Pendulum Period Calculator
By Santaji GadepatilinUpdated October 27, 2026
calculated
Hz
calculatedType in any field to change it. Press × on a value to calculate that field instead.
Period (one full swing) (s) vs Pendulum length (m) — other inputs held at your current values.
How to use this calculator
Enter the length (pivot to the centre of the bob) to get the period and frequency. Or enter a period to find the length needed.
The formula
T = 2π √(L ÷ g)
Worked example
A 1 m pendulum:
T = 2π √(1 ÷ 9.81) = 2.006 s, frequency 0.498 Hz
Period vs length
| Length | Period |
|---|---|
| 0.25 m | 1.00 s |
| 0.5 m | 1.42 s |
| 1 m | 2.01 s |
| 2 m | 2.84 s |
| 4 m | 4.01 s |
Four times the length doubles the period. This is why grandfather clocks are tall — a ~1 m pendulum ticks once per second.
Frequently asked questions
What is the formula for a pendulum's period?
T = 2π √(L/g), where L is the length to the centre of the bob and g is gravity. It does not depend on mass.
How long is a seconds pendulum?
About 0.994 m. Its full period is 2 s, so each swing in one direction takes 1 second.
Does the swing size matter?
For small angles (under about 15°) hardly at all. Larger swings take slightly longer.