Projectile motion calculator
Enter the launch speed, the angle above horizontal and the launch height above the ground. Handy for ball kicks and textbook problems.
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How to use it
- Enter launch speed, launch angle, launch height and gravitational acceleration g.
- The result appears straight away and updates as you edit.
- Copy the result, or copy a link that keeps the same values to share it.
How it is calculated
vx = v₀ cos θ, vy = v₀ sin θ, flight time T = (vy + √(vy² + 2 g h₀)) ÷ g, range R = vx × T, max height H = h₀ + vy² ÷ (2g).
Example
Inputs: Launch speed = 20 m/s, Launch angle = 45 degrees, Launch height = 0 m, Gravitational acceleration g = 9.80665 m/s². Result: Horizontal range: 40.7886 m; Maximum height above ground: 10.1972 m; Time of flight: 2.8842 s.
Limits and caveats
- Ignores air drag and spin, so real balls usually travel shorter.
- Assumes flat ground with landing at height zero.
Questions about this tool
Which angle gives the longest range?
Launching from ground level without drag, 45 degrees gives the longest range. From a raised point the ideal angle is below 45.
Why do 30 and 60 degrees give the same range?
From ground level the range is proportional to sin 2θ, which is equal for complementary angles.
Does the mass of the object matter?
No. Without air resistance, mass does not appear in the projectile equations.