Pendulum Calculator
Calculate pendulum instantly in your browser — the published formula, worked locally with no data sent anywhere.
Loading calculator…
What this tool does
Calculate pendulum instantly in your browser — the published formula, worked locally with no data sent anywhere. Simple pendulum: a point mass on a massless string, small swings (the formula is within 1% up to about 23° of swing amplitude). Period does not depend on the bob's mass or — for small angles — the amplitude; that is why pendulums keep time.
How to use the Pendulum Calculator
- Enter or select pendulum length (pivot to bob centre) in ft.
- Read the calculated result; change any measurement to compare alternatives.
Formula
period T = 2π × √(L/g), with g = 32.174 ft/s² for the foot-based length; frequency f = 1/T.
- length
- Pendulum length (pivot to bob centre) (ft, before metric conversion)
Simple pendulum: a point mass on a massless string, small swings (the formula is within 1% up to about 23° of swing amplitude). Period does not depend on the bob's mass or — for small angles — the amplitude; that is why pendulums keep time.
Worked example
For pendulum calculator, the following measurements illustrate the exact method: Pendulum length (pivot to bob centre): 2.
Inputs
- Pendulum length (pivot to bob centre)2 ft
Result
- Period (s)1.57
- Frequency (Hz)0.64
- Swings per minute38.3
- Length (m)0.61
Results explained
- Period (s)
- Period (s) from the formula above. Simple pendulum: a point mass on a massless string, small swings (the formula is within 1% up to about 23° of swing amplitude). Period does not depend on the bob's mass or — for small angles — the amplitude; that is why pendulums keep time.
- Frequency (Hz)
- Frequency (Hz) from the formula above. Simple pendulum: a point mass on a massless string, small swings (the formula is within 1% up to about 23° of swing amplitude). Period does not depend on the bob's mass or — for small angles — the amplitude; that is why pendulums keep time.
- Swings per minute
- Swings per minute from the formula above. Simple pendulum: a point mass on a massless string, small swings (the formula is within 1% up to about 23° of swing amplitude). Period does not depend on the bob's mass or — for small angles — the amplitude; that is why pendulums keep time.
- Length (m)
- Length (m) from the formula above. Simple pendulum: a point mass on a massless string, small swings (the formula is within 1% up to about 23° of swing amplitude). Period does not depend on the bob's mass or — for small angles — the amplitude; that is why pendulums keep time.
Frequently asked questions
period T = 2π × √(L/g), with g = 32.174 ft/s² for the foot-based length; frequency f = 1/T.
Simple pendulum: a point mass on a massless string, small swings (the formula is within 1% up to about 23° of swing amplitude). Period does not depend on the bob's mass or — for small angles — the amplitude; that is why pendulums keep time.
Every field is labelled with its unit — enter values in exactly the labelled unit and read the result in the labelled output unit. Fields with a unit symbol also support the site-wide imperial/metric switch, which converts before the formula runs.
It uses double-precision arithmetic and the published constants and formulas named on this page. The last displayed digit may be rounded, and real conditions can differ from the idealized model described in the assumptions.
Yes. Every calculation runs entirely in your browser; nothing you enter is uploaded, stored or shared.