VIN check digit

Work out the ninth character of a VIN from the other sixteen, with every multiplication shown, and read what a disagreement does and does not prove.

Arithmetic, not a lookup

Check a VIN against its own check digit

Position 9 of a VIN is calculated from the other sixteen characters. This page does that calculation and shows every step, so you can check it on paper.

Seventeen characters. The ninth is the one being checked — the arithmetic does not read it.

The answer

Type a VIN and press the button. Nothing is downloaded and nothing is sent: this is seventeen multiplications and a remainder.

What the check digit is

Position 9 of a VIN carries no information about the vehicle. It is a check digit: a single character calculated from the other sixteen, defined by ISO 3780 and required on every vehicle sold in North America since 1981. Its job is to catch a transcription error — an 8 read as a B, a 5 as an S, two characters swapped — before that error becomes a wrong record.

The arithmetic, in three steps

  1. Transliterate. Each digit is worth itself. Each letter is worth the value in the first table below. I, O and Q have no value because they never appear in a VIN at all — they are excluded so they cannot be confused with 1 and 0.
  2. Weight and sum. Multiply each of the seventeen values by the weight for its position, from the second table, and add the products. Position 9 has a weight of zero, which is how the check digit avoids checking itself.
  3. Take the remainder. Divide the sum by 11. The remainder is the check digit — except that a remainder of ten is written X, because it needs a single character and the digits are used up.
Letter values under ISO 3780
LetterValue
A1
B2
C3
D4
E5
F6
G7
H8
J1
K2
L3
M4
N5
P7
R9
S2
T3
U4
V5
W6
X7
Y8
Z9
Weight for each of the seventeen positions
PositionWeight
18
27
36
45
54
63
72
810
90
109
118
127
136
145
154
163
172

What a disagreement proves, and what it does not

It does not prove the VIN is fake. The check digit is mandatory in North America and optional almost everywhere else, so a car built in Europe or Japan for a non-US market may carry a ninth character that means nothing at all. A great many legitimate imports fail this test. That is why the decoder on this site decodes a VIN whose check digit disagrees rather than refusing it, and flags the disagreement alongside the answer.

What a disagreement does prove is that the seventeen characters in front of you are not internally consistent. If the vehicle was built for the North American market, the overwhelmingly likely explanation is that one character was misread or mistyped — and the second most likely is that the VIN was invented by somebody who did not know about this arithmetic.

And an agreement proves very little. Any competent forger can calculate a check digit; this page just did it. A valid check digit means the number is well-formed, not that the vehicle exists, that the plate matches it, or that its history is clean. Nothing on this site can tell you those things, and we say plainly which of them we refuse to pretend to.

The arithmetic behind this page is written out on how this site works, so you can check it by hand.