ISBN-13 check digit

This capability implements the standard ISBN-13 mod-10 rule on a twelve-digit payload—weights alternating one and three from the left—and either returns the check digit plus the completed thirteen-digit barcode, or validates a full thirteen-digit string with an explicit valid flag and the expected digit. Non-numeric input and wrong lengths fail with invalid_input instead of silent stripping, so you never store a half-cleaned ISBN. The same pure arithmetic runs free in the browser and at the published API price for automation pipelines.

How the ISBN-13 check digit is calculated

The first twelve digits form the book number payload: a three-digit GS1 prefix (almost always 978 or 979 for books), a registration-group element, a registrant (publisher) element, and a publication element whose lengths vary by agency rules. To compute it, walk the twelve payload digits from left to right with 1-based positions: multiply each odd-position digit by one and each even-position digit by three, add those products, then take the check digit as ten minus that sum modulo ten, modulo ten again so a zero remainder yields check digit zero. Compared with multi-symbology barcode validators, the search intent here is narrow: people who need an ISBN-13 check digit calculator for twelve-digit payloads, not a general UPC-or-case GTIN checker.

Input contract, modes, and error behaviour

Send a number field that contains only characters zero through nine. Wrong length is an explicit error that names the mode and the length you sent—twelve for compute, thirteen for validate—so client forms can show “need twelve digits” without guessing. Empty strings, missing number, and invalid mode values fail before any weighted sum runs and are not billed. Prefer compute when you mint or complete book numbers from a twelve-digit body; prefer validate when you gate a catalog import, POS scan, or marketplace listing on a full thirteen-digit ISBN-13 barcode. Spaces, hyphens, letters, and decimal points are rejected as non-numeric input with invalid_input so a silently stripped value never reaches storage—paste 978-0-306-40615 without the check digit and you must strip hyphens client-side first, or send the pure digit form. Mode compute is the default: the engine requires exactly twelve digits, returns check_digit as a one-character string, and returns with_check as the thirteen-digit ISBN-13 you can print on a barcode or persist in a catalog. Mode validate requires exactly thirteen digits; the response reports valid true when the trailing digit matches the recomputed expected_check_digit, and always includes payload (the first twelve digits), check_digit, expected_check_digit, and length thirteen. Alias keys such as digits, isbn, and code are accepted for the same payload field so integrations that already speak “isbn” do not need a rename. Because the path is pure parse with no clock, random source, or network, the same JSON body always yields the same JSON result on the free browser tool and on the API at $0.002 per successful request.

Where ISBN-13 check digits fit real workflows

Publishers and catalog teams receive twelve-digit internal book numbers—prefix plus registration group, registrant, and title—and must append the official ISBN-13 check digit before printing EAN-13 barcodes on covers, jackets, or stickers. Bookstore POS and receiving apps validate thirteen-digit codes at the counter so a single transposition does not create a phantom title and a stock mismatch. Library and aggregator data-quality jobs walk every ISBN-13 column in a MARC, ONIX, or CSV export, call validate mode, and quarantine rows where valid is false—catching both human edits and off-by-one bugs in generators that still emit legacy ISBN-10 without proper conversion. E-commerce and marketplace onboarding forms can recompute expected_check_digit and show a friendly correction when a seller pastes an ISBN with a mistyped last digit. Do not treat a passing ISBN-13 check as proof of title ownership, agency registration, or correct hyphenation groups; it only proves the mod-10 digit is consistent with the twelve-digit payload under the standard ISBN-13 weights.