ISBN Check Digit Calculator
ISBN-13 check digit and full number.
What it does
ISBN-13 ends with a check digit that catches typos. The first twelve digits weight alternately by one and three, sum up, and round the remainder out of ten. Scanners and catalogs run the same line before trusting a number.
The tool above runs the rule. With 978030640615 the odds give 27 with evens giving 66, so the sum is 93 and the check is 7 for a full 9780306406157. With 978186197271 the sum is 118 and the check is 2. Dashes strip first, so hyphenated pastes work.
Passing arithmetic never proves registration. Any twelve digits can checksum correctly while belonging to no book, and ISBN-10 uses a different mod eleven rule with X. Catalogs check registries after the math.
This page handles ISBN-13 only. It does not validate ISBN-10, ISSN, or barcodes beyond the thirteen digits. For print runs, confirm assignment with the agency.
How to use
- Type the first 12 ISBN digits.
- Dashes and spaces are fine.
- Read the check digit first.
- Read the full 13 digit ISBN.
- Read the sum for records.
- Validate printed barcodes against it.
Formula
- d1-12
- First 12 digits, dashes stripped.
- weights
- Alternating weights 1 and 3 from the left.
- check
- Appended 13th digit.
ISBN-13 mod 10 rule on the first 12 digits. At any non digit the page stops with a message. A passing check confirms arithmetic, never registry assignment.
Worked example
Example: ISBN starting 978030640615
Defaults: 978030640615. Dashes and spaces strip before math.
- Inputs: first 12 digits 978030640615.
- Weight: odd positions times 1, even times 3.
- Sum: 27 plus 66 is 93.
- Check: (10 minus 3) mod 10 is 7.
- Full ISBN is 9780306406157. Tool shows the same.
Reference table
| First 12 | Check | Full ISBN |
|---|---|---|
| 978030640615 | 7 | 9780306406157 |
| 978186197271 | 2 | 9781861972712 |
| 978013468599 | 1 | 9780134685991 |
| 978059600920 | 5 | 9780596009205 |
| 978149195029 | 6 | 9781491950296 |
Limits
- ISBN-13 only. ISBN-10 differs.
- Arithmetic only. No registry check.
- Digits only. Letters rejected.
- One number at a time.
Common mistakes
- Validating ISBN-10 with mod 10.
- Counting positions from zero.
- Forgetting dashes strip (they do not matter).
- Reading pass as registered.
- Mixing ISSN eight digit math.
Try it yourself
Quick checks. Answers sit tucked under each question.
First 12 digits 978186197271?
Odds 40 with evens 78 give sum 118. Check is 2 with full 9781861972712.
First 12 digits 978013468599?
Odds 39 with evens 90 give sum 129. Check is 1 with full 9780134685991.
Questions
How is the sum figured?
Odds times 1 plus evens times 3. Here 93.
How is the check digit figured?
(10 minus sum mod 10) mod 10. Here 7.
What is the full ISBN?
Append it to the 12. Here 9780306406157.
Does this do ISBN-10?
No. ISBN-10 uses mod 11 with X. This page does ISBN-13 only.
Can I paste with dashes?
Yes. Dashes strip first, so hyphenated input works.
Does pass mean registered?
No. This checks arithmetic only, not registry assignment.