Calculate projectile motion

Estimate an ideal projectile’s flight time, range, peak height, and impact speed from launch conditions.

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ToolProjectile Motion Calculator
Input
Output
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Preview

How it works

Launch speed resolves into horizontal v cos θ and vertical v sin θ components. Vertical constant-acceleration motion finds ground time, then range is horizontal speed × time, peak height adds vy² ÷ 2g, and impact speed recombines components.

  • The acceleration constant is 9.80665 m/s².
  • The model assumes level ground at the supplied launch height and no air resistance.

Worked example

20 m/s at 45 degrees
Launched from ground level, the angle that maximises range
Input
											Speed metres per second: 20
Angle degrees: 45
Output
												Range metres: 40.789
Max height metres: 10.197
Flight time seconds: 2.884
Impact speed metres per second: 20
Range feet: 133.821

When to use this

Mechanics lessons predict ball range, game prototypes plot ideal arcs, and lab reports compare measured paths with vacuum equations.

Edge cases

  • A negative launch height places the ground-crossing origin below the chosen reference.
  • Air resistance changes range and time, especially for light or fast projectiles.
  • An angle near 90° has almost no horizontal range even though peak height is large.

References