Calculation of unknown parameters of projection using known parameters. Parameters are duration, maximum height, distance, initial velocity and angle.

Creative Commons Attribution/Share-Alike License 3.0 (Unported)

This content is licensed under Creative Commons Attribution/Share-Alike License 3.0 (Unported). That means you may freely redistribute or modify this content under the same license conditions and must attribute the original author by placing a hyperlink from your site to this work https://planetcalc.com/1508/. Also, please do not modify any references to the original work (if any) contained in this content.


This calculator helps to determine parameters of projection, or ballistic motion. The parameters of projection, as shown on picture, are:
distance S,
maximum height h,
flight duration t,
initial angle \alpha,
initial velocity v_0.

The main equations are:
S=\frac{\upsilon_0^2}{g}\sin 2\alpha \\\\ h=\frac{\upsilon_0^2}{2g}\sin^2\alpha \\\\ t=\frac{2\upsilon_0 sin\alpha}{g}\

These formulae are produced from equations of accelerated motion with the assumption that there is no acceleration along x-axis and only gravity acceleration "g" along y-axis.

Calculator can find unknown parameters for any pair of known parameters.
That is, it calculates the flight duration, maximum height and travel distance of the projection from the initial velocity and angle. Or it calculates the initial velocity, travel distance and flight duration of the projection from the initial angle and maximum height. Or, etc. The only illegal combination of parameters is maximum height and flight duration. Given only these, it is impossible to find others.

PLANETCALC, Projection


Gravitational acceleration, m/s2
Digits after the decimal point: 2
Initial velocity (m/s)
Angle (degrees)
Duration (secs)
Distance (m)
Maximum height (m)

URL copied to clipboard
Creative Commons Attribution/Share-Alike License 3.0 (Unported) PLANETCALC, Projection