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Projectile Impact Velocity Calculator

Enter the initial velocity, drop height, and gravity to find the impact velocity.

How it is calculated

The tool uses v = √(v₀² + 2 g h), from energy conservation with no air resistance. v₀ is the starting speed in m/s, h the vertical drop in metres, and g the gravitational acceleration in m/s². If you leave g empty it uses 9.80665 m/s². The result is also shown in km/h (the m/s value times 3.6), together with the speed gained, v − v₀. Only the vertical drop matters: the launch direction (up, down or sideways) does not change the speed on reaching the lower level, as long as v₀ is its speed. Negative speeds, heights or gravity return no result. A value of g = 0 simply gives back v₀.

Worked example

An object thrown at v₀ = 5 m/s from a height of 20 m with standard gravity. First v₀² = 25. Next 2 × 9.80665 × 20 = 392.266. The sum is 417.266, and its square root is 20.43 m/s. In km/h that is 73.54, and the speed gained during the fall is 20.43 − 5 = 15.43 m/s. A drop from rest at the same height would reach 19.81 m/s with g = 9.81, so the 5 m/s start adds only a small amount.

Try this example →

Common mistakes

  • Adding speeds instead of squares: 5 + 19.81 gives 24.81, but the correct combination under the root gives about 20.43. The two contributions add as energy, not as speed.
  • Entering the height in centimetres, feet or kilometres. It must be metres, and the initial speed must be in m/s, not km/h.
  • Expecting the launch angle to matter. For the speed at a lower level it does not; the tool only needs the speed and the drop.
  • Using the result for a long fall through air. There is no drag here, so a skydiver or a light object reaches far less than the figure shown, because it is limited by terminal speed.
  • Typing a negative height to mean upward motion. Negative heights are rejected; use a positive drop and a positive starting speed.

About this calculator

When an object falls or is launched with some initial velocity and then drops a vertical height h, its impact speed follows directly from energy conservation: v = √(v0² + 2·g·h), where v0 is the initial velocity, g is gravitational acceleration, and h is the drop height. This comes from the same kinematic equation set as v² = v0² + 2·a·d, just applied to free fall.

This calculator solves for that final impact velocity given the initial speed, drop height, and gravity value (letting you adjust g for other planets or scenarios), a standard calculation in introductory physics classes and basic ballistics or drop-test engineering — useful for anything from a homework problem about a ball thrown off a building to estimating impact speed in a packaging drop test.

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