The Math Behind the 2010 Census
Apportionment of Representatives

 

View the PERL script used to generate the data below.


The formula used to determine the number of House Seats for each State
is the Method of Equal Proportions. Each State is automatically assigned
one seat to start with (as each State MUST have at least one seat in
Congress). First, assign seats 1 thru 50 of 435.

1: Alabama, Population 4802982
2: Alaska, Population 721523
3: Arizona, Population 6412700
4: Arkansas, Population 2926229
5: California, Population 37341989
6: Colorado, Population 5044930
7: Connecticut, Population 3581628
8: Delaware, Population 900877
9: Florida, Population 18900773
10: Georgia, Population 9727566
11: Hawaii, Population 1366862
12: Idaho, Population 1573499
13: Illinois, Population 12864380
14: Indiana, Population 6501582
15: Iowa, Population 3053787
16: Kansas, Population 2863813
17: Kentucky, Population 4350606
18: Louisiana, Population 4553962
19: Maine, Population 1333074
20: Maryland, Population 5789929
21: Massachusetts, Population 6559644
22: Michigan, Population 9911626
23: Minnesota, Population 5314879
24: Mississippi, Population 2978240
25: Missouri, Population 6011478
26: Montana, Population 994416
27: Nebraska, Population 1831825
28: Nevada, Population 2709432
29: New Hampshire, Population 1321445
30: New Jersey, Population 8807501
31: New Mexico, Population 2067273
32: New York, Population 19421055
33: North Carolina, Population 9565781
34: North Dakota, Population 675905
35: Ohio, Population 11568495
36: Oklahoma, Population 3764882
37: Oregon, Population 3848606
38: Pennsylvania, Population 12734905
39: Rhode Island, Population 1055247
40: South Carolina, Population 4645975
41: South Dakota, Population 819761
42: Tennessee, Population 6375431
43: Texas, Population 25268418
44: Utah, Population 2770765
45: Vermont, Population 630337
46: Virginia, Population 8037736
47: Washington, Population 6753369
48: West Virginia, Population 1859815
49: Wisconsin, Population 5698230
50: Wyoming, Population 568300

Total Population = 309183463

Equal Proportions are used to determine which states shall receive
seats 51 thru 435. Divide each State's population by the square root
of n(n-1) where n equals the number of potential seats for a given
State. The result is called the Priority Value.

Priority Value = Population ÷ SQRT( ( N×(N-1) ) );
where N = potential seats (2 to 53) for the state

Assign seats 51 to 435 from those states with the largest priority values.

