India Aadhaar Number Validator

An India Aadhaar number validator that checks both the structural rules published by UIDAI and the full Verhoeff dihedral-group checksum — the real algorithm behind every legitimate Aadhaar, explained step by step. Useful for developers building form validation, data-quality teams catching typos before records are submitted, or anyone who wants to understand exactly how Aadhaar check digits work without contacting a government server.

What is an Aadhaar number?

The Aadhaar is a 12-digit unique identity number issued to Indian residents by the Unique Identification Authority of India (UIDAI). Since its introduction in 2009 it has become the primary national identity credential for over 1.3 billion people. Every Aadhaar is printed on an Aadhaar card and stored in UIDAI’s Central Identities Data Repository (CIDR). The number itself does not encode any personal information such as name, address, or date of birth — it is a randomly assigned identifier whose only built-in structure is the first-digit range and a cryptographically robust check digit.

Structural rules

UIDAI’s publicly documented rules for a well-formed Aadhaar are:

1. Exactly 12 decimal digits. No letters, spaces (unless used as grouping separators), or other characters.
2. First digit 2–9. UIDAI never issues numbers beginning with 0 or 1 — those ranges are reserved and will never appear in the wild.
3. Verhoeff check digit. The 12th digit is computed from the first 11 using the Verhoeff algorithm. Processing all 12 digits right-to-left through the algorithm must yield a final checksum of 0.

The Verhoeff algorithm in detail

The Verhoeff checksum (Jacobus Verhoeff, 1969) is based on the mathematical structure of the dihedral group D5 — the symmetry group of a regular pentagon. It requires three fixed lookup tables:

• D (10 × 10 multiplication table): derived from the group operation of D5 extended to ten elements. D[a][b] gives the group product of elements a and b.
• P (8 × 10 permutation table): maps a position (modulo 8) and a digit (0–9) to a permuted digit. The 8-row cycle makes the checksum position-aware, catching transposition errors that simpler modular checksums miss.
• INV (inverse table, not needed for validation): used only when generating the check digit.

Computation: start with checksum c = 0. Traverse the digits from right (position 0) to left (position 11):

c = D[ c ][ P[ position mod 8 ][ digit ] ]

After all 12 digits, a valid number has c === 0. The “Show algorithm trace” button displays every intermediate value so you can follow exactly what each digit contributes.

Why Verhoeff beats Luhn: the Luhn algorithm (used on credit cards) detects all single-digit errors but misses some adjacent transpositions. Verhoeff detects all single-digit errors and all adjacent transpositions — it catches every swap of two neighbouring digits, which is the most frequent human data-entry mistake.

Example

The number 2345 6789 0124 is an obviously-fake example (not a real UIDAI-issued number) that satisfies all three rules: the first digit is 2, the length is exactly 12, and the 12th digit (4) is the correct Verhoeff check digit for the preceding 11 digits. Changing any single digit — for example to 2345 6789 0125 — produces a checksum of 9 instead of 0, and the validator will report the failure with the exact mismatch value.

Privacy guarantee: every check runs locally in your browser. No data is uploaded, no server is contacted, and nothing is stored. This tool does not query the UIDAI authentication API and cannot confirm whether a number is registered to anyone.