Why 45 Degrees Isn't Always the 'Best' Launch Angle

The textbook result is clean: for a projectile launched and landing at the same height with no air resistance, 45° gives the maximum possible range for a given launch speed. It's one of the most quoted facts in introductory physics.

But that result depends entirely on the launch and landing heights being equal. A shot put thrown from shoulder height lands on the ground, not back at shoulder height — and for that case, the optimal angle is actually somewhat below 45°, because the extra time spent in the air from a higher initial release favours a flatter trajectory.

Air resistance changes the picture further. For anything light or fast enough for drag to matter — a golf ball, a baseball hit hard — the optimal angle for real-world range is often noticeably lower than 45°, because a flatter trajectory spends less time fighting drag.

The 45° rule is a genuinely useful mental anchor and exactly correct for the idealised case this calculator models. But treating it as a universal 'best angle' for every real throwing or launching situation is a common oversimplification worth knowing about.