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EAN-13 check digit

EAN-13 with a check digit

EAN-13 is the 13-digit GS1 standard used in retail across nearly the whole planet. The first 12 digits identify the registered company and the specific product inside that company's own catalog, and the 13th exists only to catch a scanning or typing error: this generator accepts the 12-digit body and calculates the 13th digit automatically using the official GS1 formula.

The math behind the 13th digit

EAN-13's structure reserves its leading digits for the company prefix registered with a member GS1 organization, not for the country where the product was physically manufactured: goods made anywhere can carry the prefix of the country where the owning company is registered. The following digits identify the specific item inside that company's own numbering, and the final digit is the check digit. In the bars, the symbol splits into a left group of 6 digits and a right group of 6, each side framed by a fixed 3-module guard pattern, and the first digit is never drawn directly: it is encoded through the parity pattern chosen for the 6 left digits.
The calculation sums each of the 12 body digits multiplied by an alternating weight, 3 on the rightmost digit and 1 on the next, alternating all the way to the leftmost digit; the check digit equals 10 minus the remainder of that sum divided by 10, with a second modulo 10 turning a would-be result of 10 into 0. For 400638133393 the weighted sum reaches 89 (4x1 + 0x3 + 0x1 + 6x3 + 3x1 + 8x3 + 1x1 + 3x3 + 3x1 + 3x3 + 9x1 + 3x3), 89 modulo 10 gives 9, and 10 minus 9 produces check digit 1: the finished code reads 4006381333931.
This check digit catches any single-digit error: because the weights involved, 1 and 3, are both coprime with 10, swapping one digit for another always shifts the weighted sum away from the expected modulo 10 match, so the scanner rejects the read instead of silently accepting the wrong product or price. Worth noting: if you type all 13 digits instead of 12, the generator does not recompute or fix anything, it only validates the format (13 digits) and draws exactly the check digit you provided, even if that digit is mathematically wrong.

From a 12-digit body to the finished code

12-digit body calculated by the generator

Input: 400638133393
Expected output: 4006381333931

Weighted sum 89, modulo 10 equals 9, check digit 1.

A different product, same calculation

Input: 690123456789
Expected output: 6901234567892

The same alternating 3-and-1 weight formula applies to any GS1 prefix, only the digits themselves change the result.

Typing all 13 digits yourself

Input: 4006381333930
Expected output: Símbolo desenhado com o dígito 0 no final, sem correção

Since the body already has 13 digits, the generator only checks the format and never recomputes the check digit, even though the correct one would be 1.

Full tool FAQ

What is the difference between Code 128, EAN and UPC?

Code 128 is a dense and flexible symbology for internal operations. EAN and UPC are numeric retail standards and depend on valid commercial identification.

Is the check digit generated automatically?

Is SVG better than PNG for barcodes?

What is a quiet zone?

Can I invent an EAN for a real product?

Why does my printed barcode not scan?

Does the tool validate commercial registration?

Are barcode values sent to the server?

Frequently asked questions

Why enter only 12 digits instead of the full 13?

Because typing all 13 digits makes the generator only validate the format and draw exactly what you wrote, without recalculating anything. Entering 12 lets the official formula compute the 13th check digit for you, avoiding a code with a wrong checksum.

What does this check digit actually catch?

Single-digit substitution errors, for example a bad scanner read or a typo made while registering the product. Because the sum's weights, 1 and 3, are both coprime with 10, swapping any one digit for another always changes the modulo 10 result, so the error never slips through mathematically.

Do the leading EAN-13 digits show the country where the product was made?

No. They show the company prefix registered with the GS1 organization that issued it, not the country where the goods were physically manufactured. A factory anywhere in the world can produce goods carrying the prefix of the country where the brand's owning company is registered.

Why does the sum alternate two weights, 3 and 1, instead of weighting everything the same?

Because that alternation between two distinct weights, standardized by GS1, is exactly what every EAN, UPC and GTIN reader in the world expects when it recalculates and checks the digit. A uniform weight would catch fewer errors and, more importantly, would break compatibility with every scanner on the market.

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EAN-13 check digit

EAN-13 with a check digit

The math behind the 13th digit

EAN-13's structure reserves its leading digits for the company prefix registered with a member GS1 organization, not for the country where the product was physically manufactured: goods made anywhere can carry the prefix of the country where the owning company is registered. The following digits identify the specific item inside that company's own numbering, and the final digit is the check digit. In the bars, the symbol splits into a left group of 6 digits and a right group of 6, each side framed by a fixed 3-module guard pattern, and the first digit is never drawn directly: it is encoded through the parity pattern chosen for the 6 left digits.

The calculation sums each of the 12 body digits multiplied by an alternating weight, 3 on the rightmost digit and 1 on the next, alternating all the way to the leftmost digit; the check digit equals 10 minus the remainder of that sum divided by 10, with a second modulo 10 turning a would-be result of 10 into 0. For 400638133393 the weighted sum reaches 89 (4x1 + 0x3 + 0x1 + 6x3 + 3x1 + 8x3 + 1x1 + 3x3 + 3x1 + 3x3 + 9x1 + 3x3), 89 modulo 10 gives 9, and 10 minus 9 produces check digit 1: the finished code reads 4006381333931.

This check digit catches any single-digit error: because the weights involved, 1 and 3, are both coprime with 10, swapping one digit for another always shifts the weighted sum away from the expected modulo 10 match, so the scanner rejects the read instead of silently accepting the wrong product or price. Worth noting: if you type all 13 digits instead of 12, the generator does not recompute or fix anything, it only validates the format (13 digits) and draws exactly the check digit you provided, even if that digit is mathematically wrong.

From a 12-digit body to the finished code

12-digit body calculated by the generator

Input: 400638133393
Expected output: 4006381333931

Weighted sum 89, modulo 10 equals 9, check digit 1.

A different product, same calculation

Input: 690123456789
Expected output: 6901234567892

The same alternating 3-and-1 weight formula applies to any GS1 prefix, only the digits themselves change the result.

Typing all 13 digits yourself

Input: 4006381333930
Expected output: Símbolo desenhado com o dígito 0 no final, sem correção

Since the body already has 13 digits, the generator only checks the format and never recomputes the check digit, even though the correct one would be 1.

Full tool FAQ

What is the difference between Code 128, EAN and UPC?

Code 128 is a dense and flexible symbology for internal operations. EAN and UPC are numeric retail standards and depend on valid commercial identification.

Is the check digit generated automatically?

Is SVG better than PNG for barcodes?

What is a quiet zone?

Can I invent an EAN for a real product?

Why does my printed barcode not scan?

Does the tool validate commercial registration?

Are barcode values sent to the server?

Frequently asked questions