Calculate the path of a projectile launched at a given speed and angle. You get time of flight, range, maximum height and impact speed, assuming no air resistance. Free, private, and runs entirely in your browser.
The horizontal and vertical motions are independent. Horizontally the speed is constant, and vertically gravity slows the rise and speeds the fall. The calculator solves for the time when the projectile returns to the ground, then finds the range and height.
What angle gives the longest range? 45 degrees on level ground without air resistance. If the launch point is higher than the landing point, a slightly lower angle is best.
Does mass matter? Not without air resistance. All objects follow the same path for the same launch speed and angle.
A ball is launched at 20 m/s at 45° from ground level. The vertical speed is 14.14 m/s, so the flight lasts 2 × 14.14 ÷ 9.807 ≈ 2.88 s. The range is 14.14 × 2.88 ≈ 40.8 m and the maximum height is 14.14² ÷ (2 × 9.807) ≈ 10.2 m.
Why is the path a parabola? Because the horizontal position grows linearly with time and the vertical position changes with the square of time.
Can I use feet and mph? Convert to meters per second first. The speed calculator and the converters can help.
Galileo showed in the early 1600s that a projectile follows a parabolic path when the horizontal and vertical motions are treated separately, and he published the result in 1638. The analysis became a cornerstone of classical mechanics, and it still underlies ballistics, sports science and basic physics courses.
Use this calculator for physics problems, to model a throw or a jump, or to compare launch angles. Real projectiles lose range to air resistance, so use the results as an upper bound for light objects.
How do I find the time to reach maximum height? t = v·sinθ ÷ g, which is half the flight time from level ground.
What is the effect of launch height? A higher launch point adds to the flight time and range.