# Standardized scale for coastline length or mapping in general?

Measuring the length of a coastline depends on the scale of the measuring tool. The smaller the scale of your tool, the longer will your measured coastline be. The reason for this is the fractal property of coastlines. This is well known since a paper by Benoît Mandelbrot "How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension".

Now I was wondering if there is a standardized mapping scale to come up with global or country wise numbers of coastline length?

And furthermore, if there even is a general rule for all mapping purposes, which scale is to be used in mapping?

Is there maybe even something like an ISO standard for this?

• The following links may or may not help: coast.noaa.gov/geozone/…, shoreline.noaa.gov, shoreline.noaa.gov/data/datasheets/usgs.html
– user967
Commented Oct 19, 2014 at 16:19
• Given the widely fluctuating values for coastline length, and given the coastline paradox the ultimately belies these widely varying numbers, the only reasonable answer is no. We do have arbitrary standards for things such as mass, length and time, but those are important. (The only non-arbitrary standard for mass, length, and time would be to use natural units, and those would be completely useless for commerce.) For how to measure a coastline? How is that important? Commented Oct 19, 2014 at 22:04
• I think this question would be appropriate for gis.stackexchange.com Commented Oct 20, 2014 at 13:02
• @DavidHammen There is a number of elements of industry, economy and ecology that may rely on the length and/or shape of the coastline. Coastal management, marine engineering (harbors, shipyards, water plants), transport engineering (roads, railroads, bridges), agriculture, fisheries, tourism etc. Importance is relative. Commented Oct 23, 2014 at 16:10
• @IRO-bot - And that is not going to be some silly ISO standard. The mechanism used to measure the length of the coastline by an agency that manages an intracoastal canal is going to be very different than that used by an agency that manages wildlife in a tidal zone. The coastline paradox dictates that there can't be a standard. Commented Oct 23, 2014 at 16:15

One standard that has be used by the USA is to measure the distant between points on the coast at intervals of 30 latitude minutes, as measured on a 1:1,200,000 scale map.

See chapter 5 of Measurements from Maps: Principles and Methods of Cartometry by D. H. Maling for further information and other standards that have been used.

• Wow. Thanks, but while that seems like a helpful answer to the question as posed, it sounds like a bizarre practice. It seems like the effective measurement interval along the coastline would vary by the angle of the coastline, being most frequent for a N-S coastline, and infinite for a perfectly E-W coastline. Is this practice designed to be relevant for some specific purpose for which this isn't an issue? Commented Jun 28, 2022 at 1:22

It is not really worth worrying about unless you are proposing to walk along it, or let your pet ant walk along it, for the ant will have to walk a much greater distance than you as it follows all the wiggles that you just stride over.

Nor does it matter a jot for coastal management, which is always concerned with water bodies or areas and never with the purely conceptual length of the coastline. Coastal reporting sometimes summarises water quality by length of affected coastline, but that is merely an administrative convenience and has no significance otherwise.

The geometric length between two points defining a straight line does not depend on the size of the intervals we use to pace it out.

However, the length of a fractal coastline is quite different. The smaller the step, the greater the length. There are mathematical ways to express this and if you google around you will find them. Try looking for Koch Snowflake for example.