51: California Seat 2, PV=26404773
52: Texas Seat 2, PV=17867469
53: California Seat 3, PV=15244803
54: New York Seat 2, PV=13732759
55: Florida Seat 2, PV=13364864
56: California Seat 4, PV=10779703
57: Texas Seat 3, PV=10315788
58: Illinois Seat 2, PV=9096490
59: Pennsylvania Seat 2, PV=9004937
60: California Seat 5, PV=8349922
61: Ohio Seat 2, PV=8180161
62: New York Seat 3, PV=7928612
63: Florida Seat 3, PV=7716208
64: Texas Seat 4, PV=7294363
65: Michigan Seat 2, PV=7008577
66: Georgia Seat 2, PV=6878427
67: California Seat 6, PV=6817683
68: North Carolina Seat 2, PV=6764028
69: New Jersey Seat 2, PV=6227843
70: California Seat 7, PV=5761993
71: Virginia Seat 2, PV=5683537
72: Texas Seat 5, PV=5650190
73: New York Seat 4, PV=5606375
74: Florida Seat 4, PV=5456183
75: Illinois Seat 3, PV=5251861
76: Pennsylvania Seat 3, PV=5199003
77: California Seat 8, PV=4990033
78: Washington Seat 2, PV=4775353
79: Ohio Seat 3, PV=4722818
80: Massachusetts Seat 2, PV=4638368
81: Texas Seat 6, PV=4613360
82: Indiana Seat 2, PV=4597312
83: Arizona Seat 2, PV=4534463
84: Tennessee Seat 2, PV=4508110
85: California Seat 9, PV=4400795
86: New York Seat 5, PV=4342679
87: Missouri Seat 2, PV=4250756
88: Florida Seat 5, PV=4226341
89: Maryland Seat 2, PV=4094098
90: Michigan Seat 3, PV=4046404
91: Wisconsin Seat 2, PV=4029257
92: Georgia Seat 3, PV=3971262
93: California Seat 10, PV=3936191
94: North Carolina Seat 3, PV=3905213
95: Texas Seat 7, PV=3899001
96: Minnesota Seat 2, PV=3758186
97: Illinois Seat 4, PV=3713626
98: Pennsylvania Seat 4, PV=3676250
99: New Jersey Seat 3, PV=3595647
100: Colorado Seat 2, PV=3567304
101: California Seat 11, PV=3560418
102: New York Seat 6, PV=3545783
103: Florida Seat 6, PV=3450793
104: Alabama Seat 2, PV=3396221
105: Texas Seat 8, PV=3376634
106: Ohio Seat 4, PV=3339536
107: South Carolina Seat 2, PV=3285200
108: Virginia Seat 3, PV=3281391
109: California Seat 12, PV=3250202
110: Louisiana Seat 2, PV=3220137
111: Kentucky Seat 2, PV=3076343
112: New York Seat 7, PV=2996733
113: California Seat 13, PV=2989751
114: Texas Seat 9, PV=2977911
115: Florida Seat 7, PV=2916452
116: Illinois Seat 5, PV=2876562
117: Michigan Seat 4, PV=2861239
118: Pennsylvania Seat 5, PV=2847611
119: Georgia Seat 4, PV=2808106
120: California Seat 14, PV=2767972
121: North Carolina Seat 4, PV=2761403
122: Washington Seat 3, PV=2757051
123: Oregon Seat 2, PV=2721375
124: Massachusetts Seat 3, PV=2677963
125: Texas Seat 10, PV=2663525
126: Oklahoma Seat 2, PV=2662173
127: Indiana Seat 3, PV=2654259
128: Arizona Seat 3, PV=2617973
129: Tennessee Seat 3, PV=2602758
130: New York Seat 8, PV=2595247
131: Ohio Seat 5, PV=2586794
132: California Seat 15, PV=2576842
133: New Jersey Seat 4, PV=2542506
134: Connecticut Seat 2, PV=2532593
135: Florida Seat 8, PV=2525722
136: Missouri Seat 3, PV=2454175
137: California Seat 16, PV=2410415
138: Texas Seat 11, PV=2409249
139: Maryland Seat 3, PV=2363728
140: Illinois Seat 6, PV=2348703
141: Wisconsin Seat 3, PV=2326292
142: Pennsylvania Seat 6, PV=2325064
143: Virginia Seat 4, PV=2320294
144: New York Seat 9, PV=2288793
145: California Seat 17, PV=2264190
146: Florida Seat 9, PV=2227477
147: Michigan Seat 5, PV=2216306
148: Texas Seat 12, PV=2199333
149: Georgia Seat 5, PV=2175149
150: Minnesota Seat 3, PV=2169790
151: Iowa Seat 2, PV=2159353
152: North Carolina Seat 5, PV=2138973
153: California Seat 18, PV=2134699
154: Ohio Seat 6, PV=2112108
155: Mississippi Seat 2, PV=2105933
156: Arkansas Seat 2, PV=2069156
157: Colorado Seat 3, PV=2059584
158: New York Seat 10, PV=2047158
159: Kansas Seat 2, PV=2025021
160: Texas Seat 13, PV=2023092
161: California Seat 19, PV=2019223
162: Florida Seat 10, PV=1992316
163: Illinois Seat 7, PV=1985016
164: New Jersey Seat 5, PV=1969417
165: Pennsylvania Seat 7, PV=1965038
166: Alabama Seat 3, PV=1960809
167: Utah Seat 2, PV=1959226
168: Washington Seat 4, PV=1949529
169: Nevada Seat 2, PV=1915857
170: California Seat 20, PV=1915603
171: South Carolina Seat 3, PV=1896711
172: Massachusetts Seat 4, PV=1893606
173: Indiana Seat 4, PV=1876845
174: Texas Seat 14, PV=1873019
175: Louisiana Seat 3, PV=1859147
176: New York Seat 11, PV=1851724
177: Arizona Seat 4, PV=1851187
178: Tennessee Seat 4, PV=1840428
179: California Seat 21, PV=1822102
