Earth Curvature Calculator
Enter distance to calculate the simple spherical-Earth curvature drop before atmospheric refraction or terrain effects.
By Aryan Khan, Founder & Editor · Updated October 2026
For example, over 10 miles the surface drops 20.3 metres (about 67 feet) below a level tangent — the famous '8 inches per mile squared' rule, computed exactly.
How to use Earth Curvature Calculator
Level at your feet is not level at the horizon. Measure the difference:
The Earth Curvature Calculator computes how far the Earth's surface falls below a horizontal tangent over a given distance, on a spherical Earth. Enter the distance and read the drop in metres, feet or inches — the geometry behind horizon dip, long sight lines and a century of shoreline demonstrations.
- 1Enter the surface distance in kilometres.
- 2Read the geometric drop in metres and feet.
- 3Account separately for refraction, observer height and terrain if planning a sightline.
What people use Earth Curvature Calculator for
1. Judging what should be visible
A lighthouse, a skyline, a wind farm across the water: the drop over the intervening distance is the first term in whether it can show. The Hidden Height Calculator finishes the argument with your eye height added.
2. The shoreline test, done right
Chicago's skyline from the Michigan shore is about 53 miles — at that range the drop is roughly 570 m of geometry that refraction and tower height then negotiate with. Compute the drop first; argue about the rest second.
3. Surveying and levelling intuition
Precise levelling corrects for curvature run by run (about 0.08 m at 1 km) — this page is that correction, generalised to any distance.
4. Photography claims, checked
Long-lens photos across bays invite curvature claims in both directions. The drop over the photo's distance is a five-second calculation that settles the geometry half of the argument.
Worked examples
The old rule says drop ≈ 8 inches × (miles)². Exact spherical geometry at 1 mile gives 0.203 m — 8.0 inches. At 10 miles the rule predicts 800 inches (20.3 m) and geometry agrees to the centimetre. A rare folk formula that survives audit.
At 10 km the drop is 7.85 m — a two-storey building's worth. Anything shorter than that at 10 km, viewed from ground level with no refraction, is below the tangent line's world entirely.
Curvature drop by distance (spherical, no refraction)
Computed as R(sec(d/R) − 1) — the calculator's own formula.
| Distance | Drop | In feet |
|---|---|---|
| 1 km | 0.08 m | 0.26 |
| 1 mile | 0.20 m | 0.67 |
| 5 km | 1.96 m | 6.4 |
| 10 km | 7.85 m | 25.7 |
| 10 miles | 20.33 m | 66.7 |
| 50 km | 196.21 m | 643.7 |
| 100 km | 784.89 m | 2,574.7 |
Drop grows with the square of distance (the d²⁄2R approximation is within a percent out to ~100 km). Refraction bends light downward and reduces the effective drop — typically by roughly a seventh under standard conditions.
See the geometric effect of a curved Earth over distance
Over short everyday distances Earth curvature is tiny, but it becomes measurable across long sightlines. The calculator uses a simple spherical model with the mean Earth radius to estimate geometric drop over the distance you enter.
This is not a complete visibility model. Observer height, target height, terrain and atmospheric refraction all affect whether two objects can actually see each other. Pair this value with horizon and elevation tools when doing practical line-of-sight work.
How to interpret the result
The most common errors come from using a correct result to answer the wrong geographic question. Keep these points in mind for Earth Curvature Calculator:
- Treat climate and hardiness outputs as 30-year character, not this year's weather: a zone tells you what winters usually allow, and microclimates — walls, slopes, urban heat — shift a real garden half a zone either way.
- Remember that elevation models see bare terrain: no buildings, no forest canopy. A line-of-sight 'clear' verdict can still be blocked by a wood, and a horizon distance assumes open ground — treat results as the terrain baseline, then add land cover from local knowledge.
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 using a mean Earth radius of 6,371.0088 km.
For source details, licences and model limitations, see Data Sources and Methodology.
Key terms worth knowing
- DEM
- Digital elevation model: a grid of terrain heights, e.g. Copernicus GLO-90.
