Pendulum Period Calculator
How long does one swing of a pendulum take?
Your numbers
Your results
Period, small angle (s)
Period, small angle (s)
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Period with amplitude correction (s)
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Frequency (Hz)
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Pendulum Period Calculator by TheCalcTools
How the Pendulum Period Calculator works
Enter the pendulum length from the pivot to the centre of the bob, gravity and the swing amplitude.
For small swings the period depends only on length and gravity, not on mass.
A series correction accounts for larger amplitudes.
The formula
T = 2π√(L ÷ g)T ≈ T₀(1 + θ² ÷ 16 + 11θ⁴ ÷ 3072), θ in radians
Worked example
Using the default values shown in the calculator:
| Length (m) | 1 |
|---|---|
| Gravity (m/s²) | 9.80665 |
| Amplitude (°) | 10 |
- T = 2π × √(1 ÷ 9.80665) = 2.0064 s.
- The frequency is 0.4984 Hz.
- A 10° swing adds a tiny correction: 2.0102 s.
Result:
| Period, small angle (s) | 2.0064 |
|---|---|
| Period with amplitude correction (s) | 2.0102 |
| Frequency (Hz) | 0.4984 |
Frequently asked questions
Does the mass of the bob matter?
No. Mass cancels out, so a heavy and a light bob of the same length swing at the same rate (for small angles).
How long is a seconds pendulum?
One that takes two seconds for a full period (one second per swing) is about 0.994 m long.
Sources and further reading
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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.