Find range, maximum height and time of flight for a projectile.
Calculated instantly in your browser.
How do you calculate projectile motion?
Split velocity into vₓ = v·cosθ and v_y = v·sinθ. Time of flight t = (v_y + √(v_y² + 2gh)) ⁄ g, range = vₓ · t, and maximum height = h + v_y² ⁄ (2g). The model ignores air resistance. For example, launched at 20 m/s and 45° from the ground, a projectile travels about 40.8 m, rises 10.2 m, and lands after 2.9 s.
Understanding your result
Projectile motion splits into independent horizontal (constant velocity) and vertical (accelerated by gravity) components. The model ignores air resistance, so real distances are a little shorter.
Formula and method
vₓ = v·cosθ, v_y = v·sinθ. Time of flight t = (v_y + √(v_y² + 2gh)) ⁄ g. Range = vₓ · t. Maximum height = h + v_y² ⁄ (2g).
Worked example
Launched at 20 m/s and 45° from the ground, a projectile travels about 40.8 m and rises 10.2 m, landing after 2.9 s.
How to use this tool
- Enter the launch speed and angle.
- Optionally set an initial height.
- Read the range, height and flight time.
Common mistakes to avoid
- Forgetting to convert the angle to radians (the tool does this for you).
- Expecting air resistance to be included — it is not.
About the Projectile Motion Calculator
The Projectile Motion Calculator solves the trajectory of an object launched at an angle. Enter the launch speed, angle and starting height to get the horizontal range, maximum height, time of flight and velocity components.
Who should use this tool
Physics students, teachers and engineers working with trajectories.
Benefits
- Range, max height and time of flight at once.
- Handles a non-zero launch height.
- Shows the velocity components and steps.
- Adjustable gravity for other bodies.
Practical use cases
- Solving a launch-angle physics problem.
- Estimating how far a ball travels.
- Checking trajectory homework.
Explore all Science and Engineering tools
Frequently asked questions
What launch angle gives the longest range?
On level ground with no air resistance, 45° gives the maximum range. A launch height shifts the optimum slightly lower.
Does this include air resistance?
No. It uses ideal projectile motion. Real-world drag reduces both range and height, more so at higher speeds.