When you have your foot measured on one of those shoe store devices they can tell you what width your foot is...though it's just a guideline. Foot volume is a factor, too, and those devices won't tell you anything about that.

I could not wear women's Sidis. And men's or megas may have been wide enough, but I found the heels on Sidis to be too roomy (I have duck feet). I currently wear men's LG road and mountain shoes and they are still none too wide, even with ample extra room through the toes. A women's wide is a D, same as a men's standard width shoe.

With running shoes it's simply a matter of trying things on. I can get away with the Nikes I've tried, since they have roomy forefoot area (especially in the more minimal shoes, like the Free Runs that I've been wearing) and the uppers seem to have plenty of give. For years I wore New Balance wides, until they changed the last on their running shoes and they've not fit me right since.