Projectile Motion Calculator
Range, peak height and flight time for a launch angle and speed.
Vacuum trajectory. Air resistance shortens real ranges substantially, and more so for light or fast objects.
How it works
Split the launch velocity into horizontal and vertical components. The horizontal one never changes; the vertical one is under constant acceleration. Everything else follows.
From ground level, range is v² sin(2θ) / g, which peaks at 45 degrees and gives identical range for any pair of angles summing to 90 — 30 and 60 land in the same place, one arriving much more steeply.
Launching from a height breaks that symmetry: the optimum angle drops below 45, because extra hang time is worth more than extra vertical speed.