Passport MRZ check digits use a repeating 7–3–1 weighted sum, reduced modulo 10. For a standard TD3 passport, the document number, birth date, expiry date and a composite selection of line 2 each have defined inputs and check-digit positions. The examples below show the calculation and provide Python and JavaScript validators that preserve those positions.
How the MRZ check-digit calculation works
ICAO Doc 9303 Part 3 defines a modulus-10 checksum. Map each character to its MRZ value, multiply those values by repeating weights of 7, 3 and 1, add the products, then take the remainder after division by 10. That remainder is the check digit.
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Character values are fixed: digits map to their numeric values, letters A through Z map consecutively to 10 through 35, and the filler character < maps to zero. The weights begin again at 7 for each separate check-digit calculation. A filler contributes zero to the sum, but it still occupies a position, so the weight sequence continues.
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Example calculation
For the string 123, the weighted sum is (1 × 7) + (2 × 3) + (3 × 1) = 16. The remainder is 16 % 10 = 6, so its check digit is 6.
ICAO’s TD3 composite example has a weighted total of 448, giving 448 % 10 = 8. That example also demonstrates that filler characters contribute zero while the weights keep cycling across the entire input.
TD3 passport positions and inputs
A standard TD3 passport’s second MRZ line contains 44 character positions. ICAO Doc 9303 Part 4 defines which positions are checked. The position numbers below are one-based, as printed in the standard; code indexes are zero-based.
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| Check | Input positions on line 2 | Check digit position |
|---|---|---|
| Document number | 1–9 | 10 |
| Date of birth | 14–19 | 20 |
| Date of expiry | 22–27 | 28 |
| Composite | 1–10, 14–20, and 22–43, concatenated in that order | 44 |
The composite input deliberately omits positions 11–13 and 21. Those are not part of the composite checksum input. Do not calculate it over all of line 2 or simply concatenate every field.
Python validator for a TD3 line
This validator accepts a complete, 44-character second line, rejects characters outside the MRZ alphabet, checks the three individual digits and then checks the composite digit. It reports the result of each check rather than treating one matching digit as validation of the whole line.
WEIGHTS = (7, 3, 1)
def mrz_value(char):
if "0" <= char <= "9":
return ord(char) - ord("0")
if "A" <= char <= "Z":
return ord(char) - ord("A") + 10
if char == "<":
return 0
raise ValueError(f"Invalid MRZ character: {char!r}")
def check_digit(text):
total = sum(mrz_value(char) * WEIGHTS[i % 3]
for i, char in enumerate(text))
return str(total % 10)
def validate_td3_line2(line):
if len(line) != 44:
raise ValueError("A TD3 passport line 2 must contain 44 characters")
# Human positions 1–9 map to Python slice [0:9]; position 10 is index 9.
composite_input = line[0:10] + line[13:20] + line[21:43]
checks = {
"document_number": check_digit(line[0:9]) == line[9],
"date_of_birth": check_digit(line[13:19]) == line[19],
"date_of_expiry": check_digit(line[21:27]) == line[27],
"composite": check_digit(composite_input) == line[43],
}
return checksRun it on a line you have already parsed or captured as exactly 44 MRZ characters. A result of True means that specific digit matches its prescribed input. A false result means either the character data was read incorrectly or the digit does not match; it does not identify which character is wrong.
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Python checks for the character mapping and checksum
assert check_digit("123") == "6"
assert mrz_value("A") == 10
assert mrz_value("Z") == 35
assert mrz_value("<") == 0
assert check_digit("<1") == "7"
try:
validate_td3_line2("A" * 43)
except ValueError:
pass
else:
raise AssertionError("Expected a length error")ICAO’s worked composite example is the appropriate reference for checking the complete TD3 selection and expected composite digit: the selected input produces total 448 and digit 8. Use the exact characters and selection shown in the official example when comparing a full-line implementation.
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This version follows the same one-based ICAO positions and translates them to JavaScript’s zero-based slice boundaries. It returns a result object with a separate boolean for each checksum.
const WEIGHTS = [7, 3, 1];
function mrzValue(char) {
if (char >= "0" && char <= "9") return char.charCodeAt(0) - 48;
if (char >= "A" && char <= "Z") return char.charCodeAt(0) - 65 + 10;
if (char === "<") return 0;
throw new Error(`Invalid MRZ character: ${JSON.stringify(char)}`);
}
function checkDigit(text) {
let total = 0;
for (let i = 0; i < text.length; i++) {
total += mrzValue(text[i]) * WEIGHTS[i % 3];
}
return String(total % 10);
}
function validateTd3Line2(line) {
if (line.length !== 44) {
throw new Error("A TD3 passport line 2 must contain 44 characters");
}
// Human positions 1–10, 14–20, and 22–43; position 44 holds the digit.
const compositeInput = line.slice(0, 10) + line.slice(13, 20) + line.slice(21, 43);
return {
documentNumber: checkDigit(line.slice(0, 9)) === line[9],
dateOfBirth: checkDigit(line.slice(13, 19)) === line[19],
dateOfExpiry: checkDigit(line.slice(21, 27)) === line[27],
composite: checkDigit(compositeInput) === line[43],
};
}JavaScript checks for the character mapping and checksum
console.assert(checkDigit("123") === "6");
console.assert(mrzValue("A") === 10);
console.assert(mrzValue("Z") === 35);
console.assert(mrzValue("<") === 0);
console.assert(checkDigit("<1") === "7");
try {
validateTd3Line2("A".repeat(43));
throw new Error("Expected a length error");
} catch (error) {
console.assert(error.message.includes("44 characters"));
}These assertions exercise a digit-only sequence, alphabetic mapping, filler handling and a wrong-length input. The official ICAO example provides the expected composite result for checking the full selection. Avoid converting MRZ fields to numbers: leading zeros and fillers are characters in the checksum input.
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What a matching check digit does—and does not—show
ICAO describes the purpose of check digits as follows: “The check digits permit readers to verify that data in the MRZ is correctly interpreted.” A match establishes consistency between the characters supplied to the calculation and the displayed digit under this checksum rule. It does not prove that a passport is genuine, establish the holder’s identity, or validate an electronic chip or its signature.
This article describes the TD3 passport layout, not every machine-readable travel document. Other formats can use different line lengths, field positions and check-digit arrangements; do not apply these TD3 slices to a different document format. The algorithm and positions cited here are from the eighth edition of ICAO Doc 9303 Parts 3 and 4 (2021). For a compliance implementation, confirm the currently applicable ICAO edition and amendments.
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Quick Recap
Official ICAO references
- ICAO Doc 9303 Part 3: Common Specifications, section 4.9 and Appendix A — character values, the modulus-10 method and the purpose of check digits.
- ICAO Doc 9303 Part 4: Specifications for TD3 Size Machine Readable Passports — line structure, check-digit positions and field selections.
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