180: Michigan Seat 6, PV=1809607
181: Florida Seat 11, PV=1802117
182: Virginia Seat 5, PV=1797292
183: Ohio Seat 7, PV=1785057
184: Kentucky Seat 3, PV=1776127
185: Georgia Seat 6, PV=1776002
186: North Carolina Seat 6, PV=1746464
187: Texas Seat 15, PV=1743686
188: California Seat 22, PV=1737306
189: Missouri Seat 4, PV=1735364
190: Illinois Seat 8, PV=1719075
191: Pennsylvania Seat 8, PV=1701773
192: New York Seat 12, PV=1690385
193: Maryland Seat 4, PV=1671408
194: California Seat 23, PV=1660053
195: Florida Seat 12, PV=1645101
196: Wisconsin Seat 4, PV=1644937
197: Texas Seat 16, PV=1631069
198: New Jersey Seat 6, PV=1608022
199: California Seat 24, PV=1589380
200: Oregon Seat 3, PV=1571186
201: New York Seat 13, PV=1554928
202: Ohio Seat 8, PV=1545905
203: Oklahoma Seat 3, PV=1537006
204: Minnesota Seat 4, PV=1534273
205: Texas Seat 17, PV=1532122
206: Michigan Seat 7, PV=1529397
207: California Seat 25, PV=1524480
208: Illinois Seat 9, PV=1516081
209: Florida Seat 13, PV=1513272
210: Washington Seat 5, PV=1510099
211: Georgia Seat 7, PV=1500996
212: Pennsylvania Seat 9, PV=1500822
213: North Carolina Seat 7, PV=1476032
214: Virginia Seat 6, PV=1467483
215: Massachusetts Seat 5, PV=1466780
216: California Seat 26, PV=1464673
217: Connecticut Seat 3, PV=1462193
218: New Mexico Seat 2, PV=1461782
219: Colorado Seat 4, PV=1456345
220: Indiana Seat 5, PV=1453797
221: Texas Seat 18, PV=1444499
222: New York Seat 14, PV=1439584
223: Arizona Seat 5, PV=1433923
224: Tennessee Seat 5, PV=1425589
225: California Seat 27, PV=1409382
226: Florida Seat 14, PV=1401018
227: Alabama Seat 4, PV=1386501
228: Texas Seat 19, PV=1366359
229: Ohio Seat 9, PV=1363360
230: New Jersey Seat 7, PV=1359026
231: California Seat 28, PV=1358115
232: Illinois Seat 10, PV=1356024
233: Missouri Seat 5, PV=1344207
234: Pennsylvania Seat 10, PV=1342376
235: South Carolina Seat 4, PV=1341177
236: New York Seat 15, PV=1340180
237: Michigan Seat 8, PV=1324496
238: West Virginia Seat 2, PV=1315087
239: Louisiana Seat 4, PV=1314615
240: California Seat 29, PV=1310446
241: Florida Seat 15, PV=1304277
242: Georgia Seat 8, PV=1299900
243: Texas Seat 20, PV=1296242
244: Nebraska Seat 2, PV=1295295
245: Maryland Seat 5, PV=1294667
246: North Carolina Seat 8, PV=1278281
247: Wisconsin Seat 5, PV=1274162
248: California Seat 30, PV=1266011
249: Kentucky Seat 4, PV=1255911
250: New York Seat 16, PV=1253623
251: Iowa Seat 3, PV=1246703
252: Virginia Seat 7, PV=1240249
253: Washington Seat 6, PV=1232990
254: Texas Seat 21, PV=1232972
255: Illinois Seat 11, PV=1226570
256: California Seat 31, PV=1224492
257: Florida Seat 16, PV=1220039
258: Ohio Seat 10, PV=1219426
259: Mississippi Seat 3, PV=1215861
260: Pennsylvania Seat 11, PV=1214225
261: Massachusetts Seat 6, PV=1197621
262: Arkansas Seat 3, PV=1194627
263: Minnesota Seat 5, PV=1188443
264: Indiana Seat 6, PV=1187021
265: California Seat 32, PV=1185609
266: New York Seat 17, PV=1177574
267: New Jersey Seat 8, PV=1176951
268: Texas Seat 22, PV=1175593
269: Arizona Seat 6, PV=1170793
270: Kansas Seat 3, PV=1169146
271: Michigan Seat 9, PV=1168096
272: Tennessee Seat 6, PV=1163989
273: California Seat 33, PV=1149120
274: Georgia Seat 9, PV=1146404
275: Florida Seat 17, PV=1146027
276: Utah Seat 3, PV=1131160
277: Colorado Seat 5, PV=1128080
278: North Carolina Seat 9, PV=1127338
279: Texas Seat 23, PV=1123318
280: Illinois Seat 12, PV=1119700
281: California Seat 34, PV=1114810
282: Idaho Seat 2, PV=1112631
283: Oregon Seat 4, PV=1110996
284: New York Seat 18, PV=1110227
285: Pennsylvania Seat 12, PV=1108431
286: Nevada Seat 3, PV=1106120
287: Ohio Seat 11, PV=1103012
288: Missouri Seat 6, PV=1097540
289: Oklahoma Seat 4, PV=1086827
290: California Seat 35, PV=1082490
291: Florida Seat 18, PV=1080485
292: Texas Seat 24, PV=1075495
293: Virginia Seat 8, PV=1074087
294: Alabama Seat 5, PV=1073979
295: Maryland Seat 6, PV=1057091
296: California Seat 36, PV=1051991
297: New York Seat 19, PV=1050170
298: Michigan Seat 10, PV=1044777
299: Washington Seat 7, PV=1042067
300: Wisconsin Seat 6, PV=1040349
301: South Carolina Seat 5, PV=1038871
302: New Jersey Seat 9, PV=1037973
303: Connecticut Seat 4, PV=1033926
304: Texas Seat 25, PV=1031578
305: Illinois Seat 13, PV=1029974
306: Georgia Seat 10, PV=1025375
