Projectile Motion Calculator
Enter the launch speed, the launch angle and the starting height.
This result is an estimate only. Double-check important figures before relying on them.
How it is calculated
- Horizontal speed = v × cos θ and vertical speed = v × sin θ
- Time of flight = (vy + √(vy² + 2 × g × height)) ÷ g
- Range = horizontal speed × time
- Maximum height = height + vy² ÷ (2g)
For motion with constant acceleration in one line, use the velocity calculator.
Worked example
20 m/s at 45° from the ground:
- Time = 2.884 s
- Range = 40.79 m, maximum height = 10.20 m
Why your number may differ
Drag, spin and wind are ignored. Gravity is also set to a fixed value for the whole path.
Frequently asked questions
What is projectile motion?
The path of an object thrown or launched and then moving under gravity alone, as a curve called a parabola.
Which angle gives the longest range?
From level ground, 45°. Complementary angles, such as 30° and 60°, give the same range.
Does it include air resistance?
No. Real objects, such as a football or a shuttlecock, travel a shorter distance because of drag.