A LiDAR las file presents data in a point cloud of x, y, z coordinates and provides offsets and scaling factors, but what are the units?
LIDAR or LADAR is the determination of range by light or laser, a visible remote sensing technology using pulses of light, usually laser beams, by which distances or characteristics of the observed targets are calculated.
It depends on the country your flight was done. For example, in Brazil we used meter-based units. X and Y are representing UTM coordinates in meters, and Z is elevation from the sea level reference, also in meters. However, Z, Y and Z could also be in imperial units for example (i.e. feet). Offsets and scaling use to follow the cloud units.
This doesn't help me. From your answer am I to infer that the .las file does not include a field that describes the units? If I have a reflection at x, y, z point 1, 2, 3, I have not way of knowing from the data in the file if that's 1, 2, 3 meters, feet, km, miles, inches, cm.
There are different versions of the LAS standard. You can find the version at the beginning of the file, in the header block. For some versions the reference system is not mandatory but may appear in a variable length record. For others, it is specified in the header block as a WKT (Well Known Text). You can find the different specifications here:
https://www.asprs.org/divisions-committees/lidar-division/laser-las-file-format-exchange-activities
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