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Conversion & Calculations
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Conversions & Calculations

There are standard rules for converting an ISBN-10 into an ISBN-13.

Last updated June 23, 2009

Review the information below for a complete understanding of these conversion rules. You will also want to review the official ISBN Users' Manual.

Online Conversion Tool

The Library of Congress ISBN Converter can also be used on a one-to-one basis for automatic conversion of an ISBN-10 to an ISBN-13.Click here to access the Library of Congress online converter.

Converting an ISBN-10 to an ISBN-13 (e.g., Bookland EAN)

Drop the check digit (the last digit) from your existing ISBN-10.
For example, your ISBN-10 is 0-940016-73-7. By dropping the check digit (7), you get a 9-digit number, 0-940016-73.

Add the prefix '978' to the beginning of your 9-digit number.
Your 9-digit 0-940016-73 now becomes 12 digits, 978-0-940016-73.

Recalculate your check digit using the modules 10 check digit routine.
The modules 10 check digit routine is the current routine used to calculate the check digit for the Bookland EAN.

Here's how, using the calculations shown in Table 1-1. Please note that the values shown in the examples below may be different for each ISBN.

ISBN = 9 7 8 0 9 4 0 0 1 6 7 3
Weighting Factors 1 3 1 3 1 3 1 3 1 3 1 3
Values (product) 9 + 21 + 8 + 0 + 9 + 12 + 0 + 0 + 1 + 18 + 7 + 9 = 94

Using the 12-digit number from Step 2 (shown in Table 1-1), multiply each digit by the weighting factor shown beneath it in Table 1-1.

In this example, you have (9x1) + (7x3) + (8x1) + (0x3)...and so on.

Add the resulting values together. The sum of the example values equals 94.

Divide the sum by the modulus (which is always 10). Divide 94 by 10. The example result is 9, with a remainder of 4.

Using the standard modulus (10), subtract the remainder from 10 to get the check digit (last digit). In this example, 10 minus 4 equals the check digit of 6.

Add the check digit to the end of the 12-digit number created in Step 2. The conversion from a 10-digit ISBN to a 13-digit ISBN is complete.

The 13-digit ISBN shown in the example is 978-0-940016-73-6.

Note:
There is one exception to this formula: whenever the remainder is zero (0), the check digit is always zero (0) as well.

The algorithm for checking an ISBN-13 beginning with '979' is the same as the algorithm for ISBN-13s beginning with '978'. To validate any ISBN-13, drop the given check digit, recalculate it, and compare the result of the new calculation to the original check digit. If they match, the number is a valid ISBN-13. The same algorithm applies to any 13-digit EAN product identifier worldwide.

Algorithm for checking a converted ISBN-13 (e.g., Bookland EAN)

 

Assign the constant weighting factors associated with each position in the EAN. Multiply each digit by its associated weighting factor and add together (e.g. 9780901 69066 1).

Weighting Factors 1 3 1 3 1 3 1 3 1 3 1 3 1
Bookland EAN 9 7 8 0 9 0 1 6 9 0 6 6 1
Values 9+ 21+ 8+ 0+ 9+ 0+ 1+ 18+ 9+ 0+ 6+ 18+ 1=100

Divide the sum by 10 and the result must be a whole number with no remainder.


Converting an ISBN-13 (e.g., Bookland EAN) to an ISBN-10 - '978' FORMAT ONLY

1) Remove the prefix '978' and the check digit (last digit) from the EAN.
You are left with a nine-digit number. For example, EAN 9780940016610 becomes 094001661.

2) Recalculate the check digit.
Using the 9-digit number from Step 1 above, multiply each digit by the weighting factor shown in the table below.

In this example, you have (10x0) + (9x9) + (8x4) + (7x0)...and so on.

Weighting Factors 10 9 8 7 6 5 4 3 2
Bookland EAN 0 9 4 0 0 1 6 6 1
Values 0+ 81+ 32+ 0+ 0+ 5+ 24+ 18+ 2=162

Add the resulting values together. The sum of the example values equals 162.

Divide the sum by 11. For example, 162 / 11 = 14 with a remainder of 8. 

Subtract the remainder, if any, from 11. The result is the check digit. In this example, 11 minus 8 equals 3. Therefore, the 10-digit ISBN check digit is 3.

Add the check digit to the end of the 9-digit number created in Step 1. The conversion from a 13-digit ISBN to a 10-digit ISBN is complete.

The 10-digit ISBN shown in the example is 0-940-01661-3.

Note:
If the result is "0", the check digit is "0". If the value of the check digit is 10, that should be represented by the roman X.

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