Line of Sight to Horizon Calculator

How to use this calculator

Enter the observer height above the local surface. Add a target height when the object is raised above the same surface. Choose the shared height unit. Select the output unit that matches your work. Keep the default Earth radius for normal Earth calculations. Change it only for a special body or local model.

Select a refraction mode. Choose none for pure geometry. Choose the radio factor for common antenna planning. Use a custom factor when your field method gives one. Enter a required range when you want a pass or fail visibility check. Press calculate to see the horizon distance, target range, dip angle, curvature values, and required height.

Example data table

Horizon visibility planning

Why height changes everything

Line of sight to the horizon depends mainly on height. A higher observer sees farther because the tangent point moves away. This is true on land, at sea, and from towers. The effect is not linear. Doubling height does not double the horizon distance. The square root relation makes each extra unit of height less powerful than the previous one.

Curvature and the tangent point

The calculator treats Earth as a sphere. It draws a straight line from the observer to the tangent point. That tangent point is the geometric horizon. The formula uses Earth radius and observer height. For most practical heights, the small h squared term is tiny. It is kept here for better accuracy. This helps tall structures, aircraft, drones, and high observation points.

Target height and mutual visibility

A target above the surface has its own horizon. A lighthouse, mast, tower, ridge, or antenna can be visible beyond the observer only horizon. The total line of sight is the sum of both horizon distances. This is why two elevated points can connect across much longer ranges. The tool also tests a required range. It reports whether the target is inside the visible path.

Refraction and radio paths

Air bends light and radio waves slightly. This can extend the apparent horizon. The effect changes with weather, humidity, pressure, and temperature layers. The standard radio setting uses an effective Earth radius factor near four thirds. It is common for quick antenna checks. Optical sighting can use a smaller factor. For strict surveying, use no refraction or a project specific value.

Useful planning checks

The result includes dip angle, curvature drop, and midpoint bulge. Dip angle helps with cameras and optical instruments. Curvature drop shows how much the surface falls away over a chosen range. Midpoint bulge helps explain path clearance. These values are estimates. They do not include terrain, buildings, vegetation, waves, haze, or diffraction. Always compare the output with maps and field data.

Good input habits

Use height above the local surface, not height above sea level, unless both points use the same reference surface. Use target height only when the visible part is raised. Choose nautical miles for marine work. Choose miles, kilometers, feet, or meters for general work. Keep several decimal places when comparing small height changes. Use fewer decimals for simple public explanations.

Small changes can matter near the limit. A boat mast, ridge line, or camera tripod may add useful distance. Yet a visible horizon is not a guaranteed clear view. Fog, rain, glare, and heat shimmer can hide objects. Radio paths may still fail because of noise or interference. Optical paths may fail because of contrast. Treat the calculator as a first filter. Use it to compare setups quickly. Then verify critical routes with maps, measurements, and real observations. Document assumptions when sharing results with another planning team.