Calculating the circle distance at varying latititudes

Is there an expression out there for determining the distance around
the globe, at let's say the tropic of cancer and the tropic of
capricorn? I know that the radius of the earth is 6371 - is there
perhaps an expression which relates the circle distance at the tropic
of cancer/capricorn to the radius or even perhaps the GCD?

I am attempting to determine how the circle distances change as you
move from the equator to either of the poles.


thanks