Physical Pendulum Period Calculator

About this calculator

Unlike an idealized simple pendulum (a point mass on a massless string), a physical (compound) pendulum is any rigid body that swings about a pivot, so its period depends on how its mass is distributed rather than just its length. For small oscillations, the period is T = 2π·√(I / (m·g·d)), where I is the moment of inertia about the pivot, m is the total mass, g is gravitational acceleration, and d is the distance from the pivot to the center of mass.

This calculator takes the moment of inertia, mass, and pivot distance and returns the swing period directly from that formula. Physics students verifying lab measurements, and engineers designing pendulum clocks, seismometers, or vibration-damping mechanisms use it because real swinging objects — a metal rod, a clock's balance wheel, a swinging door — are physical pendulums, not the idealized point-mass version taught first in introductory mechanics.