CPF/CNPJ Validator

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check digit validation algorithm

How a CPF and CNPJ validator decides what counts as valid

Validating a CPF or CNPJ is not about checking a string length: it means redoing the same weighted sum that generated the document and comparing the result against its last two digits. This page walks through that algorithm working, and failing, with concrete numbers.

One algorithm, two documents, different weights

CPF and CNPJ share the same underlying idea: run modulo 11 twice over a weighted sum, once for each check digit. The difference is base length and weight tables. CPF weighs 9 digits with values from 10 to 2 and then 11 to 2; CNPJ weighs 12 characters with 5, 4, 3, 2, 9, 8, 7, 6, 5, 4, 3, 2 and then 6, 5, 4, 3, 2, 9, 8, 7, 6, 5, 4, 3, 2, resetting the count halfway because its base is longer.
That recalculation is what makes a check digit useful against typing errors. Take the synthetic CPF 111.444.777-35: redoing the sum over base 111444777, the algorithm expects 35. Swap only the last two digits by mistake, into 111.444.777-53, and the same recalculation still expects 35 but receives 53; the mismatch shows up instantly, with no registry lookup needed, just reapplying the formula to the leading digits.
The real trap: modulo 11 by itself cannot tell a structurally impossible document from a valid one. Base 111111111 closes the calculation perfectly, the computed digits come out to 11, exactly matching 111.111.111-11. Yet no CPF ever leaves the Receita Federal with all 11 digits repeated, so every serious validator adds a second test, just for single-character repeated sequences, on top of the modulo-11 arithmetic.

Three validation outcomes, three reasons

Valid CPF (synthetic)

Input: 111.444.777-35
Expected output: válido: dígito esperado 35, dígito recebido 35

Recalculating over base 111444777 returns exactly the two digits provided, so the validator approves without needing anything else.

CPF with swapped check digits

Input: 111.444.777-53
Expected output: inválido: dígito esperado 35, dígito recebido 53

Same base, same calculation, same expected result as the previous example; only the provided digit changed, and that alone is enough for the algorithm to reject it.

CPF with all digits equal

Input: 111.111.111-11
Expected output: inválido, mesmo com a conta do módulo 11 fechando certinho

The recalculation confirms 11 is the mathematically correct digit for this base; the rejection comes from a separate filter for repeated sequences, not from the arithmetic.

Full tool FAQ

Does the tool validate CPF and CNPJ through check digits?

Yes. Local validation checks the length (11 digits for CPF, 14 for CNPJ), rejects common invalid patterns like all-equal digits, and recomputes the check digits with modulo 11, comparing them against the ones entered. If the math matches, the number is considered well-formed. That applies to both numeric CNPJ and the new alphanumeric CNPJ with letters, which the tool detects automatically.

What does a valid CPF mean?

Does a valid CPF mean the person exists?

How do CPF and CNPJ check digits work, including the alphanumeric ones?

Why are repeated sequences usually treated as invalid?

Since when do CNPJ numbers with letters (alphanumeric CNPJ) exist?

Can I remove punctuation before validating CPF or CNPJ, and do lowercase letters work?

When is local validation not enough?

Frequently asked questions

Do CPF and CNPJ use the same check digit calculation?

The idea is the same, modulo 11 twice over a weighted sum, but the weights differ because a CNPJ base has 12 characters against a CPF 9; CNPJ weights reset at the fifth position, CPF weights just descend to the end.

Can a CPF with all matching digits be mathematically valid?

It can, and that is exactly what happens with 111.111.111-11: modulo 11 closes the calculation. The Receita Federal never issues a number like that, so validators treat repeated sequences as a test separate from the arithmetic.

Can the validator detect a single mistyped digit?

Yes, because it recalculates both check digits from the leading digits and compares them against what was typed; any error in the check digits or in the base changes the weighted sum and breaks the comparison.

Why doesn't validation confirm the document exists at the Receita Federal?

Because the algorithm only redoes a math calculation over the digits provided, without querying any official registry; a number can close modulo 11 perfectly and still have never been issued to anyone.

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check digit validation algorithm

How a CPF and CNPJ validator decides what counts as valid

One algorithm, two documents, different weights

CPF and CNPJ share the same underlying idea: run modulo 11 twice over a weighted sum, once for each check digit. The difference is base length and weight tables. CPF weighs 9 digits with values from 10 to 2 and then 11 to 2; CNPJ weighs 12 characters with 5, 4, 3, 2, 9, 8, 7, 6, 5, 4, 3, 2 and then 6, 5, 4, 3, 2, 9, 8, 7, 6, 5, 4, 3, 2, resetting the count halfway because its base is longer.

That recalculation is what makes a check digit useful against typing errors. Take the synthetic CPF 111.444.777-35: redoing the sum over base 111444777, the algorithm expects 35. Swap only the last two digits by mistake, into 111.444.777-53, and the same recalculation still expects 35 but receives 53; the mismatch shows up instantly, with no registry lookup needed, just reapplying the formula to the leading digits.

The real trap: modulo 11 by itself cannot tell a structurally impossible document from a valid one. Base 111111111 closes the calculation perfectly, the computed digits come out to 11, exactly matching 111.111.111-11. Yet no CPF ever leaves the Receita Federal with all 11 digits repeated, so every serious validator adds a second test, just for single-character repeated sequences, on top of the modulo-11 arithmetic.

Three validation outcomes, three reasons

Valid CPF (synthetic)

Input: 111.444.777-35
Expected output: válido: dígito esperado 35, dígito recebido 35

Recalculating over base 111444777 returns exactly the two digits provided, so the validator approves without needing anything else.

CPF with swapped check digits

Input: 111.444.777-53
Expected output: inválido: dígito esperado 35, dígito recebido 53

Same base, same calculation, same expected result as the previous example; only the provided digit changed, and that alone is enough for the algorithm to reject it.

CPF with all digits equal

Input: 111.111.111-11
Expected output: inválido, mesmo com a conta do módulo 11 fechando certinho

The recalculation confirms 11 is the mathematically correct digit for this base; the rejection comes from a separate filter for repeated sequences, not from the arithmetic.

Full tool FAQ

Does the tool validate CPF and CNPJ through check digits?

What does a valid CPF mean?

Does a valid CPF mean the person exists?

How do CPF and CNPJ check digits work, including the alphanumeric ones?

Why are repeated sequences usually treated as invalid?

Since when do CNPJ numbers with letters (alphanumeric CNPJ) exist?

Can I remove punctuation before validating CPF or CNPJ, and do lowercase letters work?