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Compound (Physical) Pendulum Period Calculator

T = 2π · √(I / (m · g · d)).

Compute the small-amplitude oscillation period of a compound (physical) pendulum: a rigid body that rotates about a horizontal pivot offset from its centre of mass. T = 2π · √(I / (m·g·d)), where I is the moment of inertia about the pivot, m is the body mass, g is gravity, and d is the distance from pivot to centre of mass.

Dr. Helena Ortiz By Dr. Helena Ortiz
Published Last reviewed 1 min read

Inputs

kg·m²
kg
m
m/s²

Results

Enter values and click Calculate to see results.
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How to use this calculator

  1. Fill in the inputs above using the units you already have.
  2. Values update automatically as you type — no submit button needed.
  3. Hover any result row for the underlying formula and intermediate values.

Formula

T = 2π · √(I / (m · g · d)).

In depth

Compute the small-amplitude oscillation period of a compound (physical) pendulum: a rigid body that rotates about a horizontal pivot offset from its centre of mass. T = 2π · √(I / (m·g·d)), where I is the moment of inertia about the pivot, m is the body mass, g is gravity, and d is the distance from pivot to centre of mass.