Projectile Motion Calculator: Range, Height, and...

What is Projectile Motion?

Projectile motion describes the curved path of an object launched into the air, subject only to gravity. The horizontal and vertical components are independent — horizontal velocity stays constant while vertical velocity changes due to gravity. This model explains ballistics, sports, and orbital insertion trajectories.

🚀 Projectile Motion Calculator

Use our free calculator for instant, accurate results.

Calculate Now →

📐 Formula

R = v₀²sin(2θ)/g | H = v₀²sin²(θ)/(2g) | T = 2v₀sin(θ)/g

R = range, H = max height, T = total time of flight. v₀ = initial speed (m/s), θ = launch angle, g = 9.81 m/s².

📝 Worked Example

Ball thrown at 20 m/s at 45°:
R = 20²×sin(90°)/9.81 = 40.8 m
H = 20²×sin²(45°)/(2×9.81) = 10.2 m
T = 2×20×sin(45°)/9.81 = 2.89 s

📝 How to Use the Calculator

Enter Initial SpeedLaunch speed in m/s or km/h.

Enter Launch AngleAngle above horizontal in degrees (45° gives maximum range on flat ground).

Set Launch HeightHeight above landing point (0 if same level).

View ResultsSee range, max height, time of flight, and velocity at any point.

❓ FAQ

What angle maximizes range?

45° on flat ground. With a height advantage (launching from a cliff), the optimal angle is less than 45°.

Does air resistance affect projectile motion?

Yes significantly for real objects. The ideal model assumes vacuum conditions. Drag reduces range and changes the optimal angle.

What is Projectile Motion?