Projectile Motion Calculator

This models ideal projectile motion (no air resistance) for an object launched at an angle θ above flat, level ground with initial speed v: time of flight t = 2v·sin(θ) ÷ g, maximum height h = v²·sin²(θ) ÷ (2g), and horizontal range R = v²·sin(2θ) ÷ g, where g is the gravitational acceleration.

Velocity and gravity just need to share the same length unit — switch the toggle to see both fields relabeled and rescaled together, and the results come out in that same unit (seconds for time either way, since only length converts). Gravity defaults to Earth's standard 9.81 m/s² but is a normal input you can change, so this also works for other bodies (the Moon's ~1.62 m/s², Mars' ~3.71 m/s²) or to model g in ft/s².

The horizontal range is maximized at a 45° launch angle for a given speed — that's why 45° is the default — and drops toward zero as the angle approaches 0° (a flat, grazing shot) or 90° (straight up, where all the motion is vertical).