By Zencalcy Editorial TeamLast reviewed About us
A real pendulum is an extended body, not a point mass on a string. Its period depends on the moment of inertia about the pivot, its mass and the distance from the pivot to its centre of mass, which makes it longer than a simple pendulum of the same pivot distance.
Period of a real rigid body swinging about a pivot.
T = 2π √(I / (m g d))
I is the moment of inertia about the pivot, m the mass, g standard gravity and d the pivot-to-centre-of-mass distance. The small-angle approximation applies.
| Symbol | Meaning |
|---|---|
| T | Period, in seconds. |
| I | Moment of inertia about the pivot, in kg·m². |
| m | Mass, in kilograms. |
| d | Pivot to centre-of-mass distance, in metres. |
T = 2π√(0.5 / (1 × 9.80665 × 0.25)) = 2.838 s. A simple pendulum 0.25 m long would take only 1.003 s, because all its mass sits at the bob.
Continue with the Rolling Kinetic Energy Calculator, Rolling Motion Calculator, or the Rotational Kinetic Energy Calculator — or browse more rotational and periodic motion tools and all physics calculators.
When the bob is small compared with the string. If the body is large — a rod, a door, a swinging sign — use the physical pendulum form.
Results are computed from the standard equations of classical mechanics. Unit conversions use the SI definitions published by NIST. Air resistance is ignored unless the calculator names a drag model.
Reference material used to build and check this calculator:
Last reviewed: September 2026. See how we build and check every tool on the about page.
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Free calculator · No signup
Content updated: September 2026