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How to use this calculator
Enter the launch speed, the angle above the horizontal, and optionally the starting height. You get the time of flight, range, maximum height and landing speed, with a graph of the path.
How it's calculated
uₓ = u cos θ and uᵧ = u sin θ. Time of flight t = (uᵧ + √(uᵧ² + 2gh₀)) / g. Range R = uₓ × t. Maximum height H = h₀ + uᵧ² / (2g). Air resistance is ignored.
Worked example
A ball is launched at 20 m/s at 45° from the ground (g = 9.8). t ≈ 2.89 s, range ≈ 40.82 m and maximum height ≈ 10.2 m.
Frequently asked questions
Which angle gives the longest range?
From level ground, 45° gives the greatest range.
Does it include air resistance?
No. Real paths are shorter because of air resistance.
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Last updated October 2026. Results are for learning and guidance; always check important work. Calculations run in your browser and are not stored.