Calculates the full trajectory of an object launched at an angle — how far it travels, how high it gets, and how long it stays in the air.
How it works
Three standard projectile-motion equations combine the launch velocity and angle to give horizontal range, maximum height, and total flight time.
What this does not include
This assumes level ground (launching and landing at the same height) and ignores air resistance — the standard simplified case taught in introductory physics.
How to use this calculator
- Enter the launch velocity and launch angle.
A worked example
A projectile launched at 20 m/s at a 45° angle: range = 40.7886 m, max height = 10.1972 m, time of flight = 2.8842 s.
Launched at 30 m/s at a 30° angle: range = 79.479 m, max height = 11.4718 m, time of flight = 3.0591 s.
What the variables mean
| Variable | Meaning |
|---|---|
| Velocity | Initial launch speed |
| Angle | Launch angle above horizontal, in degrees |
Edge cases worth knowing
45° gives the maximum range for a given launch speed — a classic physics result, which is why the first example’s lower speed (20 m/s at 45°) still achieves a range roughly half the second example’s much faster 30 m/s launch at a less optimal 30°.
This ignores air resistance — real-world range and height are somewhat lower than this idealized formula predicts, especially for lighter or less aerodynamic objects.
Frequently asked questions
What launch angle gives the maximum range?
45 degrees, assuming level ground and no air resistance — any angle above or below that reduces the range for the same launch speed.
Why does air resistance matter for real projectiles?
Air resistance slows a projectile down over its flight, reducing both range and max height below what this idealized formula predicts — the effect grows with speed and matters more for light, high-drag objects.
What happens at a 90-degree launch angle?
The projectile goes straight up and comes straight back down — the range becomes zero, even though the max height is at its greatest.
