Horizon Distance Calculator

How far can you see from a given height?

Enter an eye height and the tool returns the distance to the horizon, computed from the geometric formula d ≈ √(2Rh) with Earth's radius and the standard refraction correction that bends light slightly over the curve — about 3.86 × √(height in metres) kilometres. A beach stance (1.7 m) sees roughly 4.7 km; a 100 m cliff, about 38 km. Add a second height and you get the classic ship-to-ship figure: the sum of both horizons, the maximum range at which two observers can see each other over open water.

The page explains the physics briefly — curvature sets the geometric horizon, refraction extends it about 8% in standard conditions, and weather can stretch or shrink that — so the number arrives with its caveats rather than false precision. Elevation at the observer is your input; pull it from the elevation finder for real sites. Combine with the line-of-sight calculator when specific terrain between the points matters, or the antipode tool when the question flips from 'how far can I see' to 'what is directly under my feet, one Earth-diameter down'.

Worked examples

• Beach stance (1.7 m eyes) — puts the horizon at ≈ 5 km with standard refraction; a 100 m lighthouse deck pushes it to ≈ 39 km.
• Your antipode — for New York lies at -40.71, 105.99 — Indian Ocean, illustrating why most land antipodes are water.
• Line-of-sight check — over 10 km of terrain adds ~6 m of curvature drop even after refraction; hills taller than your mast heights plus that bulge block the view.

Reading the third dimension: terrain, visibility and deep time

Everything on a flat map is a rumour about height. Digital elevation models — satellite-derived grids like Copernicus GLO-90 at roughly 90 metres — turn the rumour into numbers: ground height at any coordinate, cross-sections along any line, ascent and descent totals for any route sketch. The models see terrain, not trees or buildings, and vertical accuracy of a few metres is typical; knowing that is the difference between using them wisely and over-trusting them.

Visibility questions add physics. Over open ground the horizon sits at about 3.86 × √(height in metres) kilometres once standard atmospheric refraction is included; between two observers the ranges add. Between specific points, terrain enters through the same DEM: sample the line, add Earth-curvature drop with the conventional refraction coefficient, and the verdict — clear or blocked, and where — follows by comparison. It is telecom planning's classic calculation, now comfortably runnable in a browser.

The deep-time companions — antipodes, climate zones, hardiness bands, seismicity — reframe your point on longer clocks. The antipode is pure geometry with a geographic punchline (usually ocean). Köppen classes and hardiness zones compress thirty years of temperature and precipitation into letters that gardeners and planners trust. Recent earthquakes are the live signature of faults. Each is an estimate with a stated recipe; together they make a portrait of place that no street map can offer.

Tips & common mistakes

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.

Include your height inputs explicitly (eye height, mast height, deck level) when sharing visibility results: the same hill answers differently for a child, an adult and a 10 m antenna, and unstated heights make numbers unreproducible.

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.

Using terrain intelligence without overclaiming it

Digital elevation models transformed what amateurs can ask of terrain, and they also created a new overconfidence: a number with decimals feels surveyed. Hold the model's nature in mind — a ~90 m grid of bare-earth heights, vertical error of a few metres, blind to buildings and canopies — and every output slots into its proper weight. Elevation at a point: planning-grade. A profile: the shape of the truth with noisy amplitude. Line-of-sight: terrain's answer, pending trees and towers. Horizon: curvature plus standard refraction over open ground. Each is genuinely useful; none is the last word.

The longer-clock tools carry the same lesson at larger scale. A Köppen letter compresses thirty years of weather into climate's shorthand; a hardiness zone compresses winter extremes into a gardener's number; recent seismicity sketches a fault's mood. Used as orientation — choosing crops, siting panels, understanding a region's tectonic character — they are superb. Used as guarantees, they fail. The discipline is to print the recipe with the result, which is what honest tools do by default.

How professionals use this

• Attach the model and vintage to every terrain number you republish (e.g. 'Copernicus GLO-90 via Open-Meteo').
• For visibility work, add land cover from local knowledge after the terrain verdict, not before.
• Average multiple years for climate-adjacent numbers; single-year values are weather wearing climate's coat.
• When a decision is expensive, upgrade terrain from DEM to survey — the tool's job is to tell you when that matters.

Step-by-step masterclass

1. 1. State the model with the number — 'Copernicus GLO-90, ~90 m, ±few metres vertical' turns an elevation claim from vibes into a citable fact.
2. 2. Add heights explicitly — Eye height, mast height, deck level — visibility answers are unreproducible without them, and the tools here keep them as named inputs.
3. 3. Layer land cover after terrain — The DEM sees bare earth; woods and walls are local knowledge you add after the curvature verdict, not before.
4. 4. Average years, not days — Climate letters and hardiness zones want 30-year character; single-year values are weather wearing climate's coat.
5. 5. Escalate when it's expensive — DEM for screening, licensed survey for decisions with money attached — knowing the upgrade point is the professionalism.

Terrain data is genuinely global (satellites don't respect borders), but its texture varies: flat plains resolve beautifully, steep forested relief noisier; seismicity tools are worldwide via USGS, while mapped fault and flood layers are US-first — the scope chips on each tool state exactly where each answer stands.

Related questions people ask

Quick glossary

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.

Antipode

The diametrically opposite point; latitude flips, longitude shifts 180°.

Köppen class

The letter-code climate system from temperature/precipitation thresholds.

Peak sun hours

kWh/m²/day expressed as hours of 1,000 W/m² — PV's linearising unit.

HUC

Hydrologic Unit Code — nested US basin numbering, 2 to 12 digits.

Terrain literacy: the habits that keep elevation honest

Using terrain data well is mostly a set of small disciplines: print the model with the number, keep the heights as named inputs, average years instead of days, and treat every verdict as the bare-earth baseline that land cover and structures may override. Practitioners also keep a feel for the model's texture — flat terrain resolves beautifully, steep forested relief noisier — and for the difference between shape and amplitude in profiles, where consumer GPS tracks and DEM samples tell complementary truths. Held together, these habits make the free stack genuinely useful for siting, scouting, teaching and curiosity, while the escalation points stay clearly marked: licensed surveys for construction, regulatory determinations for flood and seismic decisions, certified studies where financing depends on production numbers. The tools do their part by printing every recipe; the user's part is simply to read them. Finally, terrain literacy changes how questions are asked, not just answered. 'Is this site flood-prone?' becomes 'what does the elevation profile say, what does the regulatory map say, and where do they disagree?' 'Can I see the coast from here?' becomes a stated eye height, a curvature verdict and a note about the forest in between. Structured questioning like this is cheap here — every input named, every recipe printed, every limit labelled — so the habit costs seconds per query. Over a season of site visits, garden plans, antenna mounts and photo walks, those seconds compound into a genuinely different relationship with the ground: not a backdrop, but a dataset you can read, cite and, when it matters, hand to a professional with the right questions already written down.

• Cite the model: 'Copernicus GLO-90 via Open-Meteo' belongs in every republished figure.
• Store eye/mast heights with visibility results; unstated heights are unreproducible results.
• Profile comparisons: match shape first, amplitude second, and say which device logged what.

Honest limits & when to escalate

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.
• Seismic safety → national hazard models and building codes.

Data & methodology note

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.

Category context: Earth Science — Elevation, horizon distance, antipodes and other planetary calculators. This page is one of the earth science tools on MapForge; the related-tools links below and the header's Tools menu connect every sibling instrument.