Enter your height above sea level and choose your preferred unit system to calculate the distance to the horizon. The calculator returns the horizon distance using the spherical Earth formula, plus the ground arc distance and observation area — useful for sailors, hikers, and anyone curious about how far they can see.
Distance to Horizon
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Ground Arc Distance
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Observation Area
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Body Radius Used
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The horizon is the apparent line where the sky meets the ground (or sea) as seen from an observer near the surface of a spherical body. It is mathematically well-defined only when there are no obstacles blocking the line of sight — the classic example being standing on a flat beach facing the open ocean. Buildings, hills, and trees all reduce your practical visible horizon.
The standard formula uses the Pythagorean theorem. If R is the radius of the Earth and h is your height above sea level, the horizon distance d = √(h × (2R + h)). For everyday heights this simplifies closely to d ≈ √(2Rh). This calculator uses the full precise formula, and applies the correct radius for whichever celestial body you select.
At an eye height of 1.75 m above sea level on Earth, the horizon is approximately 4.7 km (about 2.9 miles) away. This is why tall people have a very slightly farther horizon than shorter people — but the effect is modest at ground level.
To see exactly 10 km to the horizon on Earth, you need to be approximately 7.85 metres above sea level. You can rearrange the formula to h = d² / (2R) for a quick approximation, where d is the desired distance and R is Earth's radius (~6,378 km).
Because the Moon has a much smaller radius (~1,737 km versus Earth's ~6,378 km), its surface curves more sharply. Standing at the same height of 1.75 m on the Moon, the horizon would be only about 2.4 km away — noticeably closer than on Earth.
Yes. The atmospheric refraction caused by light bending through layers of varying air density actually extends the visible horizon slightly beyond the geometric calculation — typically by about 7–8%. This calculator uses the geometric formula without an atmospheric correction, so treat results as a reliable theoretical lower bound rather than an exact observational measurement.
The horizon distance (d) is the straight-line distance through the air from the observer to the horizon point on the surface. The ground arc distance is the distance measured along the curved surface of the Earth between the point directly below the observer and the horizon point. For typical human-scale heights these two values are nearly identical, but they diverge at very high altitudes.
The formula works for any spherical body — only the radius changes. Selecting Mercury, Venus, the Moon, or the Sun substitutes that body's mean radius into the calculation, so you can see how different planetary sizes affect how far you'd see from the same elevation. It's a great way to appreciate just how large or small these worlds are compared to Earth.