Find a simple pendulum's period, length or gravity from T = 2π√(L/g), with frequency and gravity presets.
About this tool
Simple Pendulum Period Calculator is a free, in-browser tool for the swinging motion of a simple pendulum. Choose whether to solve for the period, the length or the local gravity, enter the other two quantities, and read the result along with the frequency and angular frequency. All calculations happen locally in your browser.
It is built on the small-angle formula T = 2π√(L/g). Rearranged, the length is L = g·(T/2π)² and gravity is g = L·(2π/T)². Frequency is f = 1/T and angular frequency is ω = 2π/T = √(g/L). Built-in gravity presets cover Earth (9.81), the Moon (1.62) and Mars (3.71) m/s².
Because the simple formula assumes a small swing, an optional amplitude field applies the first-order large-angle correction T ≈ T₀(1 + θ²/16), with the angle θ converted from degrees to radians. Enter the length in metres, gravity in m/s² and the period in seconds.
Frequently asked questions
What is the period formula?
For small swings the period of a simple pendulum is T = 2π√(L/g), where L is the length and g is gravitational acceleration. Notice the mass does not appear — a heavier bob does not change the period.
Why does the period not depend on mass or amplitude?
In the ideal small-angle model the restoring force scales with mass exactly like inertia does, so mass cancels out, and the motion is simple harmonic with an amplitude-independent period. For larger swings the amplitude correction below adds a small dependence.
What does the amplitude correction do?
The simple formula is only exact for tiny swings. Entering an amplitude applies the first-order correction T ≈ T₀(1 + θ²/16), with θ in radians, which lengthens the period slightly for wide swings.
Can I use it for other planets?
Yes. Pick a gravity preset (Earth, Moon, Mars) or type any value of g, and the period, frequency and angular frequency update instantly. Everything is computed in your browser and nothing is uploaded.