I suspect that the answer to this depends on region, so insights from multiple areas would be beneficial:
It has been my impression that in the US addressing a woman as "Madam" is considered borderline-vulgar due to the term's usage as the title of a female proprietor of a brothel.
Is it acceptable to use "Madam" when addressing a woman you do not know or should the alternative "Ma'am" (silent "D") be used? Does it depend on spoken vs. written communication?
Best Answer
In modern use in American English, the term ma'am has gained quite a bit more use than madam:
In modern use in British English, madam is slightly more popular than ma'am:
As a native American English speaker, madam seems a bit archaic but does not necessarily connote a tie with a brothel unless you refer to someone as a madam. For example, the Oxford English dictionary provides the following example for madam of a brothel:
But as a form of address, it is used differently:
The typical terms I've heard are miss for younger females and ma'am for older ones. You could potentially refer to someone as madam or ma'am in either spoken or written communication. In formal writing, for example to someone whose name you do not know, use madam in both cases. For example:
This holds in both American and British English.
In less formal writing or speech, I would suggest using whichever term is more popular for the community you are in--ma'am in American English, and madam in British English. In both, madam will seem a bit more formal.