Projectile Motion Calculator

Enter the initial velocity, launch angle and starting height — this free projectile motion calculator gives you the maximum height, horizontal range, flight time and impact velocity, with a trajectory chart. Metric and imperial units, runs entirely in your browser.

Projectile motion formulas

With initial velocity v₀, launch angle θ and initial height h₀ (g = 9.81 m/s²):

Flight time: t = (v₀·sinθ + √((v₀·sinθ)² + 2gh₀)) / g
Horizontal range: R = v₀·cosθ · t
Max height: H = h₀ + (v₀·sinθ)² / (2g)
Impact velocity: v = √(vx² + vy²), where vy at impact = v₀·sinθ − g·t

FAQ

What angle gives the maximum projectile range?

45 degrees on flat ground, ignoring air resistance. If launched from a height, the best angle drops slightly below 45° — try 40° in the calculator and compare.

Does mass affect projectile motion?

No — without air resistance, a bowling ball and a baseball launched identically follow the same trajectory. Mass cancels out of the equations. Air resistance is where mass and shape start to matter.

How do you calculate the maximum height of a projectile?

H = h₀ + (v₀·sinθ)²/(2g). Only the vertical component of velocity (v₀·sinθ) contributes to height.

What is the difference between range and distance?

Range is the horizontal distance from launch to landing point. The total path length along the curved trajectory is longer — this calculator reports range.