- Refraction coefficient
- The standard 0.13 factor bending sightlines over the curvature.
Editorial guidance: MapBench explains the method and limitations so the tool can be used as a transparent reference, not as a black-box answer. For legal boundaries, safety-critical routing, surveying, engineering, regulated decisions or official statistics, verify the result with the responsible authority or a qualified professional.
Category: Earth Science. Results are intended for everyday analysis and planning unless a page explicitly states otherwise.
Method, assumptions & limits
- This tool’s method
- Spherical geometry using a mean Earth radius of 6,371.0088 km.
- Before relying on the answer
- Check the location, height units and any model options shown by this calculator. A terrain lookup and a geometric Earth model answer different questions.
- What the result cannot establish
- Local terrain, atmospheric conditions and source resolution can matter more than numerical rounding. Do not use a planning result for safety-critical work.
Coverage: Worldwide. Search, basemap and external data requests may use third-party services; browser-based does not mean every operation is offline. Read the source and licence notes, calculation methodology and privacy policy. If a result looks inconsistent, report a correction with the inputs and mode used.
Frequently asked questions
Clear answers about the calculation, accuracy and appropriate use.
Does this include atmospheric refraction?
No. It is geometric curvature only. Refraction can make the apparent horizon farther away.
Is Earth a perfect sphere?
No. Earth is an oblate ellipsoid. The spherical model is appropriate for a simple educational estimate.
Is this suitable for engineering or legal decisions?
Treat the result as planning or educational context unless the page explicitly says otherwise. Engineering, hazard and legal decisions should use authoritative specialist data.
Why can terrain data differ between sources?
Elevation and earth datasets vary in resolution, collection date and processing method. Small local features may not be represented equally.
Can I verify the data source?
Yes. MapBench documents major providers and methodology on the Data Sources and Methodology pages.
What is the difference between drop and bulge?
Drop is measured from a tangent at one point (surveyor's view); bulge is the surface rising toward a chord between two points (link planner's view). Same circle, different ruler — at equal distances, tangent drop is four times the midpoint bulge.
Why do photos sometimes show more than the drop allows?
Refraction: temperature layers bend light, sometimes strongly (superior mirage conditions can lift distant objects dramatically). The geometric drop is the baseline; the atmosphere argues from there, in both directions.
Does my height change the drop?
The drop is a property of the surface alone. Your height changes what you can see over it — that is the horizon distance and hidden height calculation, the companion pages to this one.
Is the d²/2R shortcut safe?
For distances up to a few hundred kilometres, yes — its error stays under 1%. The calculator uses the exact circular form anyway, so the question is academic here.
What about the ellipsoid?
Local curvature varies slightly with latitude and direction (the Earth's radius of curvature runs about 6,357–6,399 km). At 100 km that shifts the drop by well under a metre — stated for completeness, invisible to most uses.
Can I see the drop?
Not with the naked eye at short range (0.08 m over 1 km hides below waves and haze) — which is exactly why instruments, not impressions, settled the question centuries ago.
How does this relate to the horizon dip angle?
The dip is the angular version: at eye level the horizon sits below horizontal by an angle that grows with your height — computed on the Horizon Distance page. Drop is distance's version of the same circle.
Related tools and resources
What stays hidden: the Hidden Height by Earth Curvature Calculator; the chord view: the Earth Bulge Calculator; your horizon: Horizon Distance.
More free tools
Sources, methodology & editorial trust
- ✓ Browser-first processing where supported
- ✓ External sources are documented
- ✓ No account required for public tools
- ✓ Review data sources
Calculations are documented with their assumptions, limitations and source context rather than presented as unexplained answers.
Reviewed and maintained by Aryan Khan, Founder & Editor of MapBench.
Part of our elevation & terrain hub
Earth Curvature Calculator sits in the elevation & terrain cluster, alongside 40 other tools that answer neighbouring questions with different methods or datasets.
You may also need
When this answer is only part of the job, these clusters cover the next step.
Read the guide behind this tool
How to Find Elevation on Google Maps — Check the elevation of any spot on Google Maps — desktop, mobile, and the precise method with exact numbers.