cyclezen

I would
subtract the teeth number of the largest cog of older (smaller ?) cassette from the largest new cog (the 11-50?) assuming the old cassette smallest cog is within 1 tooth of the new cassette (11/12?)
if the older largest cog is 42, new is 50 gives 8 teeth - every 2 teeth equals one chain link pair. so 4 more link pairs
If there's an appreciable difference in the jockey cage from old to new - measure from jockey pivot to lower jockey wheel axle , 1 inch = chain link pair.
42 cassette to 50 cassette = 4 link pairs
jockey cage is about 1 inch longer ??? 1 link pair
TTL = 5 link pairs - longer than the prior chain

Ride on
Yuri
Edit: if there's also a change in the chainrings, then you would again compare 'Large' to Large chainrings, or Large Double(triple) to whatever a 1x size used...
same math 2 teeth = 1 link pair