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Horizontal Projectile Motion Calculator

Calculate the landing distance and time of flight for an object launched horizontally from a height.

Result

Horizontal Distance (Range)
30.29 m
Time of Flight
2.02 s
Impact Speed
24.84 m/s

About the Horizontal Projectile Calculator

This calculator finds how far, how fast, and how long an object travels after launching purely horizontally from a height and falling under gravity, the classic ball-rolling-off-a-table scenario. It separates the independent horizontal and vertical motions to compute landing distance, flight time, and impact speed.

How It Works

You enter the launch height above the ground and the constant horizontal velocity at launch. The calculator first finds the fall time using only height and standard gravitational acceleration of 9.80665 m/s squared, since horizontal velocity has no effect on fall time for a purely horizontal launch. It multiplies that time by the horizontal velocity for the landing distance, and combines the horizontal velocity with the vertical velocity gained during the fall to get impact speed.

t = sqrt(2h / g); range = v x t; vertical velocity at landing = g x t; impact speed = sqrt(v^2 + (g x t)^2)

Formula & Methodology

Work it in three steps. First find fall time from height alone: t = sqrt(2h/g). Second, multiply that time by the constant horizontal velocity to get the range: range = v x t. Third, find the vertical velocity at landing (g x t) and combine it with the unchanged horizontal velocity using the Pythagorean theorem to get the total impact speed.

Examples

A ball rolling off a table

Launched horizontally at 15 m/s from a 20 m height, fall time is about 2.02 s, giving a range of roughly 30.3 m and an impact speed near 24.9 m/s.

A short, slow launch

Launched horizontally at 5 m/s from a 1.25 m height, fall time is about 0.50 s, giving a range of roughly 2.5 m and an impact speed near 7.0 m/s.

Advantages

  • Solves for three related quantities, time, range, and impact speed, from just two inputs, saving multiple formula lookups.
  • Correctly isolates fall time from horizontal velocity, avoiding the common misconception that a faster horizontal launch changes how long the object stays airborne.
  • Reports a single combined impact speed, useful for problems asking how fast something is moving the instant it lands.

Common Mistakes

  • Assuming a higher horizontal launch velocity makes the object fall faster, when fall time under horizontal launch depends only on height.
  • Confusing impact speed with the horizontal velocity alone, forgetting the vertical velocity gained during the fall must be combined with it.
  • Applying this horizontal-launch formula to a projectile launched at an upward or downward angle, where the vertical motion starts with a nonzero initial velocity.

Edge Cases to Watch For

  • A negative launch height is rejected with an error, since falling from a negative height is not a defined scenario here.
  • A height of exactly zero produces a fall time and range of zero, since the object starts already at ground level.
  • The calculation assumes no air resistance and a perfectly horizontal launch with zero initial vertical velocity; a launch at an upward or downward angle needs different projectile motion equations.

Common Use Cases

  • Physics students solving classic ball-off-a-table or object-launched-from-a-cliff kinematics problems.
  • Instructors building examples that isolate horizontal and vertical motion as independent components.
  • Hobbyists estimating landing distance for objects launched horizontally from a fixed height.
Written & fact-checked by the Calculateus TeamLast updated August 5, 2026How we verify our formulas

Frequently asked questions

How is this different from the angled Projectile Motion Calculator?

This calculator handles the specific case of an object launched perfectly horizontally from a height (like a ball rolling off a table), where the fall time depends only on height, not launch speed - the angled version handles launches at an upward angle from ground level, which is a different scenario with different equations for range and height.

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Conclusion

Because horizontal and vertical motion are independent under gravity, this calculator can determine fall time from height alone before the velocity input even matters. That separation is the core insight behind horizontal projectile motion, and the calculator makes it easy to see it play out numerically.