Last updated: 2026-07-13

Luhn Check Digit

The Luhn algorithm — also known as the mod 10 algorithm — is a checksum formula that guards long identifier numbers against accidental typos. It works by appending one extra digit, the check digit, that is derived from all the other digits. A quick arithmetic test on the complete number then reveals whether it is internally consistent. Hans Peter Luhn described the method at IBM in 1954, and it is now standardised as part of ISO/IEC 7812.

This calculator has two modes: compute a check digit for a number that does not have one yet, and validate whether a complete number satisfies the Luhn condition. It operates on any digit string, so it is equally suited to ID numbers, IMEI device identifiers, and barcodes.

How the algorithm works

Starting from the rightmost digit and moving left, every second digit is doubled. When doubling produces a two-digit number, its digits are added together — equivalently, subtract 9. All the resulting values are then summed. For a payload without a check digit, the check digit is:

$c = (10 - (S \bmod 10)) \bmod 10$

where $S$ is the weighted sum. A complete number is valid when the same weighted sum, this time including the check digit, is a multiple of 10.

Worked example — 7992739871

Take the payload 7992739871 (the neutral example from the algorithm's specification). Number the digits from the right, then double every second one starting at position 1:

The values sum to $S = 67$. The check digit is therefore:

$c = (10 - (67 \bmod 10)) \bmod 10 = (10 - 7) \bmod 10 = 3$

Appending it gives the full number 79927398713. To validate that complete number, the weighted sum comes to 70, which is a multiple of 10 — so it passes.

What errors it catches

The single check digit cannot catch every mistake, but it is tuned to the errors people actually make when copying long numbers:

• Any single-digit error — one digit typed wrong — is always detected.
• Most transpositions of two adjacent digits are detected. The one exception is swapping the pair 09 for 90 (and vice versa), because those two produce the same weighted contribution.

Because it uses a base-10 weighted sum, the Luhn scheme is a lightweight integrity check, not an error-correcting code: it can tell you that something is wrong, but not which digit is wrong. For error correction, coding-theory tools such as a Hamming Distance Calculator or a CRC Checksum Calculator are the appropriate next step.

Where Luhn check digits appear

The mod 10 scheme is embedded in many everyday identifier formats:

• IMEI numbers, the 15-digit identifiers of mobile phones, end in a Luhn check digit.
• Payment and loyalty card numbers use a trailing Luhn digit so a point-of-sale terminal can reject an obvious mistype before contacting the network.
• National and tax identification numbers in several countries include a Luhn digit.
• Product and shipping barcodes use Luhn or closely related mod 10 variants.

What passing the check does and does not mean

The Luhn algorithm is a public formula with no secret key. Passing it proves only that a number's digits are mutually consistent — never that the number was actually issued, registered, or belongs to anyone. Anyone can write down a digit string that satisfies the check.

For that reason, Luhn is used as a fast first-pass filter: reject clearly mistyped input immediately, then defer to an authoritative lookup for anything that survives. It is a data-quality aid, and this tool is meant for understanding how the checksum works and for testing arbitrary digit strings such as IDs, IMEI numbers, and barcodes. For a keyed, tamper-resistant integrity check you would use a cryptographic hash instead — see the Hash Collision Probability Calculator for why checksum length matters there.