Simple Pendulum Period Calculator

For small swing angles, a simple pendulum's period is T = 2π√(L/g), where L is the length from the pivot to the bob's center of mass and g is the local gravitational acceleration. Pick which quantity to solve for; the calculator rearranges the same formula to find it from the other two — L = g(T/2π)² when solving for length, or g = L(2π/T)² when solving for gravity.

Length and gravitational acceleration only need to share the same length unit (both in meters, or both in feet) for the formula to work — L/g always comes out in units of time² regardless of which length unit is used, so the period is in seconds either way, the same unit-agnostic reasoning this site's projectile motion calculator uses for its own velocity/gravity pair.

This is the small-angle approximation, accurate for swing amplitudes up to roughly 15-20° from vertical; a real pendulum swung much wider than that takes slightly longer per swing than this formula predicts.