# What is an ISBN?

You may have seen on Amazon or near the UPC of your book an ISBN.  What is an ISBN?  Can it be any number?  Why does the Healthcare Economist care?

### What is an ISBN?

According to Wikipedia:

The International Standard Book Number (ISBN) is a unique numeric commercial book identifier based upon the 9-digit Standard Book Numbering (SBN) code created by Gordon Foster, Emeritus Professor of Statistics at Trinity College, Dublin, for the booksellers and stationers W. H. Smith and others in 1966.

The 10-digit ISBN format was developed by the International Organization for Standardization (ISO) and was published in 1970 as international standard ISO 2108. (However, the 9-digit SBN code was used in the United Kingdom until 1974.) Currently, the ISO’s TC 46/SC 9 is responsible for the ISBN. The ISO on-line facility only refers back to 1978.”

Since 1 January 2007, ISBNs have contained 13 digits

### Can it be any number?

The answer is no. Here is why the ISBN is interesting, you can identify certain invalid ISBN yourself! How can you do this? The answer is that the ISBN system uses an check digit error detection function. A check digit is a form of redundancy check used for error detection, the decimal equivalent of a binary checksum. It consists of a single digit computed from the other digits in the message.

“The final character of a ten digit International Standard Book Number is a check digit computed so that multiplying each digit by its position in the number (counting from the right) and taking the sum of these products modulo 11 is 0. The digit the farthest to the right (which is multiplied by 1) is the check digit, chosen to make the sum correct. It may need to have the value 10, which is represented as the letter X.”

Take the book the Social Transformation of American Medicine by Paul Starr for instance.  Its ISBN is 0465079350. The sum of products is 0×10 + 4×9 + 6×8 + 5×7 + 0×6 + 7×5 + 9×4 + 3×3 + 5×2 + 0×1 = 209 ≡ 0 mod 11 (because 209/11 is exactly 19 with a remainder of 0). Thus, this ISBN is valid.

I have created a spreadsheet that you can use to check if the ISBN is valid and also see in more detail how the math works. All you need to do is enter the ISBN in the yellow box. There are additional tabs that gives examples of sample valid and invalid ISBN-10 numbers.

### Why does the Healthcare Economist care?

Two reasons: i) I like books and ii) validity checks any time you use data, whether its data on books or healthcare records.

1. George says:
2. George says: