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Projectile Motion Calculator

Enter the launch speed, angle and height to see how far a projectile travels, how high it goes and how long it stays in the air, with its flight path.

Rules last checked 10 November 2026Every step shown

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degrees above level

Height above the ground it lands on.

Distance travelled

40.79 m

Highest point
10.2 m
Time in the air
2.88 seconds
Speed when it lands
20 m/s

Launched at 20 m/s and 45°, it rises to 10.2 m and lands 40.79 m away after 2.88 seconds.

How it's worked out

  1. Across and up speeds20 × cos 45°, 20 × sin 45°14.142 and 14.142 m/s
  2. Time in the air2 × up speed ÷ g, g = 9.81 m/s²2.884 s
  3. Distance14.142 × 2.88440.79 m
  4. Highest pointup speed² ÷ (2 × g)10.2 m
Flight path
051015010203040

Distance (m) along the bottom, height (m) up the side.

  • This ignores air resistance, which shortens real throws and kicks, most of all for light or fast objects.

How it is worked out

The launch speed is split into an across part (speed × cos angle) and an up part (speed × sin angle). The across speed stays the same; gravity slows the up speed and then pulls the projectile down. The time in the air comes from when it returns to ground level, and the distance is the across speed times that time.

Launching from a height

Enter a launch height for something thrown from a hand, a cliff or a table. It stays in the air longer and lands further away.

Questions people ask

How far does a ball go at 20 m/s and 45 degrees?

About 40.8 m on level ground, ignoring air resistance. It reaches 10.2 m at its highest and lands after 2.88 seconds.

Which angle goes furthest?

45 degrees, when launched and landing at the same height and ignoring air resistance. From a height, a slightly lower angle goes further.

What value of gravity is used?

Standard gravity, 9.80665 m/s² (32.17 ft/s²).

Why do real throws fall short?

Air resistance slows the projectile all the way, so real ranges are shorter than these figures, most of all for light or fast objects such as shuttlecocks or golf balls.

Formula and rules last checked 10 November 2026Written and tested by the CalculatorDex teamReport a problem