Simple Pendulum Calculator
Use our simple pendulum calculator to calculate pendulum period (sec) and frequency (Hz) from pendulum length (ft) and gravity (g). Includes the simple pendulum formula, equation, and an explanation of how a simple pendulum works in physics.
What Is a Simple Pendulum?
A simple pendulum is an idealized pendulum model: a point mass (bob) attached to a massless string or rod, swinging back and forth under gravity with no friction.
In simple pendulum physics, the period mainly depends on the pendulum length and the acceleration due to gravity. For small swing angles, the motion is well-approximated by simple harmonic motion.
This calculator uses gravity (g) and pendulum length (L) to return the pendulum period (T) and frequency (f).
Simple Pendulum Formula
For small angles, the period of a simple pendulum is given by a square-root relationship between length and gravity.
Valid for small angles. Use consistent units for L and g.
Frequency is the number of cycles per second (Hz).
Longer length increases period; larger gravity decreases period.
How to Calculate a Simple Pendulum
- 1
Enter acceleration of gravity (g).
- 2
Enter pendulum length (L) in feet.
- 3
The calculator applies T = 2π√(L/g).
- 4
It calculates frequency as f = 1/T.
Frequently Asked Questions
Gravity pulls the bob toward the lowest point, converting potential energy to kinetic energy and back. For small angles, the restoring force leads to repeating motion with a predictable period.
For small angles, the period equation is T = 2π√(L/g).
In the ideal small-angle model, period depends on length L and gravity g. Mass does not affect the period in the ideal model.
A simple pendulum assumes a point mass on a massless string. A physical pendulum accounts for an extended body’s mass distribution and moment of inertia.
Yes. If you know period and gravity, you can rearrange: L = g × (T/(2π))^2.