Projectile Motion Calculator
Calculate projectile motion parameters — maximum range, maximum height, time of flight, and landing velocity for any launch angle and speed.
Results
What is it?
Projectile motion describes the curved path of an object launched with an initial velocity under constant gravitational acceleration (g = 9.81 m/s² on Earth). The horizontal and vertical components are independent: horizontal velocity stays constant (no air resistance), while vertical velocity changes due to gravity.
How to use
Enter the launch speed, the launch angle (0° = horizontal, 90° = straight up), and the initial height above the landing surface. Results include horizontal range, maximum height, total flight time, and speed at landing.
Example scenario
A ball is kicked at 30 m/s at 45° from ground level. At 45° the range is maximised on flat ground: range = v₀² × sin(2θ) / g = 900 × 1 / 9.81 ≈ 91.7 m. The calculator gives the same answer along with time of flight ≈ 4.32 s and max height ≈ 22.9 m.
Pro tip
45° gives maximum range only when launched and landed at the same height. With a positive initial height, the optimal angle is less than 45°. Air resistance significantly reduces real-world range — this calculator assumes a vacuum. For long-range artillery, the Coriolis effect and atmospheric density also matter.