Horizontal Projectile Motion Calculator

With this horizontal projectile motion calculator, you'll quickly find out the trajectory, time of flight, and projectile range.

Range30.2943 m99.39 ft

Time of flight2.0196 s

Maximum height20 m0 m above the launch point

Time to the apex0 sthe descent takes longer than the climb

Horizontal velocity15 m/sconstant throughout — no horizontal force

Initial vertical velocity0 m/s

Impact speed24.8448 m/sfaster than launch, by the drop in height

Impact angle below horizontal52.86°

Angle for maximum range31°below 45° because the extra height rewards a flatter, faster shot

Maximum range at that angle38.0019 m7.7076 m further than yours

Energy per kilogram at launch112.5 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.