How does Strava find climbs?

If your elevation gain between two measurements is more than 3% we will flag a start of a climb. The climb will continue as long as your average grade is greater than 3%.

So, the basic criteria for a climb is avg grade of 3% or more.
For Categorized climbs 1-4:

% Grade multiplied by distance in meters > 8000 to be at least a cat 4 climb. So, for a 4% avg grade climb, it has to be 2km at least to be categorized.

Cat 3 = 16000, 2 = 32000, 1 = 64000, HC > 80000