# What CRS for a large scale analysis

I was wondering what CRS to use when focusing on a large scale area for an analysis.
For example the Mediterranean Sea.

I need to find the distance of each sea port from another.
That means I need the distance from a port based, say in Greece, to another one based in Spain.

My first guess was using WGS84 ESPG:4326 and then using `\$length` to convert degrees into meters (not the most accurate process I admit).

I can't seem to find a CRS covering the whole Med Sea.

• You don't convert degree to m. Point. You could use 3857 or 3395, both cover the whole world using m. Though there are errors to be expected. – Erik Jan 23 '20 at 15:22

If you are measuring distance you want a equidistant projection.

For example an equidistant conic projection would work well for the Mediterranean Sea.

https://proj.org/operations/projections/eqdc.html

You are using the appropriate command.

`\$length` applied to a LineString feature which geometry has only two vertices, will measure the shortest curved distance between the vertices, along the ellipsoid.

You can define the reference ellipsoid and the units of measurements for each project, in the Project ~> Properties menu, General tab, Measurements section.

If you apply the same `\$length` expression to a LineString feature which geometry has more than two vertices, the returned value will be the addition of each shortest curved distance along the reference ellipsoid between each vertex.

That is, `\$length` returns the length of geodesic lines. (An ellipsoid of revolution has just one great circle: the equator. All other intersections between planes that contain the center of the ellipsoid and its surface, define ellipses.)

When you project vector data (i.e., coordinates of vertices) to a plane, there is no way to preserve the value of geodesic lengths between all points on a map measuring planimetric lengths in the plane of projection.

You can preserve the geodesic length along one line (maybe two), or between all points to one in particular, or between two (maybe three) points. But not between all points on a map with each other.

If you want to measure planimetric lengths in the plane of projection, you can use `length(\$geometry)` expression. The units of measurements will be those defined in the CRS of the layer. The difference between that measured planimetric length and the ellipsoidal length may be greater or lesser depending on the projection used and the location of the vertices.

Also, you can select `None / Planimetric` instead of an ellipsoid of reference, and `\$length` will return planimetric measurements in the CRS of the project.

There is no need for the data to be projected on a particular reference system, or for the map to be reprojected on a particular system: When you use `\$length` expression with a defined reference ellipsoid, the coordinates of the vertices are inversely projected to the reference ellipsoid and the expression returns the ellipsoidal distances between them.

For measurements, I would simply use the great circle distance between the ports or waypoints along the route, independent of any CRS. And for mapping a Lambert azimuthal equal-area projection.