Distance to Horizon Calculator - Line of Sight Range

The distance to horizon calculator converts an observer's height above sea level into the straight-line distance to the visible horizon, with optional adjustment for atmospheric refraction and a second observer height for two-way line-of-sight calculations. Reach for it whenever you need to know how far you can see from a beach, a lighthouse, a hilltop, an aircraft, or an antenna mast.

• • Sailing and coastal navigation: predict when a lighthouse, headland, or ship first appears over the horizon.
• • Hiking and summit planning: estimate the view range from a peak or ridge before the climb.
• • Antenna and radio link planning: size a VHF or microwave link by computing the maximum line-of-sight between two masts.
• • Physics and earth-science homework: verify textbook horizon distance, curvature drop, and dip angle results.

The model behind the calculator is d = sqrt(2 R h + h^2), where R is the mean Earth radius and h is the observer's height, combined with the standard refraction factor k = 1.14. For two observers at heights h1 and h2, the line-of-sight distance is d = sqrt(2 R h1 k) + sqrt(2 R h2 k), the sum of each observer's horizon range.

Refraction comes from a real vertical gradient of air density, so the altitude temperature calculator is a useful companion for understanding the temperature profile that drives the bending this calculator applies.

The calculator takes the observer's height, the target's height, a refraction factor, and an Earth radius, then solves the horizon geometry. The headline result is the refracted horizon distance d = sqrt(2 R h k); supporting outputs include the geometric horizon, the two-observer line of sight, and the horizon dip angle.

• R: mean Earth radius in metres (6371.0088 km by default from the IUGG).
• h: observer's eye or instrument height above mean sea level in metres.
• h_target: height of the second observer or target above sea level in metres (0 for a sea horizon).
• k: atmospheric refraction factor; 1.0 for none, 1.14 for standard sea-level air, 1.17 for a strong temperature inversion.
• alpha: angle below the true horizontal at which the observer sees the refracted horizon, returned in degrees.

The barometric formula for refraction assumes the refractive index of air decreases linearly with height, giving the constant factor k = 7/6 in a standard sea-level atmosphere. Use lower k for cold polar air, higher k for a strong temperature inversion that produces a superior mirage.

For a high observer, the calculator uses the full d = sqrt(2 R h + h^2) form rather than the small-h approximation, so the result stays accurate for a commercial jet at 10000 m where h^2 begins to matter.

According to the NOAA Ocean Service, the distance to the horizon for an observer at height h above sea level is approximately d = sqrt(2Rh) and is extended by atmospheric refraction under standard conditions.

The barometric formula that produces refraction runs through the same pressure profile the boiling point altitude calculator uses for the boiling point of water at altitude, so the two calculators share the same vertical air column.

Four ideas make the result predictable: why the Earth curves away from you, why height matters as a square root, why a thin atmospheric layer bends light, and why the horizon looks farther than pure geometry.

These four ideas compound in the line-of-sight formula, which is why nautical chart horizon tables use h1 + h2.

The vertical temperature gradient that bends light also controls where cumulus clouds form, so the cloud base calculator is a good companion for understanding how the same air column shapes both phenomena.

Enter your observer height, target height (often 0 for a sea horizon), and refraction factor. The result panel updates as you type.

1. 1 Enter the observer height: Type the height of your eye, camera, telescope, or antenna. Default 2 m matches a person on the beach.
2. 2 Choose the height unit: Switch between meters and feet for imperial heights like 5280 ft.
3. 3 Enter the target height: Type the second observer's height, or leave 0 for a sea horizon.
4. 4 Pick the refraction factor: Leave 1.14 for standard air, drop to 1.0 for cold dry air, or raise to 1.17 for a temperature inversion.
5. 5 Set the Earth radius: Use 6371.0088 km (IUGG mean), 6378.137 km (equatorial), or 6356.752 km (polar).
6. 6 Read the result panel: The headline card shows the refracted distance in your chosen unit; the secondary list shows geometric, line-of-sight, miles, nautical miles, and dip angle.

A pilot at 10000 m flying toward a 30 m lighthouse: enter 10000 for observer height, set target height to 30 m, leave the refraction factor at 1.14. The refracted horizon reads about 381.1 km, the geometric horizon about 357.1 km, and the two-observer line of sight extends to about 402.0 km.

Humidity shifts the air density gradient and therefore the refraction factor, so the absolute humidity calculator helps explain why humid mornings push the visible horizon farther than dry winter afternoons.

A single horizon distance turns vague 'how far can I see' questions into numbers that drive real decisions on land, sea, and air.

• • Plan coastal navigation: predict when a lighthouse, headland, or ship appears over the horizon given your bridge height.
• • Size amateur radio links: decide whether two antenna masts have line of sight at VHF/UHF frequencies without a path profile tool.
• • Pick a summit viewpoint: compare a 500 m hill against a 1500 m peak to see how much extra horizon each climb buys.
• • Calibrate photography framing: estimate foreground distance so the curvature does not crop your coastline subject.
• • Teach earth-shape intuition: use the same numeric output in a physics class to make Earth's curvature tangible.
• • Cross-check instruments: compare a GPS range or radar horizon against the geometric value to spot unusual atmospheric conditions.

The calculator reports both the geometric and the refracted horizon distance, so you can compare the textbook horizon with the practical one your eyes actually see.

Distance to horizon answers how far you can see on the local scale, while the air density calculator answers how dense the air column is that bends the light along the way.

The calculator returns a clean geometric number, but real horizons shift with atmospheric conditions, latitude, and observer setup. Four factors explain why.

• • The formula assumes a smooth spherical Earth and a smoothly varying atmosphere. Local terrain, hills, and buildings can hide the horizon before the geometric limit.
• • At very low observer heights (under 0.5 m) wave action and surf push the practical horizon closer than the calculator predicts.
• • Above about 100 km altitude the air density becomes so thin that k approaches 1.0 and the simple k = 1.14 assumption no longer holds.

According to the SDSU Atmospheric Refraction Page, near the horizon the atmosphere refracts light rays downward by an amount equivalent to multiplying the geometric horizon distance by a factor of about 7/6 (1.14) for standard sea-level conditions.

According to the NGA WGS 84 Reference, the IUGG defines the mean Earth radius as 6371.0088 km, with an equatorial radius of 6378.137 km and a polar radius of 6356.752 km.

The same vertical pressure gradient that bends light also drives the boiling point shift the boiling point elevation calculator computes, so reading both calculators side by side reveals the full atmospheric column.