Luhn Calculator - Validate or Generate Mod-10 Check Digits

A Luhn calculator runs the Luhn algorithm, also called the mod 10 or modulus 10 algorithm, against any number. It either validates the number by checking its last digit against the expected check digit, or generates the correct check digit to append to a payload. The algorithm is the procedure used by credit card networks, mobile carriers, and many government identification systems to catch typos before a number is sent.

• • Credit card number pre-validation: Check that a 13 to 19 digit card number passes the mod-10 checksum before sending it to a payment gateway.
• • IMEI number verification: Validate the 15-digit IMEI on a phone, required to register a device on most cellular networks.
• • SIN, NPI, and ID number checks: Test Canadian SIN, US NPI, and similar IDs that use a Luhn check digit.
• • Generate Luhn-valid test payloads: Build test card numbers, gift card codes, or sample IDs without re-implementing the algorithm.

The Luhn algorithm is not a cryptographic check, so it cannot tell you whether a card is active. It can tell you whether the digits were typed or transmitted correctly, which is why almost every payment system runs it as the first gate before any database lookup.

When you only need the leftover of a division on its own, Modulo Calculator returns the mod without the rest of the Luhn machinery.

The calculator runs the Luhn algorithm in two passes: one to compute the Luhn sum from the rightmost digit of the payload, and one to compare that sum with the existing check digit (validate) or to format the appended check digit (generate).

• inputNumber: The digit string entered by the user. Non-digit characters such as spaces, hyphens, parentheses, and slashes are stripped before processing.
• method: Validate (run the algorithm on the input with its existing last digit and compare) or generate (treat the input as the payload, run the algorithm, and append the resulting check digit to form a full valid number).
• sum: Total of every digit in the payload after the doubling-and-reduction step. A Luhn-valid number always makes sum a multiple of 10.
• checkDigit: Single 0-9 digit equal to (10 - sum mod 10) mod 10. This is what must appear at the end of a Luhn-valid number.

The doubling-and-reduction step is equivalent to splitting any doubled digit greater than 9 into its tens and ones and adding both; the calculator uses the subtract-9 form because it only touches the doubled values.

The mod-10 step at the end is also why the algorithm is called the modulus 10 algorithm: a Luhn-valid number is one whose Luhn sum plus its check digit is a multiple of 10.

According to Wikipedia - Luhn algorithm, the Luhn algorithm (also called the modulus 10 or mod 10 algorithm) was published in US patent 2,950,048A on 23 August 1960 and is specified in ISO/IEC 7812-1.

For a different kind of single-number property test, Prime Number Checker reports whether a value is prime rather than Luhn-valid.

Four short ideas explain why the algorithm works the way it does and where its blind spots are. Once these are clear, the output panel and the trace read like a checklist rather than a black box.

Knowing the blind spots matters in practice. If two Luhn-valid numbers differ only in a 09/90 swap, the Luhn check treats both as valid and the application layer has to catch the error with another rule.

The mod-10 invariant also makes the check digit unique. For any given payload there is exactly one digit 0-9 that, appended at the end, makes the total a multiple of 10.

For a different check-digit scheme that follows the same validate-or-generate pattern, the GTIN Check Digit Calculator handles UPC, EAN-13, and GTIN-14 barcodes with 3-1 weighted steps.

Enter the number, pick a method, and read the result. The calculator updates as you type, so you can paste a card number and see the validity decision live.

1. 1 Enter the number: Type or paste the digit string. The calculator strips every non-digit character (spaces, hyphens, parentheses, slashes, letters) before running the Luhn check.
2. 2 Pick a method: Choose Validate to compare the existing last digit with the algorithm output, or Generate the check digit to treat the input as a payload with no check digit yet and append a new one that makes the number Luhn-valid.
3. 3 Read the validity and check digit: Validity says Valid when the algorithm agrees with the last digit and Invalid otherwise. Generate always shows Valid because the appended digit satisfies the check. The Luhn Check Digit row shows the 0-9 digit the algorithm produces.
4. 4 Check the Luhn sum: The Luhn Sum row shows the total of every doubled-and-reduced digit. Add the check digit to it and you should always get a multiple of 10 for a valid number.
5. 5 Copy the full Luhn-valid number: The Full Luhn-Valid Number row gives you the digits-only form of the input, or the payload plus the new check digit in generate mode. Use it in a payment form or test file.

Example: a QA engineer needs a Luhn-valid test card number. They enter 424242424242424, pick Generate, and the result panel shows check digit 2, Luhn sum 78, and the full number 4242424242424242. Validity reads Valid because 78 + 2 = 80, a multiple of 10. They copy the full number into the test fixture.

When the rest of the workflow needs to translate the digit string into another base, the Base Converter moves the same digits between binary, octal, decimal, and hexadecimal with a positional breakdown.

The Luhn check is a small algorithm, but a calculator that runs it consistently turns out to be useful in more places than its size suggests.

• • Removes off-by-one doubling mistakes: The most common Luhn mistakes are starting the doubling from the wrong end or miscounting which digits to double. The calculator follows the right-to-left pattern automatically.
• • Handles both check and generate in one tool: Most reference pages only show one of the two modes. The method switch lets you validate, generate, and copy the result without leaving the page.
• • Accepts messy input: Spaces, hyphens, parentheses, and pasted card formatting are stripped before the algorithm runs, so you can paste from an email without cleaning the digits first.
• • Shows the Luhn sum and not just the verdict: The Luhn sum is reported alongside the verdict, so you can confirm the mod-10 invariant by hand. Useful for teaching, code reviews, and debugging libraries.
• • Free and offline-friendly: The whole algorithm runs in the browser with no network calls, so the calculator works on a locked-down payment testing box or in a privacy-sensitive workflow.

Together these benefits save a few minutes per use, which adds up across dozens of test cards. The biggest win is consistency: the calculator gives the same answer every time, traceable through the Luhn sum on the screen.

When the same digit-by-digit pattern is needed on a packed binary register, the Binary Operations Calculator applies AND, OR, and XOR to the bits of two integers with full column traces.

The algorithm itself is fixed, but the meaning of the verdict depends on a few choices you make when you set up the comparison. The same verdict can be useful in one context and misleading in another.

• • The algorithm is known to miss the 09/90 swap and the twin pairs 22-55, 33-66, and 44-77. Use a stronger check, such as the Verhoeff algorithm, for applications that need to catch every adjacent transposition.
• • Luhn validation confirms that a number was likely typed or transmitted correctly, not that it is real, active, or authorized. A Luhn-valid number can still be invented, expired, blocked, or unused; only the issuing system can tell you which.

Treat the calculator as a fast pre-filter. If Invalid, do not bother sending the number downstream; if Valid, send it on but expect the issuing system to apply its own length, prefix, and account checks.

According to Omni Calculator, the Luhn algorithm works by taking a number, doing basic math operations on every digit except the last, and treating the last digit as the check digit that must match the resulting sum.