Are you confused by references to 20# paper, 28# paper etc?
Do you ever ask yourself questions like:
1) How much of this 20 lb copy paper actually weighs 20 lb?
(187000 sq. inches, or 2000 sheets of US letter)
2) Why does Levenger's 60 lb paper seem like everybody else's 24 lb?
("Book" vs "bond". It IS about the same weight.)
3) Why don't 110 lb index cards seem 5.5X heavier than 20 lb copy paper?
(They aren't. "index" vs "bond".)
4) Is the whole system designed to be as arcane and confusing as possible?
(Yes)
5) How do I compare to European papers with weights in "grammage?"
(It depends. Keep reading)
I found a great link that gives the conversions more accurately than you will ever need and posted it in another thread. But discussion there had pretty well come to an end. I thought it deserves its own thread with a more searchable title. It focuses on the math and is a little short on explanation, so I will expound below. I highly recommend the 2nd and 4th tables.
The link is: http://home.inter.net/eds/paper/grammage.html
The European (and rest of world) system is based on grammage, the weight in grams of one square meter of paper, written as g/mē or gsm. One A0 size sheet is 1 mē and 1 A4 sheet is 1/16 of that. So if paper weight is 80 gsm, an A0 sheet weighs 80 g, and A4 sheet weighs 5 g. Pretty logical.
The US system only refers to the weight in pounds, but the real units are pounds/basis ream. Normally a ream is 500 sheets and a basis ream is 500 sheets that are generally NOT the size of the piece of paper you are using. Nowadays paper comes in long rolls, but basis sheets are the size of the traditional starting sheet from which products were cut, a long time ago. Different types of paper such as bond, book, index, newsprint have different size basis sheets, so the given weights are for different amounts of paper.
(NOTE: Some references say for certain types of paper a ream is different from 500 sheets, but I didn't find any practical examples.)
There is no way to compare different types of paper without considering the size in basis sheets; it is meaningless. The easiest way to compare on a common scale is to convert all to a common scale, and gsm is such a scale. The math is all worked out in the above link, but if you want to know how to do it, keep going.
If a paper is said to have a basis weight of M pounds, and the basis sheet is Lb x Wb inches, then it is M/(500*Lb*Wb) lb/inē.
This may be converted to g/mē by successive multiplication by 453.59237 g/lb and (1 in/0.0254 m)ē. The conversion factor can be calculated by collecting and simplifying terms for a specific size basis sheet as:
gsm/lb = 45359237/(32258*Lb*Wb) = 1406.139/(Lb*Wb)
For bond (common copy and writing paper) the basis sheet is 17" x 22" (cuts to 4 sheets of US letter), hence a basis ream is 4 reams of US letter), the conversion factor is 3.7597 gsm/lb (3.76 is better than needed as paper weights can vary 5% anyway).
So 24 lb bond is 90 gsm. For book paper, the basis is 25" x 38" and the conversion 1.48 gsm/lb, 60 lb book is 89 gsm. For index card stock, the basis is 25.5" x 30.5", and the conversion 1.81 gsm/lb. For common basis sizes, this is worked out and presented as a table in the link above.