Projectile Range Calculator
Find how far a projectile travels horizontally.
Find the horizontal distance a projectile covers on level ground.
How the Math Works
The Projectile Range Calculator uses the formula R = v₀²·sin(2θ) ÷ g to determine horizontal distance. Here, v₀ represents initial velocity squared, which means faster projectiles travel farther. The sine term sin(2θ) shows how launch angle affects range, peaking at 45° (sin(90°) = 1). Gravity (g ≈ 9.8 m/s²) pulls the projectile downward, reducing flight time. This formula assumes no air resistance and a flat landing surface, providing the theoretical maximum distance achievable under ideal conditions.
Practical Applications
Use this calculator when designing ballistics systems, sports strategies, or physics experiments. For example, engineers might optimize artillery trajectories, while athletes could refine throwing/kicking techniques by testing angles and velocities. Educators use it to demonstrate projectile motion principles. Input your launch speed (v₀), angle (θ), and select gravity (g) for Earth, the Moon, or other planets to instantly compute range. This tool is invaluable for quick estimates in engineering, sports science, or academic research where simplifying assumptions apply.
Day-to-Day Use
Understanding projectile range helps in everyday scenarios like planning a successful water balloon toss, optimizing soccer free kicks, or setting up backyard carnival games. It explains why throwing objects at a 45° angle maximizes distance—useful knowledge for sports or recreation. Even in daily activities, like tossing a frisbee or tossing trash into a bin, this formula offers intuitive insights into motion physics, making abstract math tangible and practical for curious minds.
Worked example
20 m/s at 45° → 40.77 m.
FAQ
Which angle gives the most range?
45° on level ground (ignoring air resistance).