Projectile Motion Calculator
Analyse the full trajectory of any projectile. Enter launch speed and angle to get range, maximum height, time of flight, and impact velocity.
Projectile Motion Physics
Key Equations
Time of flight: t = 2v₀sin(θ)/g. Maximum height: h = v₀²sin²(θ)/(2g). Horizontal range: R = v₀²sin(2θ)/g. At 45°, sin(2θ) = 1, giving maximum range. Air resistance is ignored in this model.
Optimal Launch Angle
Without air resistance, 45° gives maximum range for a level surface. With air resistance, the optimal angle is lower (typically 30–40°). For a projectile launched from a height, the optimal angle is below 45° — this calculator shows the adjustment.
Real-World Applications
Sports: ball trajectory in football, cricket, golf, basketball free throws. Engineering: artillery, water fountain design, irrigation. Physics experiments: validating equations of motion using projectile tracks.
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