Luhn Algorithm (Mod 10) — Developer Guide

The Luhn algorithm (also called Mod 10) is a simple checksum formula used to validate identification numbers. Created by IBM scientist Hans Peter Luhn in 1954, it's the standard check digit mechanism for credit card numbers, IMEI numbers, ICCID/SIM numbers, and many other identification systems. This guide covers everything a developer needs: how it works, step-by-step examples, implementations in 4 languages, and common pitfalls.

How Luhn Works

The algorithm processes digits from right to left:

1. Starting from the rightmost digit (the check digit), moving left
2. Double every second digit (i.e., every digit in an even position from the right, starting with the second-to-last)
3. If the doubled value is > 9, subtract 9 (equivalently, add the two digits of the product: e.g., 14 → 1+4 = 5, which is 14 − 9)
4. Sum all digits (the unmodified ones + the processed ones)
5. If the total mod 10 = 0, the number is valid

Step-by-Step Example

Let's validate the credit card number 4532 0123 4567 8917:

Sum = 8+5+6+2+0+1+4+3+8+5+3+7+7+9+2+7 = 70. 70 mod 10 = 0 → Valid.

Generating a Check Digit

To generate a check digit for a number without one:

1. Append 0 as a placeholder check digit
2. Compute the Luhn sum
3. If sum mod 10 = r, the check digit = (10 − r) mod 10

Example

Generate a check digit for 4532 0123 4567 891:

• Append 0: 4532 0123 4567 8910
• Luhn sum = 63
• Check digit = (10 − 3) mod 10 = 7
• Full number: 4532 0123 4567 8917

Where Luhn Is Used

Credit Card Number Structure

4532 0123 4567 8917
|||| |||| |||| ||||
|||| |||| |||| |||└── Check digit (Luhn)
|||| |||| |||| ||└─── Account identifier (last 5 = check + account)
|||| |||| |||| └──── Account identifier
|||| |||| |||└────── Account identifier
|||| |||| ||└─────── Bank number
|||| |||| |└──────── Bank number
|||| |||| └───────── Bank number
|||| |||└─────────── Bank number
|||| ||└──────────── Bank number
|||| |└───────────── Issuer identifier
|||| └─────────────── Issuer identifier
|||└──────────────── Issuer identifier
||└───────────────── Major industry: 4 = Banking
|└────────────────── MII: 4 = Visa
└────────────────--- MII: 4 = Visa

Major Industry Identifier (MII)

Code Implementations

Python

def luhn_validate(number: str) -> bool:
    """Validate a number using the Luhn algorithm."""
    digits = [int(d) for d in number if d.isdigit()]
    if len(digits) < 2:
        return False

    # Process from right to left
    total = 0
    for i, d in enumerate(reversed(digits)):
        if i % 2 == 1:  # Double every second digit from right
            d = d * 2
            if d > 9:
                d -= 9
        total += d

    return total % 10 == 0


def luhn_check_digit(partial: str) -> int:
    """Compute the Luhn check digit for a partial number."""
    digits = [int(d) for d in partial if d.isdigit()]
    # Insert 0 as check digit placeholder
    digits.append(0)

    total = 0
    for i, d in enumerate(reversed(digits)):
        if i % 2 == 1:
            d = d * 2
            if d > 9:
                d -= 9
        total += d

    return (10 - (total % 10)) % 10


# Test
print(luhn_validate("4532012345678917"))  # True
print(luhn_check_digit("453201234567891"))  # 7

JavaScript (Browser / Node)

function luhnValidate(number) {
    const digits = number.replace(/\D/g, '');
    if (digits.length < 2) return false;

    let sum = 0;
    let alternate = false;

    for (let i = digits.length - 1; i >= 0; i--) {
        let d = parseInt(digits[i], 10);
        if (alternate) {
            d *= 2;
            if (d > 9) d -= 9;
        }
        sum += d;
        alternate = !alternate;
    }

    return sum % 10 === 0;
}

function luhnCheckDigit(partial) {
    return luhnValidate(partial + '0')
        ? 0
        : 10 - ((computeSum(partial) + 0) % 10);
    // Simplified: append 0, compute sum, return (10 - sum%10) % 10
}

// Test
console.log(luhnValidate('4532012345678917'));  // true

C

#include <stdio.h>
#include <string.h>
#include <stdbool.h>

bool luhn_validate(const char *number) {
    int len = strlen(number);
    int sum = 0;
    bool alternate = false;

    for (int i = len - 1; i >= 0; i--) {
        if (number[i] < '0' || number[i] > '9') continue;
        int d = number[i] - '0';
        if (alternate) {
            d *= 2;
            if (d > 9) d -= 9;
        }
        sum += d;
        alternate = !alternate;
    }

    return (sum % 10) == 0;
}

int main() {
    printf("%d\\n", luhn_validate("4532012345678917"));  // 1 (true)
    return 0;
}

Java

public class Luhn {
    public static boolean validate(String number) {
        String digits = number.replaceAll("\\D", "");
        if (digits.length() < 2) return false;

        int sum = 0;
        boolean alternate = false;
        for (int i = digits.length() - 1; i >= 0; i--) {
            int d = digits.charAt(i) - '0';
            if (alternate) {
                d *= 2;
                if (d > 9) d -= 9;
            }
            sum += d;
            alternate = !alternate;
        }
        return sum % 10 == 0;
    }

    public static void main(String[] args) {
        System.out.println(validate("4532012345678917"));  // true
    }
}

Common Mistakes

When NOT to Use Luhn

Luhn Error Detection Rates

IMEI Check Digit

IMEI (International Mobile Equipment Identity) numbers use Luhn for the 15th digit (check digit):

IMEI: 356938035678804
TAC:  35693803  (Type Allocation Code, identifies model)
SN:   567880    (Serial number)
CD:   4         (Luhn check digit of TAC+SN)

ICCID (SIM Card) Validation

ICCID (Integrated Circuit Card Identifier) is the 19–20 digit number on SIM cards. It starts with 89 (E.164 country code for telephony) and ends with a Luhn check digit:

ICCID: 8944 5012 3456 7890 1234
       |||  |    |    |    |   |
       89   │    │    │    │   └── Luhn check digit
       │    │    │    │    └────── Account code
       │    │    │    └─────────── Account code
       │    │    └──────────────── Issuer identifier
       │    └───────────────────── Country code (44 = UK)
       └────────────────────────── E.164 telephony country code

Summary

For related tools, see our CRC Calculator for error-detecting codes, HMAC Generator for message authentication, and Hash Digest Calculator for cryptographic hashing.