Projectile Launch Angle Calculator

About this calculator

The projectile launch angle calculator solves the classic ballistics problem in reverse: given a target range R and a launch speed v on level ground, it finds the angle θ using θ = ½ arcsin(gR / v²), where g is gravitational acceleration. Because sin(2θ) = sin(180° − 2θ), this equation always has two valid solutions — a low, flat trajectory and a high, lofted one — that hit the exact same range.

The low angle gets there faster and flatter (favored when speed matters, or when the flight path must clear low obstacles), while the high angle spends longer in the air and comes down more steeply. Physics students verifying textbook kinematics problems, and hobbyists in fields like archery, ballistics, and sports science (javelin, shot put, artillery) use this calculator to find both possible launch angles instead of solving the trig by hand.