Horizon mask calculator (ridge elevation angle)
A horizon mask is the range of elevation angles that terrain blocks around you. This calculator turns one ridge into that angle from its distance and its height above your eye, then compares it with the minimum elevation angles that GPS receivers, satellite messengers, Starlink and geostationary dishes need. Earth curvature is included.
Light bends slightly downward, so a far ridge looks a little lower than plain geometry says. Below a few kilometres it hardly matters.
Used for the geostationary comparison: a TV or VSAT satellite on your own meridian, due south from the northern hemisphere.
Side view, observer at the left, with every ray drawn at its true elevation angle. The green line runs to the ridge crest and the arc gives its angle above your horizontal. The dashed rays are the minimum elevation angles GPS, Iridium, Starlink and a geostationary satellite need. Green rays pass over the crest. Amber rays run into it. Distance and height share one scale, so the view zooms out as the angles get steeper.
One ridge, one bearing. The angle assumes a spherical Earth and a bare crest, and it says nothing about other azimuths. The mask angles are typical values rather than hard limits. GNSS receivers are configurable, and Starlink’s 25° is the general case, with lower angles filed for the low-altitude shells and for high latitudes.
How it works
- 01
Measure the ridge
Pick the ridge that worries you and read two numbers off a map or an elevation profile: the horizontal distance to it, and how far its crest stands above your eye. If you only have elevations above sea level, switch input modes and the calculator does the subtraction.
- 02
Take the arctangent
The elevation angle of the crest is atan(Δh / d). A 300 m ridge 1.5 km away stands 11.3° up. Move the same ridge out to 5 km and it drops to 3.4°.
- 03
Subtract curvature and refraction
Over the first kilometres the Earth is flat enough to ignore. Farther out the surface falls away and the ray bends, which lowers the crest by d / (2·k·R) radians. At 1.5 km that is 0.007°, at 100 km it is 0.45°.
- 04
Compare with the mask angles
Every service needs its satellite at least a certain number of degrees above the horizon. GNSS receivers are usually set to a 10° or 15° mask, Iridium works down to 8.2°, Starlink user links were filed at 25°, and a geostationary satellite on your meridian sits at a fixed height that depends only on your latitude.
- 05
Remember it is one bearing
A ridge masks its own azimuth sector and nothing else. If it fills 40° of the compass rose, the other 320° are untouched. That is also why a gorge is far worse than a summit. Two steep walls mask most of the sky at once.
Formulas
- α — elevation angle above the observer’s horizontal, rad (×180/π for degrees)
- Δh — crest height above the observer’s eye, m
- d — horizontal distance to the ridge, m
- k — effective-earth-radius factor: 1 optical, 4/3 radio
- R — mean Earth radius, 6 371 000 m
- hridge — elevation of the crest, m AMSL
- heye — elevation of the observer’s eye, m AMSL
- φ — site latitude, degrees
- 0.15127 — Earth equatorial radius / GEO orbit radius (6 378 km / 42 164 km)
- el — elevation of a satellite due south (northern hemisphere), degrees
Worked example
- atan(300 / 1500) = atan(0.2) = 11.31°
- curvature at k = 1: 1500 / (2 · 6 371 000) rad = 0.007°
- α = 11.31 − 0.007 = 11.3°
- GNSS 10° mask and Iridium 8.2°: blocked, satellites lower than 11.3° on that bearing are lost
- Starlink 25°: clears the crest by 13.7°
- GEO at 47° N: el = 36.0°, clear by 24.7°
FAQ
- Why does a satellite messenger work on a summit but not in a gorge?
- On a summit almost the whole sky sits above your horizontal, so any Iridium satellite that comes over is usable. In a narrow gorge the walls can stand 40° or more above your eye on both sides, leaving a strip of sky overhead. A satellite has to cross that strip before the message goes out, and that can take many minutes.
- Does a ridge make GPS less accurate?
- Yes, indirectly. Losing part of the sky leaves the receiver with satellites bunched in one direction, and geometry, not signal strength, drives most of the error. That bunching shows up as a higher DOP value, and the position error grows roughly in proportion. A fix under a valley wall is usually worse than the same receiver gets on open ground.
- Does the ridge block the sun the same way?
- Geometrically, yes. The angle applies to anything in that direction, the sun included. Look up the sun’s altitude for your date and time in an almanac or ephemeris table, then compare it with the ridge angle. If the sun stays below that angle while it crosses the bearing, it never clears the crest. This calculator does not compute solar positions.
- Which refraction setting should I use?
- Use the optical value (k = 1) for anything you look at, including the sun. Use k = 4/3 for radio paths in a standard atmosphere, where the ray bends slightly downward and the horizon moves out. Below a few kilometres the two agree to within a hundredth of a degree.
- How do I check the whole 360° horizon?
- One angle covers one bearing. For the full circle you need the terrain in every direction. A viewshed does exactly that, walking each azimuth over elevation data and marking what stays visible. Waveshed runs one in your browser from any point you drop on the map.
One ridge is one direction. Waveshed reads the terrain angle all the way around your position from real elevation data, so you can see the whole mask instead of a single bearing.
See your horizon on the map →Related guides
- Measuring tools — the simulator reads distance and height difference straight off the terrain
- Heights: AGL vs AMSL — which height a map gives you, and what to add for your own eye level
Sources & further reading
- NOAA Technical Memorandum NOS NGS-58 — Guidelines for Establishing GPS-Derived Ellipsoid Heights ↗ — National Geodetic Survey practice: track satellites down to 10° elevation, process above 15°
- FCC 22-91 — SpaceX Gen2 Starlink partial grant ↗ — records the 25° minimum elevation angle SpaceX filed for its Ku-band user links
- Ground Control — Iridium signal strength and elevation ↗ — Iridium is designed to work with satellites as low as 8.2° above the horizon
- Geostationary orbit — Wikipedia ↗ — orbit radius 42 164 km against an equatorial radius of 6 378 km, the 0.15127 ratio
Related tools
How far can you see? Horizon distance calculator
Distance to the horizon from any height, and how much of a distant peak or ship the curve hides.
Distance & bearing calculator
Great-circle distance, bearing and elevation angle between two coordinates, summit to summit.
Satellite look angle calculator
Azimuth, elevation and slant range to a geostationary satellite from your location.
Earth bulge calculator
Height the Earth’s curvature adds mid-path, with k-factor refraction.