How to use the Projectile Motion Calculator
- Enter the launch speed and angle.
- Add a launch height if it starts above the ground.
- Read the range, flight time, maximum height and trajectory.
What does this tool do?
A projectile moves horizontally at a constant speed while gravity pulls it down. Splitting the launch velocity into horizontal and vertical parts lets you solve each direction separately.
On flat ground, 45° gives the longest range. Launching from a height shifts the best angle lower. Try other planets by changing gravity.
Why use it?
- Launch height supported.
- Trajectory table.
- Change gravity for other planets.
The formula
vₓ = v₀ cos θ, v_y = v₀ sin θ
t = (v_y + √(v_y² + 2gh₀)) ÷ g
range = vₓ t, h_max = h₀ + v_y² ÷ 2g
Accuracy and limits
- Air resistance is ignored, so real balls and arrows fall short of these figures.
Privacy
The calculation happens instantly in your browser. The numbers you enter are not sent to our servers or saved. There's no account to create and nothing to install.
Last reviewed by the M2Toolkit team.