How it works
A projectile — a thrown ball, a water jet, a long jumper — follows a parabola because gravity only pulls vertically while horizontal motion continues unchanged. Splitting motion into those two independent components is one of physics' most useful tricks.
The classic results (for level ground, no air resistance): range peaks at a 45° launch angle; maximum height grows with the square of launch speed; flight time depends only on the vertical component of velocity.
Air resistance shortens real-world ranges — noticeably for light, fast objects like golf balls, barely at all for a shot put. This calculator gives the ideal (vacuum) values, which are the correct starting point for any estimate.
Use it in real life
Sports: long jumpers take off near 20° rather than 45° because they can't maintain full sprint speed at steep take-off angles — a beautiful example of optimizing within constraints.
Gardening and firefighting: a hose's water jet is a projectile. Angle up toward 45° to reach the far flowerbed; drop the angle for close, flat coverage.
Basketball: higher launch arcs give the ball a steeper descent into the hoop, effectively enlarging the target — physics is why coaches teach arc.
Frequently asked questions
What angle gives maximum range?
45° in a vacuum on level ground. With air resistance the optimum drops to roughly 35–43° depending on the object; for launches from a height (like a shot put) the optimum is also slightly below 45°.
Does the horizontal and vertical motion really not affect each other?
Correct — gravity only changes vertical velocity. A bullet fired level and a bullet dropped at the same instant hit the ground at the same time (over flat ground, ignoring air effects).
How much does air resistance change the answer?
For dense, slow objects (shot put) only a few per cent. For light, fast ones (golf ball, football) it can cut range 20–50% — though spin and dimples add lift that partially compensates.