Energy conservation in a pendulum swing
As a pendulum swings, it continuously trades potential energy for kinetic energy and back again. At the top of its swing it’s momentarily at rest (all potential energy); at the bottom of its swing it moves fastest (all kinetic energy).
The formula
Using conservation of energy, the height the bob drops from its release angle is h = L × (1 − cosθ), where L is pendulum length and θ is the angle from vertical. Since all potential energy converts to kinetic energy at the bottom (ignoring air resistance and pivot friction), KE = m × g × h, and velocity at the bottom follows from v = √(2gh).
This assumes an idealized simple pendulum with no energy losses and treats the bob as a point mass on a massless string. Real pendulums lose a small amount of energy to air resistance and friction at the pivot each swing. This calculator is for general physics education.