Projectile Motion Calculator - Range, Maximum Height, Time of Flight & Trajectory
Projectile Motion Calculator
Range, peak height and flight time, with the trajectory drawn
All the Key Numbers
Range, peak height, flight time, time to the peak and impact speed and angle.
Drawn Trajectory
See the parabola and move along it to read the position at any moment.
Other Worlds
Switch to the Moon, Mars or Jupiter to see how gravity changes the flight.
Private
Calculated in your browser.
The Physics of a Projectile
Without air resistance, the horizontal velocity v·cos θ stays constant while gravity slows and then reverses the vertical velocity v·sin θ. The path is a parabola. On flat ground the range is v2·sin 2θ / g, which is largest at 45°. Example: at 20 m/s and 45° on Earth, the range is 40.79 m, the peak height 10.20 m and the flight lasts 2.884 s.
Launching from a height adds time in the air, and the best angle drops below 45°; the calculator shows the exact optimum. Real projectiles such as balls and arrows are slowed by drag, so they fall shorter than these ideal numbers, especially at high speed. The impact angle is measured below the horizontal.
Key Takeaways
- No air resistance: Results are the ideal, vacuum values.
- 45° is not always best: From a height, a lower angle goes further.
- Mixed units: Speed in m/s, km/h, mph or ft/s; height and distance in metres or feet.