Horizon Distance Calculator
Calculate geometric line-of-sight and surface distance to the horizon from an observer height and reference-sphere radius.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Convert height and radius to the same SI unit, form the right triangle from the sphere center to the tangent point, then distinguish straight sight-line distance from surface arc distance.
d=sqrt((R+h)^2−R^2); s=R arccos(R/(R+h))
Worked example
At 2 m above a spherical surface of radius 6371 km, the geometric straight-line horizon is about 5.05 km away and the surface arc is nearly the same distance.
Assumptions and input details
Spherical reference surface, clear tangent line and positive radius. This is a geometric horizon only: atmospheric refraction, terrain, waves, obstacles, eye height uncertainty and target height are excluded. The entered radius is explicit rather than silently choosing a regional Earth model.
References: NOAA National Geodetic Survey: geometric horizon diagram and equations
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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