Flat vs Round Earth Calculator
Compare horizon distance on a spherical Earth versus a flat surface model from observer height and see how curvature limits visibility.
Horizon Distance on a Round vs Flat Earth
On a spherical Earth, curvature limits how far you can see from a given height. On an infinite flat plane, there is no geometric horizon caused by surface curvature.
Round Earth Horizon Formula
$$d = \sqrt{(R + h)^2 - R^2}$$where \(R\) is Earth radius and \(h\) is observer height above the surface. For small heights, \(d \approx \sqrt{2Rh}\).
Example: from 2 m height, the horizon is about 5.05 km on a round Earth. A flat surface model has no curvature limit at the same height. Related tools: Distance to Horizon Calculator, Earth Curvature Calculator, and Antipode Calculator.
Frequently Asked Questions
Why is the round Earth horizon distance finite?
Curvature drops the surface below your line of sight. The tangent point sets the maximum visible distance.
Does a flat Earth have a horizon?
An infinite flat plane has no curvature-based horizon. Visibility is limited by atmosphere, obstacles, and refraction instead.
What Earth radius should I use?
This tool uses the mean radius 6,371 km, which matches standard horizon calculations.
How does observer height affect horizon distance?
Horizon distance grows with the square root of height. Doubling height increases horizon distance by about 41%.
Does atmospheric refraction change the result?
Refraction can extend the visible horizon by roughly 8% under standard conditions. This tool uses the geometric formula without refraction.
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