Earth Bulge Calculator
Calculate spherical-Earth midpoint bulge for a straight chord spanning a surface distance.
Quick answer: Estimate Earth curvature bulge at the midpoint of a sightline. Coverage: Worldwide. No account is required.
Worked examples
- Eye height near sea level — With eyes about 1.7 m above sea level, the refracted-horizon estimate is roughly 5 km.
- 100 m viewpoint — At 100 m elevation above a clear horizon, the estimate increases to roughly 39 km.
- Antipode example — New York's antipodal coordinate is approximately -40.71, 105.99.
Limits & appropriate use
Terrain intelligence carries one dominant limit: the model sees bare earth at ~90 m spacing with metres of vertical error, and is blind to canopies, walls and wires. Every downstream answer inherits it — profiles show terrain truth with noisy amplitude, line-of-sight verdicts are pending trees, horizons assume open ground, and solar radiation averages assume an unshaded panel. The second limit is temporal: climate letters and hardiness zones are thirty-year character, not this year's behaviour, and seismicity is a mood, not a hazard model. Each result here is printed with its recipe precisely so these boundaries travel with the number.
The value proposition is screening-grade truth at zero cost: orientation for sites, gardens, antennas, shoots and curiosity, with the upgrade points clearly marked. When money or safety attaches to the answer — tower siting, flood insurance, structural shading, avalanche terrain — the escalation is professional: licensed survey, certified shade studies, regulatory flood determinations and geological hazard services. A good free tool makes that ladder visible instead of pretending to be the top of it.
- Construction and tower siting → licensed topographic survey.
- Flood decisions → regulatory determinations (FEMA/FIRM in the US).
- Solar finance → certified shade and production studies.
Data & methodology
Spherical geometry comparing Earth radius with the half-chord offset at the midpoint. Elevation and radiation use Open-Meteo's open API on Copernicus/ERA5 datasets; visibility math adds standard refraction (k = 0.13). US hydrology/flood layers come from USGS and FEMA public services.
For source details, licences and model limitations, see Data Sources and Methodology.
Related tools
Category: Earth Science. Results are intended for everyday analysis and planning unless a page explicitly states otherwise.
How to use
- 1Enter sightline distance in kilometres.
- 2Read midpoint bulge.
- 3Use radio/LOS tools if refraction and antennas matter.
Methodology & accuracy
Spherical geometry comparing Earth radius with the half-chord offset at the midpoint. Read more on the methodology page.
Frequently asked questions
Does refraction change this?
The geometric bulge is a shape calculation; apparent optical/radio paths can differ because of atmospheric refraction.
Earth model?
A spherical mean-radius approximation.