Projectile Motion (Angle and Distance) Calculator

Find the launch speed, peak height, and flight time from a launch angle and horizontal range, with a trajectory sketch.

Input

Find the launch speed needed for level-ground projectile motion from the launch angle and horizontal range.

Launch angle

deg

Enter a value greater than 0 and less than 90 degrees

Horizontal range

Horizontal distance from launch to landing

Standard gravity g = 9.80665 m/s² is used.

Required launch speed

22.143453m/s

Peak height

12.5 m

Flight time

3.1933 s

Speed in km/h

79.71643 km/h

Horizontal component

15.657786 m/s

Vertical component

15.657786 m/s

Computed from R = v0² sin(2θ) / g solved for speed, giving v0 = sqrt(Rg / sin(2θ)). Air resistance is ignored.

This models level-ground projectile motion (launch and landing at the same height) with air resistance ignored.
The horizontal range is R = v0² sin(2θ) / g. Solving for the launch speed gives v0 = sqrt(Rg / sin(2θ)).
The peak height is H = vy² / (2g) and the flight time is T = 2 vy / g, where vy = v0 sin(θ) is the vertical speed component.
Standard gravity g = 9.80665 m/s² is used.
Enter a launch angle greater than 0 degrees and less than 90 degrees.

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