Projectile Motion Calculator

This calculator solves drag-free projectile motion from a launch speed and angle, with an optional launch height above the landing ground. It returns the horizontal range, the maximum height, the time of flight and the time to the apex, the impact speed and impact angle, the equation of the parabola, and a plotted trajectory with a table of positions. Two further actions run the problem backwards: the launch angle needed to hit a target, which normally has a flat answer and a lobbed one, and the launch speed needed at an angle you choose. There is no air resistance anywhere on this page, so treat the range as an upper bound for anything light or fast.

Calculator Type
Units
Measured from the horizontal. Zero is a flat throw; a negative angle is a throw aimed downward, which needs a launch height above zero.
Zero means it starts and lands at the same level.
Leave at zero for standard gravity, 9.80665 m/s^2 or 32.17405 ft/s^2. Enter 1.625 for the Moon or 3.72076 for Mars, in metric.
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Units
Zero for a target at the same level as the launch. Negative if the target is below you.
Leave at zero for standard gravity, 9.80665 m/s^2 or 32.17405 ft/s^2. Enter 1.625 for the Moon or 3.72076 for Mars, in metric.
Widget
Units
Leave at zero for standard gravity, 9.80665 m/s^2 or 32.17405 ft/s^2. Enter 1.625 for the Moon or 3.72076 for Mars, in metric.
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