Projectile motion simulator
Calculate range, maximum height and time of flight of an oblique or horizontal launch from the speed, angle and initial height, with a drawing of the trajectory.
How to useOblique and horizontal launch
Available in: 
Projectile motion simulator: what it is for
Type the initial speed, the angle, the height the object starts from and gravity. The tool splits the velocity, calculates the horizontal range, maximum height, time of flight, time to the top and the landing speed and angle, and draws the parabola to scale. It also works for horizontal launches (zero angle) and downward angles from a height.
The calculations run in your browser and ignore air resistance, as in high school physics problems.
How to use
- Enter speed, angle and initial height.
- See the results.
- Check the trajectory on the chart.
When to use it
- Studying projectile motion.
- Comparing the range of different angles.
- Solving exam problems.
Frequently asked questions
How is the range calculated?
By splitting the velocity: vx = v0·cos θ and vy = v0·sin θ. Horizontal motion is uniform and vertical motion is uniformly accelerated. Starting from the ground, the range is R = v0²·sin(2θ)/g and the maximum height is H = vy²/(2g).
Which angle gives the longest range?
Starting and landing at the same height, 45°. Complementary angles, like 30° and 60°, have the same range. When the launch starts from a height, the ideal angle is a little below 45°.
What about a horizontal launch?
It's the case with a 0° angle from a height. The fall time depends only on the height, t = √(2h/g), and the range is vx·t.
Is it really free?
Yes, 100% free. No sign-up, no subscription and no usage limits. All Tools123 tools are free and run right in your browser.