Planar vs. Euclidean distance measurements

[Craig_Eissler_Iceman]

I understand Planar vs. Geodesic measurements and Euclidean vs. Geodesic measurements.

However, is there a difference between Planar and Euclidean measurements, or are these just interchangeable terms that ArcGIS uses?

[AyanPalit]

@Craig_Eissler_Iceman my notes on this topic:

Euclidean distance is the straight-line distance between two points in Euclidean space (in theory this can be 2D or 3D). The distance is calculated using the Pythagorean theorem, relating the difference in coordinates along each axis.

Reference: Understanding Euclidean distance analysis

Planar distance is straight-line Euclidean distance calculated in a 2D Cartesian coordinate system. Here calculations are always made on a flat, 2D plane; thereby planar distance equals Euclidean distance in 2D Euclidean space but may differ if  Euclidean space is 3D.

Reference: Geodesic versus planar distance

[Craig_Eissler_Iceman]

Thanks, yes, I had already read all of that.

So I guess I should have re-framed my question to say, "why" is there potentially a difference between the two in 3D space?

[LetaFranklin]

Planar distance is like measuring the path along the surface accounting for the Earth's curvature but ignoring elevation changes. It treats the earth if it were a perfect 2D plane.

Euclidean distance is the direct, straight-line measurement, cutting through the Earth as if tunneling between the two points.

If you were flying between San Francisco and New York, your flight path would follow a curved trajectory due to the Earth’s shape (similar to planar distance). This is how a crow would fly between the two cities, if it could fly without stopping for breaks, of course. A Euclidean distance is a straight line through the earth, ignoring the planet’s curvature entirely. AI tells me that tunnel would be 6-9 miles below the surface at the midway point 🙂