Physics / Motion
Projectile Motion Calculator (Range, Height, Time of Flight)
Work out how far a projectile travels, how long it is in the air, how high it goes, and how fast it lands, from the launch speed, angle, and height, with the parabolic path drawn to scale. Ignores air resistance, as school physics does.
Projectile Motion Calculator (Range, Height, Time of Flight): The horizontal and vertical speeds are u cos θ and u sin θ. Gravity slows the vertical part, so the time of flight solves h + u sin θ · t − ½gt² = 0, and the range is the horizontal speed times that time. At 20 m/s and 45° from the ground, the projectile flies 2.88 s, reaches 10.20 m, and lands 40.79 m away. Runs 100% locally in your browser with zero server file uploads.
- Category
- School & study tools
- Runs
- In your browser
- Cost
- Free · no sign-up
- Availability
- Ready to use
Runs entirely in your browser
Without air resistance the horizontal speed stays constant and gravity slows the climb, so the path is a parabola. From level ground, 45° gives the longest range; from a height, a slightly lower angle goes further. Real balls fly shorter, because drag grows with speed. The impact speed follows from energy: v² = u² + 2gh.
Worked example
A ball thrown at 15 m/s and 30° from a 10 m cliff has a vertical speed of 7.5 m/s. It rises to 12.87 m above the ground, lands after 2.38 s, 30.98 m out, at 20.52 m/s; the same as √(15² + 2 × 9.81 × 10), as energy conservation says.
Other planets
Set gravity to 1.62 m/s² for the Moon or 3.71 for Mars: the same throw goes about six times further on the Moon. For constant-acceleration motion in a straight line, use the kinematics calculator.
How to use it
- Enter or drag the launch speed, angle, and height.
- Change gravity for other planets if you like.
- Read the range, time, maximum height, and impact speed, and see the path.
Privacy & limitations
Everything is calculated in your browser.
Related tools
Frequently asked questions
Which angle goes furthest?
45° from level ground, if there is no air resistance. Launching from a height, the best angle is a little lower; with real air drag, lower still.
Why do two angles give the same range?
From level ground, complementary angles such as 30° and 60° land at the same place: the steeper one goes higher and stays up longer, but moves sideways more slowly.
Does the mass matter?
Not without air resistance: a heavy and a light ball launched the same way follow the same path.
Free tool · runs in your browser · no account required