Projectile Motion Calculator
Find the range, maximum height and flight time of a projectile, ignoring air resistance.
About the Projectile Motion Calculator
Enter the launch speed, launch angle, starting height and gravity. The calculator gives the range, flight time, maximum height and impact speed, with the path drawn to scale.
Horizontal motion is at constant speed v cos θ; vertical motion is uniformly decelerated by gravity. From ground level the range is v² sin 2θ ÷ g, greatest at 45°. Launching from a height extends the flight time. Real projectiles also feel drag.
The formula
x = v cos θ · t; y = h + v sin θ · t − ½ g t²
Worked example
Launched at 20 m/s at 45° from the ground
- Range: 20² × sin 90° ÷ 9.807 = 40.79 m
- Flight time 2.88 s
- Highest point 10.2 m after 1.44 s
Questions people ask
Why is 45° best?
From flat ground, sin 2θ is largest at 45°.
Does mass matter?
Not without air resistance.