Pendulum Period Calculator

Compute a simple pendulum period T=2π√(L/g) from length and gravity, plus frequency, angular frequency, and a large-amplitude correction.

Input

Enter the string length and gravity to calculate a simple pendulum period.

String length L

Length of the string holding the bob, in meters

Gravitational acceleration g

m/s²

Default is standard gravity 9.80665 m/s². Adjust it by location.

Amplitude angle θ0

deg

Maximum swing angle in degrees, used for the large-amplitude correction.

Period T

2.006409s

Frequency f

0.498403 Hz

Angular frequency ω

3.131557 rad/s

Period with large-amplitude correction

2.021689 s

Period increase

0.761544 percent

The period is T=2π√(L/g) in the small-amplitude limit. For larger swings a factor of about 1+θ0²/16 is applied.

The period is T=2π√(L/g), where L is the string length and g is gravitational acceleration.
This formula holds in the small-amplitude approximation, where the swing angle is small.
Frequency is f=1/T and angular frequency is ω=2π/T.
For larger swings the period grows, so a first-order correction of about 1+θ0²/16 is shown for amplitude angle θ0.
The default gravity is standard gravity 9.80665 m/s². It varies by location, so adjust it if needed.

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