307: California Seat 37, PV=1023164
308: Florida Seat 19, PV=1022036
309: Pennsylvania Seat 13, PV=1019608
310: Louisiana Seat 5, PV=1018296
311: Massachusetts Seat 7, PV=1012175
312: North Carolina Seat 10, PV=1008321
313: Ohio Seat 12, PV=1006908
314: Indiana Seat 7, PV=1003215
315: New York Seat 20, PV=996279
316: California Seat 38, PV=995874
317: Texas Seat 26, PV=991108
318: Arizona Seat 7, PV=989501
319: Tennessee Seat 7, PV=983750
320: Kentucky Seat 5, PV=972825
321: Minnesota Seat 6, PV=970359
322: California Seat 39, PV=970003
323: Florida Seat 20, PV=969589
324: Hawaii Seat 2, PV=966517
325: Texas Seat 27, PV=953694
326: Illinois Seat 14, PV=953571
327: New York Seat 21, PV=947650
328: Virginia Seat 9, PV=947256
329: California Seat 40, PV=945442
330: Michigan Seat 11, PV=945036
331: Pennsylvania Seat 14, PV=943973
332: Maine Seat 2, PV=942625
333: New Hampshire Seat 2, PV=934402
334: New Jersey Seat 10, PV=928392
335: Missouri Seat 7, PV=927591
336: Georgia Seat 11, PV=927487
337: Ohio Seat 13, PV=926220
338: Florida Seat 21, PV=922263
339: California Seat 41, PV=922094
340: Colorado Seat 6, PV=921073
341: Texas Seat 28, PV=919003
342: North Carolina Seat 11, PV=912061
343: New York Seat 22, PV=903549
344: Washington Seat 8, PV=902456
345: California Seat 42, PV=899872
346: Maryland Seat 7, PV=893405
347: Illinois Seat 15, PV=887726
348: Texas Seat 29, PV=886747
349: Iowa Seat 4, PV=881552
350: Florida Seat 22, PV=879343
351: Wisconsin Seat 7, PV=879255
352: Pennsylvania Seat 15, PV=878791
353: California Seat 43, PV=878695
354: Alabama Seat 6, PV=876900
355: Massachusetts Seat 8, PV=876569
356: Indiana Seat 8, PV=868810
357: New York Seat 23, PV=863371
358: Michigan Seat 12, PV=862696
359: Oregon Seat 5, PV=860574
360: Mississippi Seat 4, PV=859743
361: California Seat 44, PV=858493
362: Ohio Seat 14, PV=857513
363: Arizona Seat 8, PV=856933
364: Texas Seat 30, PV=856679
365: Tennessee Seat 8, PV=851952
366: South Carolina Seat 6, PV=848235
367: Virginia Seat 10, PV=847251
368: Georgia Seat 12, PV=846675
369: Arkansas Seat 4, PV=844729
370: New Mexico Seat 3, PV=843960
371: Oklahoma Seat 5, PV=841853
372: Florida Seat 23, PV=840241
373: New Jersey Seat 11, PV=839762
374: California Seat 45, PV=839198
375: North Carolina Seat 12, PV=832594
376: Louisiana Seat 6, PV=831435
377: Illinois Seat 16, PV=830392
378: Texas Seat 31, PV=828584
379: Kansas Seat 4, PV=826711
380: New York Seat 24, PV=826614
381: Pennsylvania Seat 16, PV=822034
382: California Seat 46, PV=820752
383: Minnesota Seat 7, PV=820103
384: Florida Seat 24, PV=804470
385: Missouri Seat 8, PV=803317
386: California Seat 47, PV=803099
387: Texas Seat 32, PV=802273
388: Connecticut Seat 5, PV=800876
389: Utah Seat 4, PV=799850
390: Ohio Seat 15, PV=798301
391: Washington Seat 9, PV=795892
392: Kentucky Seat 6, PV=794308
393: Michigan Seat 13, PV=793565
394: New York Seat 25, PV=792861
395: California Seat 48, PV=786190
396: Nevada Seat 4, PV=782145
397: Illinois Seat 17, PV=780017
398: Georgia Seat 13, PV=778828
399: Colorado Seat 7, PV=778449
400: Texas Seat 33, PV=777581
401: Maryland Seat 8, PV=773711
402: Massachusetts Seat 9, PV=773061
403: Pennsylvania Seat 17, PV=772167
404: Florida Seat 25, PV=771620
405: California Seat 49, PV=769978
406: New Jersey Seat 12, PV=766594
407: Virginia Seat 11, PV=766368
408: Indiana Seat 9, PV=766218
409: North Carolina Seat 13, PV=765875
410: New York Seat 26, PV=761756
411: Wisconsin Seat 8, PV=761458
412: West Virginia Seat 3, PV=759266
413: Arizona Seat 9, PV=755743
414: California Seat 50, PV=754422
415: Texas Seat 34, PV=754365
416: Tennessee Seat 9, PV=751351
417: Nebraska Seat 3, PV=747839
418: Ohio Seat 16, PV=746743
419: Rhode Island Seat 2, PV=746172
420: Florida Seat 26, PV=741349
421: Alabama Seat 7, PV=741116
422: California Seat 51, PV=739481
423: Illinois Seat 18, PV=735407
424: Michigan Seat 14, PV=734698
425: New York Seat 27, PV=733000
426: Texas Seat 35, PV=732494
427: Pennsylvania Seat 18, PV=728006
428: California Seat 52, PV=725121
429: Georgia Seat 14, PV=721055
430: South Carolina Seat 7, PV=716889
431: Florida Seat 27, PV=713363
432: Washington Seat 10, PV=711867
433: Texas Seat 36, PV=711857
434: California Seat 53, PV=711308
435: Minnesota Seat 8, PV=710230

