Projectile Range Calculator

About this calculator

For a projectile launched with speed v at angle θ over level ground (ignoring air resistance), range R = v²sin(2θ)/g, maximum height h = v²sin²θ/(2g), and time of flight t = 2v·sinθ/g, where g is gravitational acceleration (9.81 m/s² on Earth). Range is maximized at a 45° launch angle, and any two angles that sum to 90° (like 30° and 60°) produce the same range — a classic result from this formula.

Physics students use this to master projectile motion — decomposing velocity into horizontal and vertical components and treating them independently. It also has real applications: sports scientists analyze the launch angles of a thrown javelin or shot put, ballistics and artillery calculations historically relied on this exact model, and engineers use it for water-jet or fire-hose trajectory planning. Enter the launch speed and angle to get range, height, and flight time.