Grammage

Grammage and basis weight, in the pulp and paper industry, are the area density of a paper product, that is, its mass per unit of area. Two ways of expressing the area density of a paper product are commonly used:

Expressed in grams per square metre, regardless of its thickness . This is the measure used in most parts of the world. It is often notated as gsm on paper product labels and spec sheets.
Expressed in terms of the mass per number of sheets of a specific paper size. The convention used in the United States and a few other countries using US-standard paper sizes is pounds per ream of 500 sheets of a given basis size. The traditional British practice is pounds per ream of 480, 500, 504, or 516 sheets of a given basis size. Japanese paper is expressed as the weight in kilograms per 1,000 sheets.
Grammage

In the metric system, the mass per unit area of all types of paper and paperboard is expressed in terms of grams per square metre. This quantity is commonly called grammage in both English and French, though printers in most English-speaking countries still refer to the "weight" of paper.

Typical office paper has, therefore a typical A4 sheet weighs. The abbreviation gsm instead of the standard g/m² symbol is also widely encountered in English-speaking countries.
Typically grammage is measured in paper mill on-line by a quality control system and verified by laboratory measurement.

Basis weight

Basis weight of paper is the density of paper expressed in terms of the mass of a ream of paper of given dimensions and a sheet count. The American and the traditional British systems are largely the same, with only minor differences: the paper dimensions and the sheet count are different.

United States

In the US system, the weight is specified in avoirdupois pounds and the sheet count of a paper ream is usually 500 sheets. However, the mass specified is not the mass of the ream that is sold to the customer. Instead, it is the mass of the uncut "basis ream" in which the sheets have some larger size. Often, that is a size used during the manufacturing process before the paper is cut to the dimensions in which it is sold. So, to compute the mass per area, one must know

the mass of the basis ream,
the number of sheets in that ream, and
the dimensions of an "uncut" sheet in that ream.

The standard dimensions and sheet count of a ream vary according to the type of paper. These "uncut" basis sizes are not normally labelled on the product, are not formally standardized, and therefore have to be guessed or inferred somehow from trading practice. Historically, this convention is the product of pragmatic considerations such as the size of a sheet mold.
By using the same basis sheet size for the same type of paper, consumers can easily compare papers of differing brands. Twenty-pound bond paper is always lighter and thinner than 32-pound bond, no matter what its cut size, and 20-pound bond letter size and 20-pound bond legal size papers are the same weight paper with a different cut size.
However, a sheet of common copy paper that has a basis weight of does not have the same mass as the same size sheet of coarse paper. In the former case, the standard ream is 500 sheets of paper, and in the latter, 500 sheets of paper. Here are some basic ream sizes for various types of paper. Units are inches except where noted.
Sheets can be cut into four sheets, a standard for business stationery known conventionally as letter sized paper. So, the ream became commonly used. The book-paper ream developed because such a size can easily be cut into sixteen book sized sheets without significant waste.
Early newsprint presses printed sheets in size, and so the ream dimensions for newsprint became, with 500 sheets to a ream. Newsprint was made from ground wood pulp, and ground wood hanging paper was made on newsprint machines. Newsprint was used as wrapping paper, and the first paper bags were made from newsprint. The newsprint ream standard also became the standard for packaging papers, even though in packaging papers kraft pulp, rather than ground wood, was used for greater strength.
Paper weight is sometimes stated using the "#" symbol. For example, "20#" means "20 pounds per basis ream of that kind of paper". When the density of a ream of paper is given in pounds, it is often accompanied by its "M weight". The M weight is the weight of 1000 cut sheets. Paper suppliers will often charge by M weight, since it is always consistent within a specific paper size, and because it allows a simple weight calculation for shipping charges.
For example, a 500-sheet ream of 20# copy paper may be specified "10 M". 1000 cut sheets will weigh, half of the four reams of cut paper resulting from the 20# basis ream of paper.

