The curvature of a planet hides distant objects below the horizon. From a beach (eye height 1.7 m) the horizon is only about 4.7 km away; from an airliner at 11 km it is about 375 km. Atmospheric refraction usually lets you see a little farther.
How to use the Distance to Horizon Calculator
- Height above the surface
- Celestial body
- Custom radius
Results update as you type, every field has its own unit menu, and everything is calculated in your browser.
How it works
Choose the celestial body (or enter a radius) and your height above the average surface.
Inputs explained
| Field | What to enter |
|---|---|
| Height above the surface | Units: m, cm, mm, km, in, ft … |
| Celestial body | Choose one: Earth, Moon, Mars, Mercury … |
| Custom radius | Units: km, m, mi, nmi, ft |
What each result means
- Distance to the horizon = sqrt(2×[R]×[Height above the surface] + [Height above the surface]^2)
- With standard refraction (Earth, k = 7/6) = sqrt(2×[R]×7÷6×[Height above the surface])
- Horizon dip angle = deg(acos([R]÷([R] + [Height above the surface])))
Example values
How the main result changes when Height above the surface changes and everything else stays at the example values above:
| Height above the surface (m) | Distance to the horizon (km) |
|---|---|
| 0.85 | 3.291 |
| 1.28 | 4.0306 |
| 1.7 | 4.6542 |
| 2.13 | 5.2035 |
| 2.55 | 5.7002 |
| 3.4 | 6.582 |
Formula
d = √(2·R·h + h²) ≈ 3.57·√h km (h in m, on Earth)
Worked example
Inputs — Height above the surface: 1.7 m; Celestial body: Earth.
Results — Distance to the horizon = 4.6542 km; With standard refraction (Earth, k = 7/6) = 5.0271 km; Horizon dip angle = 0.0419 °.
Key terms
- Horizon
- Where the line of sight touches the curved surface.
Frequently asked questions
How far is the horizon at sea?
About 4.7 km for an eye height of 1.7 m.
Why can I sometimes see farther?
Atmospheric refraction bends light around the curve.
How far can you see from Mount Everest?
Roughly 335 km in theory.
Is the horizon farther on the Moon?
No – the Moon is smaller, so the horizon is closer (about 2.4 km at 1.7 m).