☄️ Projectile Motion
Calculate exactly how far, how high, and how long a projectile will travel given initial velocity and launch angle.
The Comprehensive Guide to Projectile Motion Calculator
What is a Projectile Motion Calculator?
The Projectile Motion Calculator is a classical mechanics tool that computes the exact trajectory, maximum height, total horizontal range, and flight time of any object launched into the air, governed solely by initial velocity, launch angle, and gravity.
The Mathematical Formula
Predicting flight paths in physics simulations.
Calculation Example
If you kick a soccer ball at 20 m/s at a 45° angle from the ground (h₀ = 0):
- Max Height: (20² × sin²(45°)) / (2 × 9.81) = 10.19 meters
- Total Flight Time: (2 × 20 × sin(45°)) / 9.81 = 2.88 seconds
- Total Distance (Range): (20² × sin(2 × 45°)) / 9.81 = 40.79 meters
Strategic Use Cases
- Physics Homework: Instantly check answers for classical mechanics problems involving thrown balls, fired cannons, or leaping athletes.
- Sports Analytics: Determine the optimal launch angle for maximum distance in track and field events (shot put, javelin) or golf drives.
- Game Development: Program accurate and realistic physics engines for archers, grenades, or jumping mechanics in video games.
Frequently Asked Questions
Does this factor in air resistance (drag)?
No, this calculator assumes a complete vacuum. In the real world, air resistance causes the projectile to fall shorter and steeper than the perfectly symmetrical parabolas calculated here.
What angle gives the maximum possible range?
Assuming you launch from and land on flat ground (h₀ = 0), a 45-degree angle will always mathematically yield the absolute maximum horizontal range.
How accurate is this calculator?
Our calculator uses industry-standard formulas to provide the most accurate results possible. However, it should be used for informational purposes only and not as a basis for formal calculations or legal advice.