United Kingdom

Overview of the traditional British system

Like the American system, the traditional British system also involves the use of basis weight to express the area density of paper in the course of buying and selling paper. The British paper industry exclusively used basis weight before 1968.
In the traditional British system, basis weight is also expressed in terms of the weight of an imaginary ream of paper of a certain size. The underlying concept is that a ream of paper of the stated paper size and of the same thickness as the paper the parties are dealing with would have the stated weight. The weight is expressed in pound. As to paper sizes, they can, theoretically, be any sizes, but, by custom, a number of common sizes emerged. In the 1960s, even the metric A1 and A2 had been used as basis sizes alongside the British ones.
The following are common British basis sizes :
One ream in the context of basis weight can be 480 sheets, 500 sheets, 504 sheets, or 516 sheets: there is no fixed rule on when a certain definition was applied; however, starting from the 1950s, the trend of moving towards 500 sheets emerged.
Basis weight is commonly expressed in terms of pound per ream of paper of a certain size, in the format of 'lb '. Since there are basis reams of different sizes, unless the context leaves no room for ambiguity, the number of sheets in the basis ream is also given after the paper size to avoid misunderstanding: in such case, basis weight is expressed in the format of 'lb ', such as '21lb large post 480'. In the United Kingdom, '#' has never been used to express paper weight because it is called 'hash', instead of 'pound', in British English.
Demy traditionally plays the role of the default basis size for expressing basis weights: in the British paper industry, there was a device, called 'demy scale', that was used to measure the weights of different paper samples in pound per ream of demy paper.
Below is a list of common basis weights of paper stocked by British paper merchants:

Conversion between British basis weights, American basis weights, and grammage

It is possible to convert between different basis weights – both British and American – and grammage using different conversion formulae.
To convert between the basis weights of different paper with the same basis‑ream size, the following formula can be employed:
Area of one sheet of paper in the target ream × Weight of the source ream ÷ Area of one sheet of paper in the source ream
To convert between the basis weights of different paper with different basis‑ream sizes, the relevant formula is below:
× Weight of the source ream ÷
To convert between the basis weights of the same paper with different basis‑ream sizes, one may either use the previous formula or the one below:
Weight of the source ream × Applicable conversion factor from the table below

To → From ↓	480	500	504	516
480	...	1.042	1.05	1.075
500	0.96	...	1.01	1.032
504	0.95	0.992	...	1.022
516	0.93	0.969	0.977	...

To convert from a basis weight to its equivalent grammage, the following is the applicable formula:
Weight of the basis ream × 703,125 ÷ Area of one sheet of paper in the basis ream in square inch × Number of sheets of paper in the basis ream
To convert from grammage to the equivalent basis weight, the formula below can be used:
Area of one sheet of paper in the basis ream in square inch × Number of sheets of paper in the basis ream × Value of gram per square metre ÷ 703,125
Utilising the aforementioned formulae, it is possible to work out the conversion factors for converting between various British and American units of basis weight and the gram per square metre:
Using British basis sizes and the 500‑sheet basis‑ream, and with the help of the aforementioned conversion formulae or conversion factors, it is possible to express the paper weights of different types of paper in everyday life using British units of basis weight: the typical photocopier paper that is used as all‑purpose paper is 17 or 19 ; personal and business letter paper, especially that with engraved letterheads, is typically 24–29 ; greetings cards are usually 85–106 ; newspaper paper is typically 15–23 ; business cards are usually 128–149 ; two‑ply toilet rolls and paper kitchen towels are 7 and 17, respectively; and the typical department‑store wrapping paper is commonly 46–65. In the traditional British system, large post, double crown, and double imperial are common British basis sizes for writing paper, printing paper and other paper that is not writing or wrapping paper, and wrapping paper, respectively. '500' is omitted because it is clear from the context that a 'ream' is 500 sheets.

Caliper

Paper thickness, or caliper, is a common measurement specified and required for certain printing applications. Since a paper's density is typically not directly known or specified, the thickness of any sheet of paper cannot be calculated by any method. Instead, it is measured and specified separately as its caliper. However, paper thickness for most typical business papers might be similar across comparable brands. If thickness is not specified for a paper in question, it must be either measured or guessed based on a comparable paper's specification.
Caliper is usually measured in micrometres, or in the United States also in mils. Commonly, 20-pound bond paper ranges between roughly in thickness.
The paper density is calculated by dividing the grammage over the caliper, and is usually expressed in grams per cubic centimetre to cancel out the mathematical need for unit conversions between metres and micrometres.