Maximum Height Calculator – Projectile Motion

Use this maximum height calculator to figure out what is the maximum vertical position of an object in projectile motion.

Maximum height23.8996 mabove the ground

Range55.1938 m181.08 ft

Time of flight4.4155 s

Time to the apex2.2078 sexactly half the flight

Horizontal velocity12.5 m/sconstant throughout — no horizontal force

Initial vertical velocity21.6506 m/s

Impact speed25 m/sequal to the launch speed — energy is conserved

Impact angle below horizontal60°

Angle for maximum range45°45° exactly from level ground

Maximum range at that angle63.7323 m8.5385 m further than yours

The complementary angle 30°55.1938 mthe same range from level ground — a high lob and a flat shot can land together

Energy per kilogram at launch312.5 J/kg

The formula

range = v cos θ × t, apex = h + v²sin²θ ÷ 2g

Two independent motions

The whole subject reduces to one observation: horizontal and vertical motion do not interact. With no air resistance nothing pushes or pulls horizontally, so the horizontal velocity never changes; vertically, gravity acts exactly as it would on a dropped object. A bullet fired horizontally and a bullet dropped from the same height hit the ground at the same moment.

From level ground 45° gives the greatest range, and complementary angles — 30° and 60°, say — give identical ranges by different routes, one high and slow, one flat and fast. Launching from a height breaks that symmetry: the extra fall time rewards horizontal speed, so the optimal angle drops below 45°, which is why the page solves for it rather than assuming.

Air resistance is neglected throughout, and for anything small, fast or light that is a serious omission — a real projectile's range can be a fraction of the vacuum figure, and its trajectory is not symmetric, falling more steeply than it rose.