 s.
What is the formula for pendulum period?
For small swings, period = 2π × √(length ÷ g). For larger swings the period is multiplied by about 1 + θ²/16 + 11θ⁴/3072, with θ in radians. The pendulum period calculator applies it exactly and rounds only the displayed answer to six significant figures.
Does the mass of the bob matter?
No. A heavy and a light bob on the same length swing with the same period.
What length gives a one second swing?
About 0.248 m for a swing of one second, which is a half period; a two-second period needs 0.994 m.
Why add a correction for the swing angle?
Wide swings take slightly longer than the simple formula says. The correction matters above about 10 degrees.
Is this pendulum period calculator free and private?
Yes. It is free, needs no account and runs in your browser, so the numbers you type are not uploaded or stored.