Projectile Speed and Angle from Altitude and Distance
Find the launch speed and angle from a known peak height and horizontal range, with flight time and a trajectory sketch.
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Input
Enter the peak height and horizontal range to back out the launch speed and angle needed.
m
Height of the trajectory peak in meters
m
Horizontal distance from launch to landing in meters
Gravity uses the standard value g = 9.80665 m/s² and air resistance is ignored.
Result
Launch speed v0
28.009498m/s
Launch angle θ
45deg
Flight time
4.03924 s
Time to peak
2.01962 s
Launch speed (km/h)
100.834194 km/h
Horizontal speed
19.805706 m/s
Vertical speed
19.805706 m/s
The angle comes from tanθ = 4h ÷ R and the speed from v0 = √(2gh) ÷ sinθ. Flight time is T = 2√(2h ÷ g).
How it works
- From the peak height h and horizontal range R, this tool back-solves the launch speed and angle for projectile motion with no air resistance.
- The angle comes from tan of theta equals 4h divided by R, and the speed is the square root of 2gh divided by the sine of the angle.
- Flight time equals 2 times the square root of 2h divided by g, and the time to reach the peak is half of that.
- Gravity uses the standard value g equals 9.80665 m per second squared, with launch and landing at the same height.
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