[Proj] Distance measured in Mercator projection

[Shannon Scott]

Hello,
Please forgive my ignorance, I know very  little about map projections.  
I apologize if this list is not the appropriate place to post this question.
If I understand correctly, in the Mercator projection, 1 unit of space 
is equal to 1 meter at the equator.
As you move away from the equator, the longitudinal lines are stretched 
to make the lat and long intersect at 90 degree angles.
How would I calculate the length in meters of 1 unit of space in the 
Mercator projection at a specific latitude?
Any advice of pointers are appreciated.
Thank you.
Shannon