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Inside Check Numbers
As a follow-up to my previous post on credit card account numbers, I decided to document what the funny-looking numbers at the bottom of your checks represent, including how to calculate the check digits.

MICR

First, you might be wondering exactly why the numbers are printed in such a weird font. The reason lies in how these numbers are read. Back in the 70s, when the current routing system was devised, computers were unable to optically recognize characters. A technology called Magnetic Ink Character Recognition (MICR) was created to allow computers to read these characters. As a check goes through a MICR reader, the ink (containing ferrous metals) is magnetized. The ink then passes over a read head, similar to one used in tape players. Each character gives off a unique waveform that can easily and uniquely identify the character being passed over the read head. Therefore, each character was designed in such a way so that it gives off a unique waveform, yet is still human-readable.

The Routing Number

The routing number, contained between the two routing/transit start/stop symbols (), is made up of the following components:

XXXXYYYYZ
XXXX	Federal Reserve Routing Symbol
YYYY	American Bankers Association Institution ID
Z	Check digit

The Federal Reserve Routing Symbol

Usually, the first two digits of the Federal Reserve Routing Symbol indicate which of the twelve federal reserve districts the bank is in. Numbers in the range of 21 to 32, indicate a "thrift institution," although assignment of these numbers was ended in 1985. To get the Federal Reserve district number from one of these numbers, simply subtract 20. For example, if the first two digits is 32, it indicates it is a "thrift institution" in the 12th Federal Reserve district (the western US). Routing symbols that start with 00 indicate the check is issued by the US government (except federal banks). Routing symbols that start with 80 are reserved for travelers checks, and all others are reserved.

The third digit of the Federal Reserve Routing Symbol indicates which branch office of the district the check should be routed through. A 1 indicates the main office of the district, with digits 2-5 indicating a branch office. For example, in the 12th Federal Reserve district (the western US), 1 indicates San Francisco, 2 indicates Los Angeles, 3 indicates Portland, 4 indicates Salt Lake City, and 5 indicates Seattle.

The forth digit indicates the availability of funds. A 0 indicates immediate availability, a 1-5 indicates which state in the district the paying bank is located, and a 6-9 indicates a special collection arrangement.

The Federal Reserve Routing Symbol is the denominator in the transit number printed in the top-right corner of a check.

The ABA Institution ID

The full ABA institution ID is actually made up of two parts, separated by a dash. You can find the full ABA institution ID printed in the upper-right hand corner of your checks, as the numerator in the transit number. For example, it may look like: 96-1234. The part before the dash (the prefix) indicates the city or state the bank is located in. Numbers from 1 to 49 represent cities, while numbers from 50 to 99 indicate states. For states, numbers 50-58 represent eastern states, 59 represents Alaska, Hawaii, and US territories, 60-69 represent southeastern states, 70-79 represent central state, 80-88 represent southwestern states, and 90-99 represent western states.


A full list of the ABA prefixes:

1    New York, NY
2    Chicago, IL
3    Philadelphia, PA
4    St. Louis, MO
5    Boston, MA
6    Cleveland, OH
7    Baltimore, MD
8    Pittsburgh, PA
9    Detroit, MI
10   Buffalo, NY
11   San Francisco, CA
12   Milwaukee, WI
13   Cincinnati, OH
14   New Orleans, LA
15   Washington D.C.
16   Los Angeles, CA
18   Kansas City, MO
19   Seattle, WA
20   Indianapolis, IN
21   Louisville, KY
22   St. Paul, MN
23   Denver, CO
24   Portland, OR
25   Columbus, OH
26   Memphis, TN
27   Omaha, NE
28   Spokane, WA
29   Albany, NY
30   San Antonio, TX
31   Salt Lake City, UT
32   Dallas, TX
33   Des Moines, IA
34   Tacoma, WA
35   Houston, TX
36   St. Joseph, MO
37   Fort Worth, TX
38   Savannah, GA
39   Oklahoma City, OK
40   Wichita, KS
41   Sioux City, IA
42   Pueblo, CO
43   Lincoln, NE
44   Topeka, KS
45   Dubuque, IA
46   Galveston, TX
47   Cedar Rapids, IA
48   Waco, TX
49   Muskogee, OK
50   New York
51   Connecticut
52   Maine
53   Massachusetts
54   New Hampshire
55   New Jersey
56   Ohio
57   Rhode Island
58   Vermont
59   Alaska, American Samoa, Guam, Hawaii, Puerto Rico, Virgin Islands
60   Pennsylvania
61   Alabama
62   Delaware
63   Florida
64   Georgia
65   Maryland
66   North Carolina
67   South Carolina
68   Virginia
69   West Virginia
70   Illinois
71   Indiana
72   Iowa
73   Kentucky
74   Michigan
75   Minnesota
76   Nebraska
77   North Dakota
78   South Dakota
79   Wisconsin
80   Missouri
81   Arkansas
83   Kansas
84   Louisiana
85   Mississippi
86   Oklahoma
87   Tennessee
88   Texas
90   California
91   Arizona
92   Idaho
93   Montana
94   Nevada
95   New Mexico
96   Oregon
97   Utah
98   Washington
99   Wyoming

The second part of ABA institution ID is limited to 4 digits, and is included in the MICR routing number. Since there are more than 10,000 institutions in the US, this number is obviously not unique to an institution. However, it is assigned so that it is unique inside the ABA prefix and Federal Reserve branch office area. Therefore, its meaning is not ambiguous inside the MICR routing number.

The Check Digit

The check digit ensures the number was read or keyed in without error. The algorithm used to compute the check digit of the routing number is as follows:

Take the first, fourth, and seventh digit, multiply them by 7, and add them to the total.
Take the second, fifth, and 8th digit, multiply them by 3, and add them to the total.
Take the third and sixth digit, multiply them by 9, and add them to the total.

The check digit is the 1s digit of the total. Note that if you take the check digit, multiply it by 9, and add it to the total, the sum will be evenly divisible by 10.

The Account Number

The account number precedes the ANSI "on-us" symbol (). The check digit algorithm is the same as the one used to verify the routing number. However, because account numbers are of variable length, it can be somewhat tricky to determine which multiplier to use with what digit. The best way to go about it is to work backwards from the last digit of the account number, not including the check digit. Working backwards, the pattern of multipliers is 3-7-9. For example, if you have the account number 123456, you would compute the check digit like so:

Account Number	1	2	3	4	5	6
Multiplier	9	7	3	9	7	3
Product	9	14	9	36	35	18

Sum of products = 121, which means the check digit is 1.