Horizon Distance at Sea Level: 2.77 Miles for a 6-Foot Observer

The distance to the horizon depends solely on the observer's height above the surface (assuming standard refraction and spherical Earth).

The Formula

d (miles) = 1.2246 × √h (feet) or d (km) = 3.5697 × √h (meters).

Derived from Pythagoras: (R + h)² = R² + d² → d ≈ √(2Rh) for h ≪ R (Earth radius R ≈ 3,959 mi / 6,371 km). The constant 1.2246 includes standard atmospheric refraction (k ≈ 0.13), which bends light downward, extending the geometric horizon by ~7.35%.

For a 6-Foot (1.83 m) Person

• **Geometric (no refraction):** √(2 × 3959 × 6/5280) = 2.57 mi.
• **With standard refraction:** 1.2246 × √6 = **2.77 miles (4.46 km).**

Practical Implications

• Ship's bridge (15 m / 50 ft): 13.5 mi / 21.7 km.
• Lighthouse (30 m / 100 ft): 19.1 mi / 30.7 km.
• Mountain (1,000 m): 113 km.

Caveats

• Refraction varies with temperature gradient (super-refraction / ducting can extend horizon 2×; sub-refraction shrinks it).
• Waves/swell hide lower portions of distant objects.
• Height = eye level, not top of head.

So at sea level, a 6-ft person sees **2.77 miles** to the horizon—where sky meets water, and curvature hides the rest.