The isolation of Mt. Everest is undefined, though it's understood that it is the most isolated point on Earth.  Sometimes its isolation is defined to be the circumference of the Earth, though that is of questionable validity since it depends on the path taken around the globe.

Sometimes isolation is described as the distance to the nearest higher peak, because this is easy to calculate from a list of peaks and elevations.  This measure is an upper bound on true isolation.

I also have a separate calculation of global prominence here.

In 2017 I attempted to calculate the true isolation of every peak in the world.  To do this, I started with Jonathan de Ferranti's global terrain data set at viewfinderpanoramas.org.  Jonathan's data is based on the Shuttle Radar Topography (SRTM) mission, which used radar from the Space Shuttle to measure elevations.  This radar was unable to see many interesting areas, including the tops of many high mountains, so Jonathan filled these so-called "voids" with several different methods, producing near-perfect coverage of the Earth.

SRTM covered only land between about 60 degrees north and south latitude.  Outside these areas, Jonathan found elevations from other surveys, and by digitizing topographic maps.  Topographic maps could also be used in places like the U.S. where they are easily available.

The SRTM data has a resolution of 90 meters per pixel at the equator.  Closer to the poles, pixels get closer together in the longitudinal direction.  SRTM is a digital surface model (DSM), meaning that it includes buildings and tree tops, rather than the elevation of the bare ground.  This is because the wavelength of the radar could not penetrate vegetation.  This has important implications to isolation measurements in flat, vegetated areas.

The data is divided into files each representing one square degree on the Earth's surface.  Each file is a square grid of 1201 by 1201 samples.  The edges of each tile are repeated in the neighboring tiles.  Since the number of samples is constant, the area represented by each sample is largest at the equator, and dramatically smaller near the poles.

I retrieved Jonathan's files and wrote several C++ programs to process them.  The steps were roughly these:

Here's some more information on how each step was performed:

1: Find peaks

In flat areas like the top of a mesa, there might be no samples higher than all 8 neighbors.  Thus, any point at least as high as all 8 neighbors must be considered a peak.  This can generate large connected areas where each sample is considered a peak with the same elevation.  I performed a flood-fill to reduce each connected area to a single representative (roughly, the NW corner of the area).

Edge and corner samples have only 5 or 3 neighbors in the tile.  It is safe to consider these samples as peaks if they are at least as high as their neighbors in the tile, though they may be lower than a nearby sample in a neighboring tile.  This generates some spurious peaks that are removed later when a minimum isolation threshold is applied.

In order to avoid generating duplicate peaks in the shared samples of SRTM data tiles, only the top and left edges of each tile were examined.  The right and bottom edges were examined when processing neighboring tiles.

2: Find higher ground

Starting with a peak's tile, I search outward in concentric rectangles around the peak's location, looking for a higher sample.  These rectangles need to be wider than they are tall to cover an equal distance in the latitude and longitude directions.  The aspect ratio is the cosine of the latitude (in radians).

If one of these rectangles overlaps the edge of the tile, or if no higher ground is found in the tile, then neighboring tiles also need to be searched.  In similar fashion to the search inside a tile, neighboring tiles are searched in concentric rings.  Within a tile, fast approximations to distance are good enough, but as distances become larger, a slower and more precise calculation is required.  I used the standard haversine formula for a spherical Earth during this step.

Calculations took about 10 hours on a modern laptop.  A bunch of optimizations were necessary to get the speed within reason.

3: Calculate isolation

I used a more precise distance formula assuming an elliptical cross-section for the Earth to determine true isolation.  This only matters for very large isolation values.  Because the terrain samples are 90 meters apart, the resultant values are only good to one decimal place.

4: Map to known peaks

I wanted to determine the isolation value of real mountains that people have heard of.  To do this, I used the peak database from peakbagger.com, which contains about 70,000 peaks with locations, elevations, and names.  It also contains isolation values, most of which are next-highest-peak distances, but some of which were determined by hand.  These initial guesses were a great help in debugging.

In order to match peaks in the database, it was important to use the database's elevations for peaks.  Small changes in peak elevations can have a dramatic impact on isolation.  SRTM takes the average elevation in each sample area, which tends to undershoot true peak elevations.  So, in Step 1 above, I wrote Peakbagger's peak elevations to each tile as it was read in from disk.  This was a very tiny fraction of all of the peaks that were found automatically, but it included the vast majority of peaks that people care about.

After this step, I had two outputs.  The first was a list of each Peakbagger peak's ID, name, ILP, and true isolation value.  The second was a much larger list of millions of peaks with location, ILP, and isolation.  In order to keep this second list manageable, I applied an isolation cutoff of 1km, although I didn't exclude any peak from the Peakbagger database, because I wanted its exact isolation even if it was less than 1km.

I analyzed peakbagger.com's database from January 20, 2017, which contained 67,587 peaks.  After matching, the peaks were classified as follows:

latitude,longitude,elevation in feet,ILP latitude,ILP longitude,isolation in km

Elevation is in feet to avoid losing precision when converting to meters.  That could make peaks with small elevation differences appear to be the same height, which would distort the isolation calculation.  Only the first decimal place of the isolation value is meaningful.  The peaks are sorted by decreasing isolation (Mt. Everest, with its undefined isolation, is listed last.)