Free Fall Calculator (Time & Impact Velocity)

Under constant gravity g with no air resistance, an object falling a height h starting at downward speed v₀ follows h = v₀t + ½gt². Solving that quadratic for the positive root gives the fall time t = (−v₀ + √(v₀² + 2gh)) ÷ g, and the impact speed follows from v = v₀ + gt, which simplifies to v = √(v₀² + 2gh).

Height, initial velocity, and gravity only need to share the same length unit — the same reasoning this site's Projectile Motion calculator uses — so the metric/imperial toggle just relabels and rescales all three fields together; nothing in the formula itself is hardcoded to one system. Gravity defaults to Earth's standard 9.81 m/s² but is a normal, editable input, so this also works for the Moon (~1.62 m/s²) or Mars (~3.71 m/s²).

This ignores air resistance entirely, which is accurate for a dense, compact object falling a modest distance but increasingly wrong for a light or large-surface-area object falling a long way, since drag eventually caps real-world falling speed at a terminal velocity — see this site's Terminal Velocity calculator for that opposite idealization.