Calculate range, maximum height and flight time of a projectile launched at an angle.
Horizontal and vertical motion are independent: horizontal velocity stays constant while vertical motion is uniformly accelerated. Launching from a height extends flight time and shifts the optimal angle below 45 degrees. The 45-degree optimum only holds for launch and landing at the same height; from any elevation the best angle is lower.
Projectile Motion
Range = vₓ t, with t from solving h₀ + v_y t − ½ g t² = 0
Range = vₓ t, with t from solving h₀ + v_y t − ½ g t² = 0 Horizontal and vertical motion are independent: horizontal velocity stays constant while vertical motion is uniformly accelerated. Launching from a height extends flight time and shifts the optimal angle below 45 degrees.
The 45-degree optimum only holds for launch and landing at the same height; from any elevation the best angle is lower.
This calculator takes 4 inputs: Launch speed, Launch angle, Launch height, Gravitational acceleration. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.