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Mihsaba›Simple Pendulum Calculator

Simple Pendulum Calculator

Calculate a simple pendulum’s period and frequency from length and gravitational acceleration using the small-angle approximation.

These are idealized models: collision assumes sticking, free fall ignores air drag, and the pendulum uses the small-angle approximation.

How to use

Under the small-angle approximation, a simple pendulum follows T=2π√(L/g), so period depends on length and gravity but not bob mass in this model.

  1. Enter pendulum length from pivot to bob center of mass.
  2. Enter g.
  3. Review period and frequency.

How it is calculated

T=2π√(L/g); f=1/T

Example

Example: a 1 m pendulum at g=9.80665 m/s² has a period of about 2.006 s.

Important notes

The small-angle approximation is most accurate at small amplitudes; large angles slightly lengthen the period and require a more exact model.

Frequently asked questions

Does bob mass change period?

Not in the ideal simple-pendulum model.

How does length affect period?

T scales with √L.

What if gravity decreases?

The period increases as 1/√g.