Projectile Motion Calculator

Calculate range, maximum height, time of flight, and trajectory for projectile motion

Input Values

Results

What is Projectile Motion?

Projectile motion is the motion of an object thrown or projected into the air, subject to only the acceleration of gravity. The object is called a projectile, and its path is called its trajectory.

Projectile Motion Formulas

Range (R):

R = (v₀² × sin(2θ)) / g

Maximum Height (H):

H = (v₀² × sin²(θ)) / (2g)

Time of Flight (T):

T = (2v₀ × sin(θ)) / g

Horizontal Position (x):

x = v₀ × cos(θ) × t

Where:

  • v₀ = Initial velocity (m/s)
  • θ = Launch angle (degrees)
  • g = Gravitational acceleration (9.81 m/s²)
  • t = Time (s)

How to Use the Calculator

  1. Enter the initial velocity in meters per second
  2. Enter the launch angle in degrees
  3. Click "Calculate" to get all projectile motion parameters
  4. View the step-by-step solutions and trajectory plot

Example Calculation

For a projectile launched at 50 m/s at 45°:

Range: R = (50² × sin(90°)) / 9.81 = 255.1 m

Maximum Height: H = (50² × sin²(45°)) / (2 × 9.81) = 63.7 m

Time of Flight: T = (2 × 50 × sin(45°)) / 9.81 = 7.2 s