Just for grins show where additional seats would have gone.

436: North Carolina Seat 14, PV=709062
437: Missouri Seat 9, PV=708459
438: New York Seat 28, PV=706336
439: New Jersey Seat 13, PV=705164
440: Montana Seat 2, PV=703158
441: Louisiana Seat 7, PV=702691
442: Oregon Seat 6, PV=702656
443: Ohio Seat 17, PV=701443
444: Virginia Seat 12, PV=699595
445: California Seat 54, PV=698011

Show how many House Seats each state received.

Alabama - 7 seats
Alaska - 1 seats
Arizona - 9 seats
Arkansas - 4 seats
California - 53 seats
Colorado - 7 seats
Connecticut - 5 seats
Delaware - 1 seats
Florida - 27 seats
Georgia - 14 seats
Hawaii - 2 seats
Idaho - 2 seats
Illinois - 18 seats
Indiana - 9 seats
Iowa - 4 seats
Kansas - 4 seats
Kentucky - 6 seats
Louisiana - 6 seats
Maine - 2 seats
Maryland - 8 seats
Massachusetts - 9 seats
Michigan - 14 seats
Minnesota - 8 seats
Mississippi - 4 seats
Missouri - 8 seats
Montana - 1 seats
Nebraska - 3 seats
Nevada - 4 seats
New Hampshire - 2 seats
New Jersey - 12 seats
New Mexico - 3 seats
New York - 27 seats
North Carolina - 13 seats
North Dakota - 1 seats
Ohio - 16 seats
Oklahoma - 5 seats
Oregon - 5 seats
Pennsylvania - 18 seats
Rhode Island - 2 seats
South Carolina - 7 seats
South Dakota - 1 seats
Tennessee - 9 seats
Texas - 36 seats
Utah - 4 seats
Vermont - 1 seats
Virginia - 11 seats
Washington - 10 seats
West Virginia - 3 seats
Wisconsin - 8 seats
Wyoming - 1 seats
 


  United States Census 2010 Home  
 
  State Population and the Distribution of Electoral Votes and Representatives  
  2012 - 2020 Federal Representation by People per House Seat, Senate Seat, and Electors  
 
  An Historical Analysis of the Electoral College  
 
  The Math Behind the 2010 Census Apportionment of Representatives  
  PERL script used to generate the Apportionment