What is the Verhoeff checksum?

The Verhoeff algorithm is a check-digit scheme published in 1969 that uses the dihedral group D5 rather than simple arithmetic. This lets it detect all single-digit errors and all adjacent transposition errors.

How does Verhoeff differ from Luhn?

Luhn misses one transposition case (swapping 0 and 9), whereas Verhoeff catches every adjacent transposition. Verhoeff achieves this with multiplication, permutation and inverse tables instead of doubling and summing.

What tables does Verhoeff use?

It uses a 10x10 multiplication table d for the dihedral group D5, a permutation table p indexed by position modulo 8, and an inverse table inv. The tool implements the standard published tables.

Where is Verhoeff used in practice?

India's Aadhaar identity number uses a Verhoeff check digit. It is also used in other identifiers where strong protection against single-digit and transposition typos is required.

Does a valid checksum mean the number is registered?

No. A valid Verhoeff checksum only confirms the digits are internally consistent. It does not prove the identifier was issued or is active; that requires the relevant official lookup.

Verhoeff Checksum Checker

The Verhoeff algorithm is a check-digit method designed by Jacobus Verhoeff in 1969. Unlike simpler schemes, it is built on the dihedral group D5, which lets it catch every single-digit error and every adjacent transposition — including the 0-and-9 swap that the Luhn algorithm misses. This checker validates numbers and computes the correct check digit in your browser.

How it works

Verhoeff relies on three lookup tables: a multiplication table d, a permutation table p, and an inverse table inv.

To validate, start with c = 0. For each digit, processed from the right at position i, set c = d[c][p[i mod 8][digit]]. The number is valid if c ends at 0.
To generate a check digit for a payload, run the same loop with the position index offset by one, then the check digit is inv[c].

The permutation table is what makes the algorithm position-sensitive, and the non-commutative group multiplication is what catches transpositions.

Example

The payload 236 has Verhoeff check digit 3, so 2363 is valid. Changing the last digit to 2364 makes the checksum fail, which the tool reports along with the correct expected digit.

Notes

The tool implements the standard published d, p and inv tables, so its results match reference implementations and real-world Aadhaar check digits. A valid checksum confirms internal consistency only, not registration. All computation runs locally and nothing leaves your browser.