How the Spanish DNI letter is calculated (and why it exists)

When the Spanish DNI incorporated the control letter in 1990, the goal was twofold: to detect typing errors when entering the number and to make document forgery harder. The letter acts as a check digit, just like the control digit of an IBAN or the last digit of an EAN-13 barcode.

The algorithm step by step

• •Take the DNI number (8 digits, without the letter).
• •Divide it by 23 and keep the remainder (modulo operation).
• •The remainder will be a number between 0 and 22.
• •Look up that number in the 23-letter table to get the control letter.

The letter table

The official sequence is: T R W A G M Y F P D X B N J Z S Q V H L C K E. Remainder 0 corresponds to T, remainder 1 to R, remainder 2 to W… and so on up to remainder 22, which corresponds to E. The letters I, O, Ñ and U are excluded to avoid visual confusion with the digits 1, 0 and with Ü or V.

Practical example

DNI number 12345678. Divide 12,345,678 ÷ 23 = 536,768 remainder 14. Number 14 in the table corresponds to the letter Z. So the full DNI would be 12345678Z. You can verify this against any official database.

NIE: the variant for foreigners

The NIE (Número de Identidad de Extranjero) starts with X, Y or Z. To calculate the control letter, X is replaced with 0, Y with 1 and Z with 2, then the same algorithm as the DNI is applied. For example, a NIE starting with Y is treated as if it started with 1, the modulo 23 is applied and the result is looked up in the same table.