Determining OG from the Pre-Boil Gravity?

Anyone know how to estimate the original gravity of your wort by taking a reading before the boil off?

EX:
My 7 gallons of wort is 1.065. If my final volume is 5.5 gallons what is my OG?

Assuming you boil down to exactly 5.5g, and transfer the whole 5.5g to the primary, then your OG would be (1.065 - 1.000) * 7 / 5.5 + 1.000 = 1.083.
Unfortunately, the transfer to the primary will not normally be 100% efficient, and to estimate your OG you will have to estimate the amount of wort lost during the transfer. Assuming you lose x gallons, the formula would be modified to
OG = (1.065 - 1.000) * 7 / (5.5 + x) + 1.000, so if you lose 2 pints it would be
(1.065 - 1.000) * 7 / ( 5.5 + 0.25) + 1.000 or 1.079

-a.

hey ajf , i'm not sure what gets left behind will change the grav. when you boil off to the 5.5 gal volume, won't the wort all have a grav of 1083 (including the 2 pts). So the 5.5 gals(less 2 pts) will have a grav of 1083 as will the 2 pts left behind?? Otherwise, the grav of the 2 pts left behind is going to be pretty darn high ( apply conservation of mass theory here).
hey maybe i'm seeing this wrong.... i'm interested in sorting it out though ....
in my own head ....
brewfie

Yes, if you boil down to 5.5g, you'll have a gravity of 1.083, but if you leave 2 pts behind, you will end up with only 5.25g in the fermenter (still at 1.083)

-a.

Thanks for the help guys. Those things really bug the hell out of me until I figure them out (or someone else does.