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A passport MRZ check digit is the remainder of a modulus-10 calculation: map each character to its ICAO value, multiply the values by repeating weights 7, 3, 1, add the products, and take the total modulo 10. For the common TD3 passport, each check digit uses a specific line-2 field or set of fields; the composite digit does not cover every character on the line.
The 7-3-1 check-digit calculation
ICAO Doc 9303 Part 3 defines a modulus-10 checksum. Read the exact input characters from left to right, convert each to a value, multiply by the corresponding repeating weight, add the products, then take the remainder when the sum is divided by 10. That remainder is the check digit. The weights start again at 7 for each separate check-digit calculation.
| MRZ character | Value |
|---|---|
| Digits 0–9 | The digit’s numeric value |
| Letters A–Z | 10–35 in alphabetical order (A = 10, B = 11, …, Z = 35) |
| Filler < | 0 |
For mapped values v[i], the calculation is sum(v[i] × [7, 3, 1][i mod 3]) mod 10. Filler characters contribute zero to the sum, but still occupy a position, so they do not pause or reset the weight sequence.
Example calculation
For the input 123, multiply 1 × 7, 2 × 3, and 3 × 1. The sum is 16, and 16 modulo 10 is 6, so the check digit is 6. For a letter, apply its mapped value: A is 10, so as a one-character input its product is 10 × 7 = 70, and its check digit is 0.
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TD3 passport line-2 positions
The common TD3 passport format has 44 character positions on its second MRZ line. ICAO Doc 9303 Part 4 defines the following inputs and check-digit positions. Positions here are counted from 1, as a person reads the line.
| Check | Input characters | Check digit location |
|---|---|---|
| Document number | Positions 1–9 | Position 10 |
| Date of birth | Positions 14–19 | Position 20 |
| Date of expiry | Positions 22–27 | Position 28 |
| Composite | Positions 1–10, 14–20, and 22–43, concatenated in that order | Position 44 |
The composite input intentionally excludes positions 11–13 and 21. Do not calculate it over the whole line or include those skipped positions. The individual checks and the composite check are separate calculations, and each starts its weights at 7.
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Python validator for a TD3 line
This example validates the four check digits in a line-2 string. It requires exactly 44 characters and accepts only the MRZ alphabet: uppercase letters, digits, and <. It reports malformed input separately from a check-digit mismatch.
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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")
# Reject unsupported characters even in positions outside the checks below.
for char in line:
mrz_value(char)
checks = {
"document number": (line[0:9], line[9]),
"date of birth": (line[13:19], line[19]),
"date of expiry": (line[21:27], line[27]),
"composite": (line[0:10] + line[13:20] + line[21:43], line[43]),
}
return {
name: {"expected": check_digit(data),
"actual": actual,
"valid": check_digit(data) == actual}
for name, (data, actual) in checks.items()
}The slices use zero-based indexes: for example, human-readable positions 1–9 become Python slice line[0:9]. The composite slice combines positions 1–10, 14–20, and 22–43 in order, leaving out the specified gaps.
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JavaScript validator for a TD3 line
The same mapping and position rules apply in JavaScript. This version returns a result for each check and throws an error for a line with the wrong length or an unsupported character.
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");
}
// Reject unsupported characters, including outside the checked fields.
for (const char of line) mrzValue(char);
const checks = {
"document number": [line.slice(0, 9), line[9]],
"date of birth": [line.slice(13, 19), line[19]],
"date of expiry": [line.slice(21, 27), line[27]],
"composite": [line.slice(0, 10) + line.slice(13, 20) + line.slice(21, 43), line[43]],
};
return Object.fromEntries(
Object.entries(checks).map(([name, [data, actual]]) => {
const expected = checkDigit(data);
return [name, { expected, actual, valid: expected === actual }];
})
);
}Both examples preserve the MRZ as characters rather than converting fields to numbers. That matters because leading zeroes and filler characters are part of the input sequence.
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Testing the calculation without claiming a passport is valid
Use small cases to check the mapping and weight cycle, then check the composite calculation against ICAO’s published TD3 example. ICAO’s example uses the specified lower-line input positions 1–43; the weighted products total 448, and 448 modulo 10 gives composite digit 8.
- Digits:
123gives6(7 + 6 + 3 = 16; remainder 6). - Letters:
ABCmaps to 10, 11, 12; 70 + 33 + 12 = 115, so the check digit is5. - Filler:
<1gives 3; the filler contributes zero at weight 7, and the digit 1 uses the next weight, 3. - Length and positions: reject a TD3 line 2 unless it has 44 characters. A line of a different length cannot be safely checked with these TD3 positions.
- Published composite example: reproduce ICAO’s concatenated inputs and confirm the expected result is
8; do not substitute the entire line for the specified composite sequence.
What a passing check digit does—and does not—show
ICAO describes the purpose this way: “The check digits permit readers to verify that data in the MRZ is correctly interpreted.” A match means the tested characters are consistent with the checksum rule. It does not establish that the passport is genuine, that its data is authentic, or that an electronic chip or digital signature is valid.
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TD3 is not every travel document
This article’s positions apply to TD3 passports, the common two-line, 44-character-per-line format. Other machine-readable travel-document formats can have different line lengths, field layouts, and check-digit positions. Do not reuse these slices for TD1 or TD2 documents. For compliance work, consult the current ICAO Doc 9303 edition and applicable amendments; the cited Part 3 and Part 4 specifications are eighth-edition publications from 2021.
Sources: ICAO Doc 9303 Part 3, common specifications; ICAO Doc 9303 Part 4, TD3 specifications.
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