Projectile Initial Speed Calculator (Angle and Peak Height)

Find the launch speed, range, and flight time from the launch angle and maximum height. Shows the trajectory.

Input

Enter the launch angle and maximum height to compute the required initial speed and related values.

Launch angle θ

deg

An angle greater than 0 and less than 90 degrees

Maximum height h

The peak height reached on the trajectory

The standard gravity g = 9.80665 m/s squared is used.

Required initial speed v0

19.805706m/s

Range R

40 m

Flight time T

2.856174 s

Initial speed (per hour)

71.300542 km/h

Horizontal speed vx

14.004749 m/s

Vertical speed vy

14.004749 m/s

v0 = sqrt(2 g h) / sin(theta); range R = v0 squared times sin(2 theta) / g; flight time T = 2 v0 sin(theta) / g. Air resistance is ignored.

The maximum height h is set by the vertical launch speed vy = v0 sin(theta), giving h = (v0 sin(theta)) squared divided by (2 g).
Solving for the initial speed gives v0 = sqrt(2 g h) divided by sin(theta).
The flight time is T = 2 v0 sin(theta) / g and the range is R = v0 squared times sin(2 theta) / g.
Air resistance is ignored and launch from level ground is assumed. The standard gravity g = 9.80665 m/s squared is used.
Enter a launch angle greater than 0 and less than 90 degrees, and a positive maximum height.

Tell us what you think of this calculator.