Every touchdown pass is a physics problem solved by instinct — launch angle, release speed, and gravity negotiating the rest. A projectile's flight splits cleanly in two: horizontal motion coasts at constant speed while vertical motion rises and falls under gravity. Three numbers describe the whole arc — the Horizontal Range R = v₀²·sin(2θ)/g, the Maximum Height H = v₀²·sin²θ/g·(1/2), and the Total Time of Flight t = 2·v₀·sinθ/g — and 45 degrees gives the longest throw on flat ground because sin(2θ) peaks there.

This calculator takes your launch and returns the arc. Type the release speed into the Launch Velocity (v0) box — a strong NFL throw leaves the hand near 60 mph, about 88 ft/s — the angle above horizontal into the Launch Angle (θ) box, and leave the Gravitational Acceleration (g) box at Earth's 32.2 ft/s². The three result boxes report the Horizontal Range (R), the Maximum Height (H), and the Total Time of Flight (t). Fireworks crews planning a Fourth of July shell, outfielders judging a fly ball, and golfers choosing a club all live inside these three equations.

With the pre-filled defaults — Launch Velocity (v0) 20 m/s, Launch Angle (θ) 45 ° (degrees), Gravitational Acceleration (g) 9.80665 m/s² — the Projectile Motion Calculator returns Horizontal Range (R) 40.7886 m, Maximum Height (H) 10.1972 m, Total Time of Flight (t) 2.8842 s. Change any input and those results update instantly, so you can see exactly how each number you enter moves the answer.