Horizon & Earth Curvature Calculator
How far can you see? The distance to the horizon depends on your height above the surface. From sea level at 1.7m height, you can see about 4.7 km. Climb a 100m tower and the horizon extends to 36 km. This calculator also shows how much of a distant object is hidden behind Earth's curvature, explaining why ships disappear "hull first" over the horizon.
Target Object
How We Calculate This
Horizon distance uses d = √((R+h)² - R²) ≈ √(2Rh) for small h, where R = 6,371,000 m (mean Earth radius). Curvature drop at distance x is approximated as x²/(2R). Target visibility compares combined horizon distances.
Frequently Asked Questions
How is horizon distance calculated?
The geometric formula is d = √(2Rh + h²), where R is Earth's radius (6,371 km) and h is observer height. For small heights, this simplifies to d ≈ √(2Rh), or approximately d ≈ 3.57√h (km, h in metres).
Does atmospheric refraction affect this?
Yes! Light bends in the atmosphere, typically extending the visible horizon by about 8%. This calculator shows the geometric horizon; actual visibility may be slightly greater in clear conditions.
Why do ships disappear hull-first?
Because Earth curves away from the observer. The hull is closest to the water and disappears first as the ship moves beyond the horizon. The mast, being higher, remains visible longer.
How much does Earth curve per kilometre?
Earth drops about 8 cm per kilometre, or about 8 metres over 10 km. The formula for drop at distance d is approximately d²/(2R), where R is Earth's radius.
Can I see the Eiffel Tower from 100 km away?
The Eiffel Tower is 330m tall. From 100 km away, about 320m would be hidden by curvature (assuming you're at sea level). Only the very tip would be geometrically visible, though atmospheric effects could change this.
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