Distance to Horizon Calculator

The horizon is the apparent boundary where a curved planetary surface blocks the direct line of sight. As an observer rises above the surface, the tangent point moves farther away and the visible horizon expands. This calculator models the observer, planet center, and tangent point as a right triangle. It uses d = √(2Rh + h²), where d is straight-line distance to the horizon, R is planetary radius, and h is observer height above the surface. The calculator converts the entered radius to meters, evaluates the exact geometric equation, and reports kilometers. For heights that are very small compared with Earth's radius, the h² term contributes little and the familiar approximation d ≈ √(2Rh) works well. At an eye height of two meters on a smooth spherical Earth, the geometric horizon is about 5.05 kilometers away. At one hundred meters it is about 35.70 kilometers away. Horizon range grows with the square root of height, so doubling observer height does not double viewing distance. To double geometric range, height must increase by roughly a factor of four. The result represents the direct tangent line, not distance measured along the curved surface. At ordinary terrestrial heights those values are close, but they diverge at great altitude. The model also treats the body as a perfect sphere. Earth is an oblate spheroid, and local curvature varies with latitude and viewing direction. Mountains, waves, buildings, trees, and elevation of the target can alter what is actually visible. If both observer and target are elevated, calculate each one's horizon distance and add them for an approximate maximum line-of-sight separation. Atmospheric refraction usually bends light slightly toward Earth's surface and can extend the optical horizon beyond the purely geometric value. Weather gradients can increase, decrease, or distort that effect, while radio propagation often uses an effective Earth-radius model. This tool deliberately reports the uncorrected geometric baseline so assumptions remain clear. It is useful for navigation intuition, photography planning, tower sight lines, astronomy, and classroom geometry. Do not use a simple horizon estimate as the sole basis for maritime navigation, radio engineering, aviation separation, or safety-critical visibility decisions.