Projectile Motion Calculator

Calculate range, max height, and flight time of a projectile from launch speed and angle.

m/s
°
m
m/s²

Projectile Motion Equations

Projectile motion describes the path of an object launched into the air, subject only to gravity. The horizontal and vertical motions are independent, with the velocity split into components: vₓ = v₀·cos θ and v_y = v₀·sin θ.

  • Range: R = v₀²·sin(2θ) / g (when h = 0)
  • Maximum height: H = v_y² / (2g) above the launch point
  • Time of flight: t = 2·v_y / g (when h = 0)
  • Impact speed: √(vₓ² + (v_y − g·t)²)

Effect of Launch Angle

When the launch and landing heights are equal (h = 0), a launch angle of 45° produces the maximum range for a given initial speed. Complementary angles (for example 30° and 60°) yield the same range. Raising the launch height shifts the optimal angle slightly below 45°.

Assumptions

  • No air resistance or drag is considered.
  • Gravity is constant and acts straight down.
  • The projectile is treated as a point mass.

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Note: This calculator assumes ideal projectile motion with no air resistance and constant gravity. Results are based on idealized physics equations and may differ from real-world scenarios.

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