@JeremyECrawford Does crouching (such as behind cover) count as being prone? Does it take extra movement to stand up from crouching?
— PJ Elliott (@Dachimotsu) November 18, 2017
There are no rules for crouching. #DnD https://t.co/reWfCt590x
— Jeremy Crawford (@JeremyECrawford) November 18, 2017
This is the sort of thing typically handled by a DM. See also, character size interacting with cover. If crouching produced a static mechanical effect, it would get into weird territory pretty quickly.
Imagine an 8 foot tall Goliath crouching down to a 4 foot tall profile. Do they get a bonus for “Crouching”, while their 4 foot tall Dwarven ally who is standing fully erect doesn’t? That’d be weird.
If you want your character to crouch, the GM should determine how much effect it has on the fly. I’d think most effects should be tied to the cover system. If you’ve got a 4 foot tall boulder, the Dwarf mentioned above can take full cover behind it without even ducking, while the Goliath would get only half cover at full height, and possibly three quarters or even full cover if they crouch behind it.