Because every google search returned old information (as well as the Number Crunching Thread in the archives), I just wanted to post an updated version of the formula used to calculate the cost of Social Policies, since it appears to have changed.
So let's assume the following:
pb(k): The base cost of policy k. Depends only on the number of policies already purchased.
n: The number of cities in your empire. (settled and annexed cities count towards n but puppeted cities do not)
p(n,k): The total cost of policy k. Depends on cities you control and policies already purchased.
And because policy cost is also dependent upon map size, difficulty, and game speed:
pm: map size modifier for cities (0.15 for Standard and below, 0.1 for Large, 0.075 for Huge)
pd: map difficulty modifier (0.5 for Settler, 0.67 for Chieftan, 0.85 for Warlord, 1 for Prince and above)
ps: game speed modifier (0.67 for Quick, 1 for Standard, 1.5 for Epic, 3 for Marathon)
base cost of next policy = speed modifier * difficulty modifier * (base policy cost + (3 * number of policies)^2.01)
pb(k) = ps * pd * (25 + (3k)^2.01)
imprecise cost of next policy = base cost of next policy (1 + map size modifier * number of non-capital cities)
pc(n,k) = pb(k) * (1 + pm(n - 1))
And now to round that off to a nice even multiple of 5:
final cost of next policy = 5 * round down (imprecise cost / 5)
p = 5 * floor(pc(n,k) / 5)
Summary:
Formulas
pb(k) = ps * pd * (25 + (3k)^2.01)
pc(n,k) = pb(k) * (1 + pm(n - 1))
p = 5 * floor(pc(n,k) / 5)
Modifiers
Map Size (pm)
Duel: 0.15
Tiny: 0.15
Small: 0.15
Standard: 0.15
Large: 0.1
Huge: 0.075
Difficulty (pd)
Settler: 0.5
Chieftan: 0.67
Warlord: 0.85
Prince: 1
King: 1
Emperor: 1
Immortal: 1
Diety: 1
Speed (ps)
Quick: 0.67
Standard: 1
Epic: 1.5
Marathon: 3
Table of Social Policy Costs (num. cities over num. policies, assuming Standard size, speed, and a difficulty of Prince or above)
So let's assume the following:
pb(k): The base cost of policy k. Depends only on the number of policies already purchased.
n: The number of cities in your empire. (settled and annexed cities count towards n but puppeted cities do not)
p(n,k): The total cost of policy k. Depends on cities you control and policies already purchased.
And because policy cost is also dependent upon map size, difficulty, and game speed:
pm: map size modifier for cities (0.15 for Standard and below, 0.1 for Large, 0.075 for Huge)
pd: map difficulty modifier (0.5 for Settler, 0.67 for Chieftan, 0.85 for Warlord, 1 for Prince and above)
ps: game speed modifier (0.67 for Quick, 1 for Standard, 1.5 for Epic, 3 for Marathon)
base cost of next policy = speed modifier * difficulty modifier * (base policy cost + (3 * number of policies)^2.01)
pb(k) = ps * pd * (25 + (3k)^2.01)
imprecise cost of next policy = base cost of next policy (1 + map size modifier * number of non-capital cities)
pc(n,k) = pb(k) * (1 + pm(n - 1))
And now to round that off to a nice even multiple of 5:
final cost of next policy = 5 * round down (imprecise cost / 5)
p = 5 * floor(pc(n,k) / 5)
Summary:
Formulas
pb(k) = ps * pd * (25 + (3k)^2.01)
pc(n,k) = pb(k) * (1 + pm(n - 1))
p = 5 * floor(pc(n,k) / 5)
Modifiers
Map Size (pm)
Duel: 0.15
Tiny: 0.15
Small: 0.15
Standard: 0.15
Large: 0.1
Huge: 0.075
Difficulty (pd)
Settler: 0.5
Chieftan: 0.67
Warlord: 0.85
Prince: 1
King: 1
Emperor: 1
Immortal: 1
Diety: 1
Speed (ps)
Quick: 0.67
Standard: 1
Epic: 1.5
Marathon: 3
Table of Social Policy Costs (num. cities over num. policies, assuming Standard size, speed, and a difficulty of Prince or above)
Code:
n = 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
k = 0 25 25 30 35 40 40 45 50 55 55 60 65 70 70 75
1 30 35 40 45 50 55 60 65 75 80 85 90 95 100 105
2 60 70 80 85 95 105 115 125 135 140 150 160 170 180 190
3 105 120 140 155 170 185 200 220 235 250 265 285 300 315 330
4 170 195 220 250 275 300 325 350 375 405 430 455 480 505 535
5 255 290 330 370 405 445 485 525 560 600 640 675 715 755 790
6 355 410 465 515 570 625 680 730 785 840 895 950 1000 1055 1110
7 475 550 620 695 765 835 910 980 1055 1125 1195 1270 1340 1410 1485
8 615 710 805 895 990 1080 1175 1270 1360 1455 1545 1640 1730 1825 1920
9 775 895 1010 1125 1245 1360 1475 1595 1710 1825 1945 2060 2175 2295 2410
10 955 1095 1240 1385 1525 1670 1815 1960 2100 2245 2390 2530 2675 2820 2960
11 1150 1325 1495 1670 1840 2015 2190 2360 2535 2705 2880 3050 3225 3400 3570
12 1365 1570 1775 1980 2185 2390 2595 2800 3010 3215 3420 3625 3830 4035 4240
13 1600 1840 2080 2320 2560 2800 3045 3285 3525 3765 4005 4245 4485 4725 4965
14 1855 2130 2410 2690 2965 3245 3525 3805 4080 4360 4640 4915 5195 5475 5750
15 2125 2445 2765 3085 3405 3720 4040 4360 4680 5000 5320 5640 5955 6275 6595
16 2415 2780 3145 3505 3870 4230 4595 4960 5320 5685 6045 6410 6775 7135 7500
17 2730 3135 3545 3955 4365 4775 5185 5595 6005 6415 6825 7235 7640 8050 8460
18 3055 3515 3975 4435 4895 5350 5810 6270 6730 7190 7645 8105 8565 9025 9480
19 3405 3915 4430 4940 5450 5960 6475 6985 7495 8005 8520 9030 9540 10050 10560
20 3775 4340 4905 5470 6040 6605 7170 7735 8305 8870 9435 10000 10570 11135 11700
21 4160 4785 5410 6030 6655 7280 7905 8530 9155 9780 10400 11025 11650 12275 12900
22 4565 5250 5935 6620 7305 7990 8675 9360 10045 10730 11415 12100 12785 13470 14155
23 4990 5740 6485 7235 7985 8735 9480 10230 10980 11730 12475 13225 13975 14725 15470
24 5435 6250 7065 7880 8695 9510 10325 11140 11955 12770 13585 14400 15215 16030 16850
25 5895 6780 7665 8550 9435 10320 11205 12090 12975 13860 14745 15630 16510 17395 18280
26 6375 7335 8290 9250 10205 11160 12120 13075 14035 14990 15945 16905 17860 18820 19775
27 6880 7910 8940 9975 11005 12040 13070 14105 15135 16165 17200 18230 19265 20295 21330
28 7400 8510 9620 10730 11840 12950 14060 15170 16280 17390 18500 19610 20720 21830 22940
29 7935 9130 10320 11510 12700 13890 15085 16275 17465 18655 19845 21040 22230 23420 24610
30 8495 9770 11045 12320 13595 14870 16145 17420 18695 19965 21240 22515 23790 25065 26340
