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Projectile Motion Calculator

Calculate the range, maximum height and flight time of a projectile from its launch speed, angle and launch height (no air resistance).

How to use

  1. 1Enter the launch speed, angle above horizontal and starting height.
  2. 2Read the flight time, range and peak height.

How it's calculated

vₓ = v cos θ, v_y = v sin θ. Time = (v_y + √(v_y² + 2g h₀)) ÷ g. Range = vₓ × time. Max height = h₀ + v_y² ÷ 2g.

Frequently asked questions

What angle gives the longest range?

45° when launching from ground level with no air resistance. From a height, the best angle is a bit lower.

Why is real range shorter?

Air resistance slows the projectile, especially fast or light objects. This calculator ignores drag.

What value of g is used?

Standard gravity, 9.80665 m/s².