Popular Heights Table
| Height | Distance to Horizon (km/mi) |
|---|---|
| Eye level (1.7m / 5.6ft) | 4.8 km / 3.0 mi |
| Standing (1.8m / 6ft) | 5.0 km / 3.1 mi |
| 10-story building (30m / 100ft) | 19.6 km / 12.2 mi |
| Ship deck (10m / 33ft) | 11.3 km / 7.0 mi |
| Airplane (10km / 33k ft) | 357 km / 222 mi |
| Mount Everest top (8.8km / 29k ft) | 336 km / 209 mi |
Formula and Steps
Distance to horizon follows d ≈ 3.57 × √h (km, h in meters) for geometric view, adjusted by refraction factor k: d = 3.57 × √(h / k).
- Convert height h to meters.
- Apply square root: √h.
- Multiply by 3.57 (Earth’s radius factor).
- Divide by √k for refraction (k=1 geometric, k=0.14 standard).
Visual Height Comparison
Real-World Examples
- Sailors spot ships’ masts first over horizon due to height advantage.
- Pilots from 35,000ft see 245 miles ahead on clear days.
- From beaches, horizon appears closer in humid air from refraction bend.
- Mountain climbers gain extra view range with elevation.
Cultural Notes
Ancient sailors measured horizon distances to estimate landfalls, varying by metric/imperial traditions—British nautical miles (1.852km) vs. statute miles affect ship logs.
Frequently Asked Questions
Why two distances: geometric vs. visual?
Geometric ignores air bend; visual adds refraction for actual sight line over curve.
Does temperature change results?
Yes, warmer air increases refraction; tool’s high humidity option simulates this.
Earth flatness assumption?
Formulas use spherical Earth radius of 6371km; precise for most heights.
Height from sea level or ground?
Eye height above surface; for hills, use total from sea level minus terrain.
References
- Wikipedia, “Horizon”, https://en.wikipedia.org/wiki/Horizon
- Ringbell, “Distance to the horizon”, https://www.ringbell.co.uk/info/hdist.htm
- Omni Calculator, “Distance to Horizon”, https://www.omnicalculator.com/physics/distance-to-horizon
- Reddit r/dataisbeautiful, “Distance to the horizon when viewed from various heights”, https://www.reddit.com/r/dataisbeautiful/comments/czmwxs/distance_to_the_horizon_when_viewed_from/