Projectile Motion Calculator

Use this Projectile Motion Calculator to estimate time of flight, horizontal range, maximum height, and velocity components from launch speed, angle, initial height, and gravity.

Calculation Method

Initial velocity is separated into horizontal and vertical components:

v_x = v₀ × cos(θ)

v_y = v₀ × sin(θ)

Time of flight to the reference landing level is:

t = [v_y + √(v_y² + 2gh₀)] ÷ g

Horizontal range:

R = v_x × t

Maximum height:

H = h₀ + v_y² ÷ (2g)

Example

For a projectile launched at 20 m/s and 45° from ground level on Earth:

v_x ≈ 14.14 m/s

v_y ≈ 14.14 m/s

Time of flight ≈ 2.88 s

Range ≈ 40.77 m

Maximum height ≈ 10.19 m

Important Note

This is an ideal projectile-motion model. It assumes constant downward gravity and no air resistance, wind, spin, or aerodynamic lift. The 45° maximum-range rule applies only when launch and landing heights are equal under these ideal conditions.

Source

• OpenStax University Physics — Projectile Motion