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Projectile Motion Calculator
Find range, height and flight time from launch speed and angle.
Range
—
Horizontal distance.
| Max height | — |
|---|---|
| Flight time | — |
| Velocity | — |
| Angle | — |
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Enter your figures above to see the step-by-step working.
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How the Projectile Motion Calculator Works
For a projectile launched from ground level with no air resistance, the horizontal range is the initial velocity squared times the sine of twice the launch angle, divided by gravity. Launch at 20 m/s and 45° and it travels about 40.8 meters, peaking near 10.2 meters, with roughly 2.9 seconds in the air.
The 45° angle gives the maximum range on level ground. Height depends on the vertical part of the velocity; range on both parts. This ignores air resistance, so real projectiles fall a bit shorter.
range = v² × sin(2θ) ÷ g
Frequently Asked Questions
What angle gives the longest range?
45 degrees on level ground with no air resistance. Angles above or below travel the same distance in symmetric pairs (30° and 60° match).
How do you find the range of a projectile?
Square the launch speed, multiply by the sine of twice the angle, and divide by gravity (9.81 m/s²).
Does this include air resistance?
No — it’s the ideal vacuum case. Real projectiles fall a little short and peak a little lower because of drag.