Pendulum Period Calculator (Small and Large Angles)
A pendulum’s period is the time for one full swing there and back. For small swings it depends only on length and gravity; for big swings it gets longer, and this calculator gives the exact value.
Standards:
- AP1 Unit 7
- IB C.1
- CCSS HSA-CED.A.4
Our alignment; not reviewed by the standards bodies.
The equation
Worked example
- Given
- Length L (m): 1 m
- Amplitude θ₀ (°, below 180): 60 °
- Answer
- Small-angle period T₀: 2.0064 s
- Exact period T: 2.1532 s
- Longer than small-angle by: 7.32 %
- Check
- A 1 m pendulum has T₀ = 2.006 s, and at 60° the exact period is 1.0732 times longer, matching elliptic-integral tables; the build checks both.
Assumptions
Simple pendulum: point mass, light rigid string, no friction, standard gravity 9.80665 m/s².
Go deeper
Sources
- D. Halliday, R. Resnick, J. Walker, Fundamentals of Physics, 12th ed., Wiley, 2021.
- J. R. Taylor, Classical Mechanics, University Science Books, 2005.