Pendulum Calculator
Fill in the length or the period of a pendulum, and leave the other blank.
This result is an estimate only. Double-check important figures before relying on them.
How it is calculated
- Period = 2π × √(length ÷ g)
- Length = g × period² ÷ (4π²)
- Frequency = 1 ÷ period
For the energy of a swinging mass, see the potential energy calculator.
Worked example
A pendulum 1 m long:
- T = 2π × √(1 ÷ 9.80665) = 2.0064 s
Why your number may differ
The formula is for small angles, below about 15°. A wide swing takes slightly longer, and a heavy rod or string adds error.
Frequently asked questions
What is the formula for a pendulum?
T = 2π × √(L ÷ g), where T is the time of one full swing, L the length and g the gravity.
Does the mass matter?
No. The period of a simple pendulum depends only on its length and gravity, not on the weight of the bob.
How long is a pendulum with a 2 second period?
About 0.994 m, which is why it is called the seconds pendulum, a half swing taking one second.