Enter the launch speed, angle and (optional) launch height to compute the time of flight, maximum height and horizontal range of a projectile, ignoring air resistance.
Projectile motion treats horizontal and vertical motion independently. Horizontally the speed is constant (v₀cosθ); vertically the projectile decelerates, stops rising, then falls under gravity g.
From the launch speed v₀, angle θ and height h₀ the calculator finds the peak height H, the total time of flight T (until it returns to ground level) and the horizontal range R = v₀cosθ × T. Air resistance is ignored, which is a good approximation for dense, slow objects.
From ground level (launch height = 0), the maximum range is achieved at a launch angle of 45°. If launched from a height above the landing point, the optimal angle is slightly less than 45°.
For a launch from height h₀, time of flight T = [v₀sinθ + √((v₀sinθ)² + 2gh₀)] / g. From ground level this simplifies to T = 2v₀sinθ / g.
Maximum height H = h₀ + (v₀sinθ)² / (2g). Only the vertical component of the launch velocity contributes.
No. Ignoring air resistance, the trajectory depends only on launch speed, angle, height and gravity — not on the projectile's mass. A heavy and a light ball launched identically follow the same path.