# Luhn Algorithm Calculator

URL: https://speedycalculator.com/calculators/math/luhn-algorithm/
Last updated: 2026-10-30

> The Luhn algorithm calculator computes the check digit for a number (credit card, IMEI, national ID) or validates a complete number with the mod-10 checksum.

## Inputs

- Mode
- Number

## Results

- Result
- Checksum
- Full number with check digit

## Formula

```
From the right, double every second digit (subtract 9 if > 9) and add all digits; valid if the total is divisible by 10
```

## Explanation

The Luhn (mod 10) algorithm, patented by IBM's Hans Peter Luhn in 1960, catches almost all single-digit typing errors and most swaps of adjacent digits. It protects credit card numbers, IMEI codes and many ID numbers.

### How to use the Luhn Algorithm Calculator

- **Mode**
- **Number**

Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.

### How it works

Choose whether you want a check digit or a validation, then enter the digits (spaces are ignored). This is purely a typo check – it says nothing about whether a card exists.

## Worked example

Inputs — Mode: Generate a check digit; Number: 7992739871.

Results — **Result = Check digit: 3**; Checksum = Sum with every second digit doubled (from the right) = 67, so the check digit is (10 − 7) mod 10 = 3; Full number with check digit = 79927398713.

## Key terms

- **Check digit**: A digit added to detect errors.

## FAQ

**Does a valid Luhn number mean a real card?**
No – it only checks for typing mistakes.

**Which errors does Luhn miss?**
Swapping 09 and 90, and some twin errors like 22 ↔ 55.

**Where is it used?**
Credit cards, IMEI numbers, Canadian SIN and many loyalty cards.

**Is the algorithm secret?**
No, it is public and in the public domain.


## Sources

- [Wolfram MathWorld – Luhn algorithm](https://mathworld.wolfram.com/LuhnAlgorithm.html)