Calculate range, max height, and flight time of a projectile given initial velocity and launch angle.
| Quantity | Formula |
|---|---|
| Horizontal velocity | Vx = V·cos(θ) |
| Vertical velocity | Vy = V·sin(θ) |
| Max height | H = h + Vy²/(2g) |
| Flight time | t = (Vy + √(Vy²+2gh))/g |
| Range | R = Vx × t |
Maximum range occurs at 45° (from ground level with no air resistance).
For low-speed projectiles (balls, arrows), air resistance reduces range by 20-40%. This calculator assumes vacuum conditions. Real trajectories require numerical simulation.
45 degrees from ground level. If launching from a height, the optimal angle is slightly less than 45 degrees.
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Open →Enter the initial velocity, launch angle, and initial height. The calculator shows maximum height, range, flight time, and trajectory path.
Range = v₀² × sin(2θ) / g. Max Height = v₀² × sin²(θ) / (2g). Flight Time = 2 × v₀ × sin(θ) / g. g = 9.8 m/s².
Ball launched at 20 m/s at 45°: Range = 40.8 m, Max Height = 10.2 m, Flight Time = 2.88 s. 45° gives maximum range on flat ground.
45° launch angle gives maximum range (on level ground). In reality, air resistance significantly reduces range. For different launch/landing heights, use the quadratic formula for flight time.