This is a straightforward question, but I couldn’t find anything on Google.
Stephen King’s books often uses the phrase “quarter of” when giving the time, for example “quarter of three”. Does this mean “quarter to three” or “quarter past three”?
Also, is this just a New England phrase? I don’t think I’ve ever seen or heard it anywhere else.
It means 15 minute to[the hour]. I grew up in California, born 1960, heard and used that way all my life.
People used “quarter of” in West Texas when I was growing up, but not exclusively. Other variations were used, too.
I have never figured out how “a quarter of eight” can mean 7:45. A quarter of eight is two.
Seconded that it is common in California, and just for “quarter.” You also hear things like “ten of [i.e., to] eight,” “five of four,” etc. (although I understand that 7 of 9 is something quite different).
I am British, and when I first came to California I noticed it a lot (“Quarter of four? 
You mean one?”), but I have gotten used to it now. I assumed it was a general USAian thing, like calling trousers “pants,” but maybe not. I guess if I hear an American say “quarter to four” it sounds normal so I just don’t notice it.
Quarter of, to, till three = 2:45.
Quarter after, past three = 3:15.
Not in Metric. 
So, is the “bottom half” of the hour the half from :30 to :60 or the half from :15 to :45?
Are people really this young? In the era before digital clocks, everybody spoke this way. Have we lost all those concepts so quickly?
Excuse me, I must dodder off aimlessly.
I dated a girl in college who went to high school with a girl who thought “quarter past three” meant 3:25. She would have been in high school between 1982 and 1986.
I didn’t understand “quarter of” until now! Then again, I’ve never heard anyone say it.
Thanks everyone. I’m surprised, I had guessed that it meant “past”.
Hmm…I just realised, maybe it was originally “off” rather than “of”? “Ten off five”, for example, makes much more sense than “ten of five”.
Don’t worry about being old just yet! It’s a question of location, not age. I only know the words “to” and “past”.
It’s quarter to three, there’s no one in the place except you and me…
So make it one for my baby and one more for the road
I’ve heard “quarter of” used all my life here in the Western U.S., mostly by older people. Always thought it was kind of a generalization, a foreshortened way of saying “it is within a quarter-hour of 3:00 pm” (or whatever).
SS
I was born and raised in Southern California, and I heard ‘quarter of’ frequently. Myself, I used ‘quarter to’.
I wonder if the usage is related to German? ‘Quarter of’ indicates a quarter of an hour until the next (stated) hour. In German, 30 minutes before the next hour is said by halb (‘half’) and the next hour. So 0730 would be ‘halb acht’. (For other increments they use vor – ‘before’ – and nach – ‘after’. e.g., 0845 is Viertel vor neun or 1011 is Elf nack zehn.)
Note that quarter of the hour is just the specific case. It’s also common to hear other references - Ten of the hour, Five of the hour (or five of three), etc.
And a German would probably say Zehn Uhr elf instead of Elf nach zehn. (Not that that has anything to do with the OP.)
Upper Midwestern - when my mom was a girl the town still had a German newspaper; but never heard “of,” only “tuh.”
AFAIK, it is standard throughout the US. On the other hand, “quarter to” is also used and understood, but much less common. One of the things I had to unlearn when moving to Canada was not to say “quarter of”, since I would be asked whether that was “quarter to” or “quarter after/past”. In the 42 years since, it is much better understood, doubtless owing to TV. Another one, of course, was “zed” instead of “zee”, but “zee” is also more widely understood now.