Luhn Algorithm Checker
Analyze the mathematics behind credit card check digit verification. View an interactive digit-by-digit calculation table illustrating the ISO/IEC 7812 Modulo 10 formula.
Interactive Luhn Algorithm (Mod 10) Inspector
Enter any number or PAN to examine step-by-step digit doubling, summation, and checksum verification.
Step-by-Step Calculation Breakdown
| Index | Digit | Position (from right) | Operation | Doubled | Reduced Value |
|---|---|---|---|---|---|
| 1 | 7 | 10 | Keep (×1) | - | 7 |
| 2 | 9 | 9 | Double (×2) | 18 | 9 |
| 3 | 9 | 8 | Keep (×1) | - | 9 |
| 4 | 2 | 7 | Double (×2) | 4 | 4 |
| 5 | 7 | 6 | Keep (×1) | - | 7 |
| 6 | 3 | 5 | Double (×2) | 6 | 6 |
| 7 | 9 | 4 | Keep (×1) | - | 9 |
| 8 | 8 | 3 | Double (×2) | 16 | 7 |
| 9 | 7 | 2 | Keep (×1) | - | 7 |
| 10 | 1 | 1 | Double (×2) | 2 | 2 |
| 11 | 3 | 0 | Check Digit | - | 3 |
| Sum of Reduced Values: | 70 | ||||
How it works: Beginning from the check digit at position 0 (rightmost), every second digit to the left is multiplied by 2. If the product exceeds 9, 9 is subtracted from it. Finally, all values are summed. If sum % 10 === 0, the number satisfies ISO/IEC 7812.
Synthetic cards are generated strictly for software engineering, user-interface validation, and automated QA tests. They are not issued by financial institutions, carry no credit balance, and are not intended or verified for live payment authorization.
The Mathematics of the Luhn Algorithm
Invented by IBM scientist Hans Peter Luhn in 1954 and patented in 1960, the Luhn algorithm is a simple checksum formula used to validate a variety of identification numbers, notably payment cards, IMEI numbers, and Canadian Social Insurance Numbers.
It is designed not as a cryptographic hash, but rather as an error-detection mechanism intended to detect accidental mistypes, such as single-digit entry errors and most adjacent digit transpositions (with known exceptions such as 09 ↔ 90).
For a comprehensive mathematical breakdown, worked examples, and check digit synthesis formulas, read our dedicated Luhn Algorithm Guide.
Frequently Asked Questions
What is the Luhn algorithm? ↓
The Luhn algorithm, also called Modulo 10, is a checksum formula used with identifiers including payment-card numbers, mobile-device IMEI numbers, and Canadian Social Insurance Numbers (SIN). The Luhn algorithm detects single-digit errors and helps detect many common digit-entry mistakes, including most adjacent digit transpositions. A known exception is the transposition 09 ↔ 90.
How does the step-by-step calculation table work? ↓
The calculator processes digits from right to left, doubles every second digit, subtracts 9 if the product exceeds 9, sums all resulting values, and checks whether the total is evenly divisible by 10.
Can I calculate the check digit for an incomplete number? ↓
Yes. By computing the partial sum of your number's payload, you can find the check digit that brings the sum up to the nearest multiple of 10. Learn the exact arithmetic in our Luhn Algorithm Guide.
Does passing the Luhn check mean a number is authorized for payment? ↓
No. The Luhn algorithm is an offline mathematical checksum. It does not verify account existence, issuer status, available balance, CVV/CVC, expiration status, or payment authorization, and this checker does not contact a card issuer or payment network. Passing the checksum only means the number satisfies the Luhn calculation; it does not indicate that the number is authorized for live payment use.
Does this checker send the entered number to a server? ↓
The Luhn calculation runs locally in your browser and does not intentionally submit the entered number to our application server. Use synthetic test data rather than real payment credentials.
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