How Many Decimal Digits for Storing Longitude & Latitude?

Recently I came across this tweet containing the image below and it made me laugh … albeit not in the original way the tweet intended. The tweet was joking that “Anyone is able to open a GeoJSON file” and included the Microsoft Word screen shot seen below as a response to someone else tweeting that “Handing in a project as @GeoJSON. Let’s see if I get the usual “I can’t open this file” even though […]”. What was funny to me was seeing longitude and latitude coordinates stored with 15 decimal digits right of the decimal point. There are many memes about “German efficiency” but few about “German accuracy” 😁. Clearly it is time for another blog post about storage resolution and positional accuracy. The last blog post came on the heels of the national open elevation release of England with insane vertical resolution.

Longitude and latitude coordinates are stored with 15 decimal digits right of the decimal points.

By default LAStools will use 7 decimal digits to store longitude and latitude coordinates to a LAS or LAZ file. But what do 15 decimal digits mean for longitude and latitude coordinates? How “accurate” are the corresponding coordinates when converted to projected  coordinates? I took the second coordinate pair [ 10.049567988755534, 53.462766759577057 ] shown in the screen shot above and converted it from longitude and latitude to the easting and northing values of the WGS 84 / UTM 32N projection that has EPSG code 32632. Before conversion we quantize these numbers to have 5 through 15 decimal digits and then record the absolute difference to the coordinate pair that uses the most digits.

Number o decimal digits for longitude and latitude coordinate and absolute difference in projected position.

The table above shows that – at least for this particular longitude and latitude coordinate pair located in Germany – that 7 digits are sufficient to store coordinates with centimeter [cm] accuracy and that 8 digits are enough to store coordinates with millimeter [mm] accuracy. Any additional digit right of the decimal point will only be necessary when we need micrometer [um] or nanometer [nm] accuracy, which is very unlikely to be the case in most geospatial applications.

This means we could remove the 7 or 8 right most digits of each number from the screenshot that was tweeted and make this GeoJSON file even smaller, faster, and easier to store, transmit, open, and read. After this post was tweeted there was a follow-up tweet suggesting to have a look at this site for a more detailed analysis of what accuracy each digit in a longitude and latitude coordinate can store.

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