Projectile Motion Calculator
Calculate maximum height, range, and time of flight for a projectile.
Enter launch velocity and angle to see the full trajectory.
Projectile Results
Projectile Motion describes the path of an object launched at an angle, affected only by gravity.
Max Height = (v₀ × sin θ)² / (2g)
Range = (v₀² × sin 2θ) / g
Time of Flight = (2 × v₀ × sin θ) / g
Where:
- v₀ = initial velocity
- θ = launch angle
- g = 9.81 m/s² (acceleration due to gravity)
Key facts:
- 45° gives maximum range (on flat ground)
- Complementary angles (e.g., 30° and 60°) give equal range
- Maximum height occurs at half the total flight time
- Air resistance is ignored in this ideal calculation
Real-world applications:
- Sports (basketball arc, golf drives, soccer kicks)
- Engineering (water fountains, irrigation)
- Military (artillery, ballistics)
At 45° launch angle:
- Range is maximized
- Height = Range / 4