Distance to Horizon Calculator
Distance to horizon calculator — find how far the horizon is visible from a given height, with atmospheric refraction correction.
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Enter a height, then press calculate.
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Enter a horizon distance, then press calculate.
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Enter both heights, then press calculate.
The Geometry Behind It
The line of sight from the observer to the horizon is tangent to Earth’s surface, forming a right triangle with Earth’s radius. With standard atmospheric refraction, the practical approximation d ≈ 3.86 × √h is used (h in meters, d in kilometers) — the horizon appears about 8% farther away.
Verified anchor example: eyes at 1.7 m → horizon 4.6542 km (no refraction) or 5.0328 km (with standard refraction).
Frequently Asked Questions (FAQ)
What is the distance-to-horizon formula?
For an observer at height h above sea level, the line-of-sight distance to the horizon is d = sqrt(2 × R × h), with R = 6,371,000 meters (Earth’s mean radius). With standard atmospheric refraction, the practical approximation d = 3.86 × sqrt(h) is used, with h in meters and d in kilometers. Verified example: eyes at 1.7 m see the horizon 4.6542 km away without refraction, or 5.0328 km with standard refraction.
Why are there options with and without atmospheric refraction?
The atmosphere bends light slightly downward, so the horizon appears about 8 percent farther than pure geometry. The no-refraction formula gives a theoretical lower bound, while the 3.86 factor accounts for bending under standard atmospheric conditions. For navigation, photography, and amateur radio, use the refraction-corrected result.
How far is the horizon for eyes 1.7 m high?
4.65 km (2.89 miles) without refraction, or 5.03 km (3.13 miles) with standard atmospheric refraction.
How do you compute height from an observed horizon distance?
Invert the formula: h = d² / (2 × R). If the horizon line is 10 km away, your eye height is about 7.85 m above sea level (no refraction). This calculator’s Height from Distance mode computes it automatically, including the refraction-corrected version.
How does the two-point mode work, e.g. for a lighthouse?
The maximum line-of-sight distance between two elevated points is the sum of their horizon distances: d = d1 + d2. Example: a 50 m lighthouse and an observer’s eye 10 m above the sea can see each other up to 36.53 km, or 39.50 km with standard refraction.
How accurate is this horizon distance calculator?
The formula assumes Earth is a perfect sphere of radius 6,371 km and a flat sea surface. Actual refraction varies with temperature, pressure, and humidity, so treat the refraction-corrected result as an estimate. For casual use, navigation, photography, and tower planning, the accuracy is more than sufficient.
How far is the horizon from the top of Mount Everest?
From the summit of Everest (8,848.86 m), the geometric horizon is 335.79 km (208.65 miles) away. For comparison, from 100 m height it is 35.70 km.
Which units does this calculator support?
Meters, kilometers, miles, and feet for all inputs. Results are always shown in kilometers and miles, plus meters or feet as a bonus. For a more complete length unit conversion, see our Length Unit Converter tool.
Free tool by NRTechStudio