Distance to Horizon Calculator
Enter your eye height above the ground and get the geometric distance to the horizon in kilometres and miles, the dip angle below horizontal, and the refraction-adjusted range.
Height unit
km
Geometric straight-line distance to the horizon
- 1
Inner term h(2R + h)
1.7 × (2 × 6,371,000 + 1.7) = 21,661,403 - 2
Horizon distance d = √(h(2R+h)) ÷ 1000
√21,661,403 ÷ 1000 = 4.65
How does this calculator work?
The horizon distance is d = √(h(2R+h)), where h is eye height and R is Earth's radius (6371 km). At 1.7 m the horizon is ≈4.65 km away. A refraction-adjusted version uses d = √(2Rh/(1−k)) with k ≈ 0.13 for standard atmosphere. The dip angle α = arccos(R/(R+h)) shows how far below horizontal the horizon sits.
Formula
How this is calculated
The horizon is the point where a line of sight from the observer, tangent to the Earth's surface, touches the ground. For a spherical Earth of radius R, the tangent from an eye at height h above the surface has length d = √(h(2R + h)), derived directly from the Pythagorean theorem applied to the triangle formed by the Earth's centre, the observer, and the tangent point. For typical human heights (h ≪ R), the h² term is negligible and the simpler approximation d ≈ √(2Rh) is accurate to better than 0.01%.
The default Earth radius is 6371 km (the IUGG mean radius, 2025 values unchanged). You can change it to model the Moon (1737 km), Mars (3390 km) or any other spherical body. Atmospheric refraction bends light slightly downward, extending the effective horizon by roughly 6–8% under standard conditions. The refraction-adjusted distance uses the commonly accepted terrestrial refraction coefficient k ≈ 0.13 (from ISO 1151 / geodesy literature): d_refr = √(2Rh / (1 − k)).
The dip angle is the angle below the true horizontal at which the horizon appears. For a ship officer or pilot it matters for sextant corrections. The formula is α = arccos(R / (R + h)), measured in degrees below horizontal.
Frequently asked questions
At eye level 1.7 m above the ground on Earth, the geometric horizon is about 4.65 km (2.89 miles). Atmospheric refraction extends this to roughly 4.93 km under standard conditions.
Because the formula is d ≈ √(2Rh): distance grows with the square root of height. Doubling h extends the horizon by a factor of √2 ≈ 1.41, so you need 4× the height for twice the range.
The atmosphere bends light toward the Earth's surface, making the horizon appear slightly farther than the purely geometric calculation. The standard refraction coefficient k ≈ 0.13 extends the horizon by about 7% over the geometric value.
Also known as
TG we-Calculate Editorial Team. (2026). Distance to Horizon Calculator [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/distance-to-horizon-calculator
TG we-Calculate Editorial Team. "Distance to Horizon Calculator." TG we-Calculate. 2026. https://we-calculate.com/calculator/distance-to-horizon-calculator.
TG we-Calculate Editorial Team, "Distance to Horizon Calculator," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/distance-to-horizon-calculator
@misc{wecalculate_distance_to_horizon_calculator, title = {Distance to Horizon Calculator}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/distance-to-horizon-calculator}}, year = {2026}, note = {TG we-Calculate} }
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