Result
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Facts and limits of this method
| Formula without refraction | d (km) = 3.57 × √(height, m) |
|---|---|
| Formula with refraction | d (km) = 3.86 × √(height, m) |
| For a height of 1.7 m | ≈4.65 km without refraction, ≈5.03 km with refraction |
| Earth's radius | Taken as 6371 km (mean radius) |
When it misleads you
- The formula assumes a perfectly smooth spherical Earth with no mountains, trees or other obstructions on the line of sight — in reality, terrain can either open up a farther view or block the horizon sooner than the calculated distance.
- Atmospheric refraction (the bending of light rays in the atmosphere) extends the visible horizon distance by about 8% on average; the 3.86 coefficient is a common approximation for standard atmospheric conditions, not a physical constant — actual refraction differs under non-standard pressure or temperature.
- The calculation doesn't account for air clarity (haze, fog) — even if the horizon is geometrically visible, poor visibility conditions may prevent seeing it with the naked eye at the full calculated distance.
- The result is the straight-line distance along the line of sight (accounting for Earth's curvature), not the arc length along the planet's surface — at the heights typical for this calculation, the difference between them is negligible.
How it is calculated
The entered height is converted to meters (multiplied by 0.3048 if feet is selected).
The distance to the horizon is computed using the approximate formula d = k × √h, where k is a coefficient (3.57 without refraction or 3.86 with it) and h is the observer's height in meters.
This formula is a simplification of the exact geometric relationship d = √(2Rh + h²), where R is Earth's radius; for observer heights small compared to Earth's radius, the h² term can be neglected, giving the square-root-of-height formula.
The result in kilometers is additionally converted to miles by dividing by 1.609344.
Questions and answers
Why does the horizon appear farther with refraction?
The atmosphere bends light rays, so light from points beyond the geometric horizon still reaches the observer's eye — the visible horizon ends up about 8% farther than pure sphere geometry predicts.
How much farther can you see from a greater height?
The distance grows as the square root of height, not linearly — to see twice as far, you need to climb four times as high.
Does the calculator account for terrain?
No, the calculation assumes a perfectly smooth sphere with no mountains or other obstructions — in reality, terrain can either open up a farther view or block the horizon sooner than the calculated distance.
Is my data sent anywhere?
No, the whole calculation runs in your browser.