Projectile Range & Height Calculator

About this calculator

This calculator solves the classic projectile motion problem from Newtonian mechanics: an object launched at speed v and angle θ above the horizontal, moving under gravity alone with no air resistance. The three headline results come from splitting velocity into horizontal and vertical components — range R = v²sin(2θ)/g, maximum height H = v²sin²θ/(2g), and time of flight T = 2v·sinθ/g — using standard gravity g = 9.80665 m/s².

These equations are a staple of introductory physics courses, but they also underpin real work in ballistics, artillery and sports-equipment design, and coaching analysis of throwing or kicking angles (the range formula shows why 45° maximizes distance on level ground). Enter a launch speed and angle and the calculator returns all three values together, so you can see how changing the angle trades off height against distance.