Verhoeff Check Digit
The Verhoeff algorithm appends a single check digit to a number so that every single-digit error and every adjacent-digit transposition is detected — a property the more common Luhn checksum does not have. It uses the dihedral group D₅ with a permutation table. This tool computes the Verhoeff check digit for a number body and validates a number that already has its check digit appended. Runs locally in your browser.
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Verhoeff works in the dihedral group D₅ (the symmetries of a pentagon). For each digit read right-to-left it combines a permuted digit into a running value using a 10×10 multiplication table d and an 8-row permutation table p; the check digit is the inverse inv[c] of the final value. Validation runs the same pass over all digits (including the appended one) and passes iff the result is 0. Unlike Luhn, which misses some adjacent transpositions (e.g. 09 ↔ 90), Verhoeff catches all single-digit errors and all adjacent transpositions, plus most twin errors and jump transpositions. Input is decimal digits only. Pairs with the Luhn Validator, ISBN Validator, and IBAN Validator tools. Everything runs locally — nothing leaves your browser.