Calculate how far you can see to the horizon based on observer elevation, atmospheric refraction, and target height using Earth geometry.
The distance to horizon calculator determines the maximum distance an observer can see to the geometric horizon based on their elevation above the Earth's surface. Using the relationship between observer height and Earth's curvature, it computes both the geometric (ideal) and refracted (atmospheric) horizon distances.
For an observer at sea level (eyes at 1.7 m), the horizon is roughly 4.7 km away. Climbing higher dramatically increases visibility — from a 100-meter hill, you can see about 36 km. This relationship follows a square-root function, so each additional meter of elevation yields diminishing returns in horizon distance. The calculator also accounts for atmospheric refraction, which typically extends the visible horizon by about 7% under standard conditions.
Mariners, pilots, surveyors, and telecommunications engineers all rely on horizon distance calculations for navigation, antenna placement, line-of-sight radio links, and search-and-rescue planning. This tool also computes the maximum visibility distance to elevated targets (like ships, buildings, or mountains) by combining observer and target horizon distances.
Knowing the distance to the horizon is essential for navigation, construction planning, and telecommunications. Mariners need it to estimate when landmarks or ships will appear over the horizon. Radio engineers calculate it for antenna placement and microwave link budgets. Photographers use it to plan shots, and hikers use it to estimate visibility from mountain peaks. This calculator handles both simple queries and professional use cases with refraction and target height inputs.
Geometric horizon distance: d = √(2·R·h + h²) where R = 6371 km and h is observer height in km. Refracted distance uses effective radius R_eff = k·R where k ≈ 1.07. Total visibility to a target: d_total = d_observer + d_target. Dip angle: θ = arccos(R / (R + h)).
Result: 36.94 km refracted horizon distance
At 100 m elevation with standard refraction (k=1.07), the effective Earth radius is 6817 km. The horizon distance is √(2 × 6817 × 0.1 + 0.01) ≈ 36.94 km.
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Standing at 1.7 m (average eye height), the geometric horizon is about 4.65 km (2.9 miles). With atmospheric refraction, it extends to roughly 4.83 km.
The refraction coefficient (k) accounts for atmospheric bending of light, typically 1.07 for standard conditions. It increases in temperature inversions and decreases in dry, clear air.
This calculates distance to the geometric horizon. Line-of-sight between two elevated points is the sum of both horizon distances, which this calculator supports via the target height input.
The geometry involves a right triangle tangent to a circle; Pythagoras theorem yields d² = 2Rh + h², which simplifies to d ≈ √(2Rh) for small heights. Use this as a practical reminder before finalizing the result.
Radar uses a refraction coefficient of about 4/3 (1.33) rather than the optical 1.07, so radar horizon is slightly farther than visual horizon.
No. This assumes a smooth spherical Earth. Mountains, valleys, and buildings will block the actual line of sight before the geometric horizon.