Projectile Motion Calculator
Enter launch speed, angle, and starting height to get flight time, peak height, range, and the velocity components.
Set the launch speed, the angle above the horizontal, and how high off the ground you start. The calculator splits the velocity into components and works out how long it stays airborne, how high it climbs, and how far it lands. Gravity is fixed at 9.81 m/s².
Time of flight
2.883s
Max height
10.194m
Range
40.775m
Horizontal velocity (vₓ)
14.142m/s
Vertical velocity (v_y)
14.142m/s
How it works
Every launch is really two motions happening at once. The horizontal part coasts along at a steady speed, while the vertical part slows, stops at the top, and falls back down under gravity. Split the launch speed with a little trigonometry — speed times the cosine of the angle goes sideways, speed times the sine goes up — and the rest follows.
The vertical velocity tells you how long the flight lasts and how high it climbs. From those you get the range: the horizontal speed multiplied by the total time in the air. Start from ground level and a 45° angle gives the farthest throw. Launch from a rooftop or a cliff and the numbers shift, because the object has extra height to fall through before it lands.
This model ignores air resistance, so it's the classic textbook version. Real footballs and arrows fall a bit short of these figures because drag bleeds off speed, but for learning the physics — or sanity-checking a homework answer — the ideal case is exactly what you want.
Frequently asked questions
Why is 45 degrees the best angle for distance?
When you launch from ground level, 45° splits the speed evenly between going up and going forward, which maximizes range. Steeper angles buy hang time but sacrifice horizontal reach; shallower ones do the opposite. If you launch from a height, the optimal angle drops slightly below 45°.
What does the initial height change?
Starting higher gives the projectile extra time to fall, so it stays in the air longer and travels farther. That's why a shot put released from shoulder height lands beyond where the simple ground-level formula predicts.
Does this account for air resistance?
No. It assumes a vacuum, so gravity is the only force acting after launch. That keeps the math clean and matches most physics coursework, but a real projectile will fall a little short of these ideal numbers.