A Parabola from Two Simple Rules

A projectile's flight is a combination of two independent motions: constant horizontal velocity and constant vertical acceleration. This projectile motion calculator combines them into the classic parabolic path — computing where the object lands, how high it climbs, and how long it flies.

Velocity, Angle, and Height

The launch velocity splits into vₓ = v·cosθ and vᵧ = v·sinθ. Time to apex is vᵧ/g, maximum height adds vᵧ²/2g to the starting height, and flight time is the full solution of the vertical position equation. Range is simply horizontal speed times that total time.

Why 45 Degrees Is the Sweet Spot

On level ground, range follows v²sin(2θ)/g, which is largest at exactly 45°. The chart shows why: shallower launches have less airtime, steeper ones less horizontal speed. Adjusting gravity in Advanced Options lets you compare the same throw on Earth, the Moon, or Mars.