# Pitch – metric module – diametral pitch – circular pitch – tooth thickness – tooth depth – base pitch

For all the above, we have always limited to the metric module system. In the Anglo-Saxon countries, the “diametral pitch” system is in use (number of teeth of a wheel per inch of the pitch diameter expressed in inch). Also still being used is the “circular pitch” system or “transverse pitch ” in inch or fraction number in inch. In the “Diametral pitch” system is the pitch diameter (expressed in inches) equal to the quotient d = Z/P.

As the metric module system is easier to handle for calculations in metric sizes, one can replace the diametral pitch in the common formulas by the corresponding module value in the metric system. Below are the ratios between the different systems:
m = 25,4/DP = 25,4*CP/pi = 8,0850711*CP
DP = pi/CP = 25,4/m (with CP in inch)
CP = pi/DP = m/8,0850711

Tooth depth
The total depth of the tooth, indicated in the tables, is a theoretical value calculated on the basis of a theoretical dedendum of 1.16 or 1, 25 x module. In practice, the dedendum is variable and depends on the hobbing tool and the required tooth thickness. The foot circle diameter is thus not a reference dimension. The following tables provide the below information:

Pitch in mm (p)
Metric module – (to be avoided in pitch system) (m)
Diametral pitch (DP)
Circular pitch (CP)
Tooth thickness (S)
Tooth depth in mm for c = 0,16*m (h)
Base pitch for pressure angle 14°30’ & 20°00’ (Pb)
To avoid module (..)

 p m DP CP S h pb a=14°30’ a=20°00’ 0,62831 0,2000 0,3142 0,432 0,6083 0,5904 0,78540 0,2500 0,3927 0,540 0,7604 0,7380 0,94248 0,3000 0,4712 0,648 0,9125 0,8856 0,99746 0,3175 80 0,4987 0,686 0,9657 0,9373 1,00531 0,3200 0,5027 0,691 0,9733 0,9447 1,09557 (0,3487) 0,5478 0,753 1,0607 1,0295 1,10828 0,3528 72 0,5541 0,762 1,0730 1,0414 1,24682 (0,3969) 64 0,6234 0,857 1,2071 1,1716 1,25664 0,4000 0,6283 0,864 1,2166 1,1809 1,32994 0,4233 60 0,6650 0,914 1,2876 1,2497 1,41372 0,4500 0,7069 0,972 1,3687 1,3285 1,57080 0,5000 0,7854 1,080 1,5208 1,4761 1,58750 (0,5053) 1/16″ 0,7937 1,091 1,5369 1,4918 1,66243 0,5292 48 0,8312 1,143 1,6095 1,5622 1,88496 0,6000 0,9425 1,296 1,8249 1,7713 1,99491 0,6350 40 0,9975 1,372 1,9314 1,8746 2,04204 (0,6500) 1,0210 1,404 1,9770 1,9189 2,19911 (0,7000) 1,0996 1,512 2,1291 2,0665 2,21657 0,7056 36 1,1083 1,524 2,1460 2,0829 2,35619 (0,7500) 1,1781 1,620 2,2811 2,2141 2,49364 0,7938 32 1,2468 1,715 2,4142 2,3433 2,51327 0,8000 1,2566 1,728 2,4332 2,3617 2,65988 0,8467 30 1,3299 1,829 2,5752 2,4995 2,82743 (0,9000) 1,4137 1,944 2,7374 2,6569 2,84987 0,9071 28 1,4249 1,959 2,7591 2,6780 3,14159 1,0000 1,5708 2,160 3,0415 2,9521 3,17500 (1,0106) 1/8″ 1,5875 2,183 3,0739 2,9835 3,32485 1,0583 24 1,6624 2,286 3,2189 3,1243 3,62711 1,1545 22 1,8136 2,494 3,5116 3,4084 3,92699 1,2500 1,9635 2,700 3,8019 3,6902 3,98982 1,2700 20 1,9949 2,743 3,8627 3,7492 4,43314 1,4111 18 2,2166 3,048 4,2919 4,1658 4,71239 1,5000 2,3562 3,240 4,5623 4,4282 4,76250 (1,5160) 3/16″ 2,3812 3,274 4,6108 4,4753 4,98728 1,5875 16 2,4936 3,429 4,8284 4,6865 5,00000 1,5915 2,5000 3,438 4,8407 4,6985 5,49779 1,7500 2,7489 3,780 5,3227 5,1662 5,69975 1,8143 14 2,8499 3,919 5,5182 5,3560 6,28319 2,0000 3,1416 4,320 6,0831 5,9043 6,35000 (2,0213) 1/4″ 3,1750 4,366 6,1477 5,9670 6,64970 2,1167 12 3,3248 4,572 6,4379 6,2487 7,06858 2,2500 3,5343 4,860 6,8434 6,6423 7,25422 2,3091 11 3,6271 4,988 7,0232 6,8167 7,85398 2,5000 3,9270 5,400 7,6038 7,3803 7,93750 (2,5266) 5/16″ 3,9687 5,457 7,6847 7,4588 7,97965 2,5400 10 3,9898 5,486 7,7255 7,4984 8,63938 2,7500 4,3197 5,940 8,3642 8,1184 8,86627 2,8222 9 4,4331 6,096 8,5839 8,3316 9,42478 3,0000 4,7124 6,480 9,1246 8,8564 9,52500 (3,0319) 3/8″ 4,7625 6,549 9,2216 8,9506 9,97456 3,1750 8 4,9873 6,858 9,6568 9,3730 10,00000 3,1831 5,0000 6,875 9,6815 9,3969 10,21018 3,2500 5,1051 7,020 9,8850 9,5944

 p m DP CP S h pb a=14°30’ a=20°00’ 10,99557 3,5000 5,4978 7,560 10,6453 10,3325 11,11250 (3,5372) 7/16″ 5,5562 7,640 10,7585 10,4423 11,39949 3,6286 7 5,6997 7,838 11,0364 10,7120 11,78097 3,7500 5,8905 8,100 11,4057 11,0705 12,56637 4,0000 6,2832 8,640 12,1661 11,8085 12,70000 (4,0425) 1/2″ 6,3500 8,732 12,2955 11,9341 13,29941 4,2333 6 6,6497 9,144 12,8758 12,4974 13,35176 4,2500 6,6759 9,180 12,9265 12,5466 14,13717 4,5000 7,0686 9,720 13,6869 13,2846 14,28750 (4,5479) 9/16″ 7,1437 9,823 13,8324 13,4259 14,92256 4,7500 7,4613 10,260 14,4472 14,0226 15,70796 5,0000 7,8540 10,800 15,2076 14,7607 15,87500 (5,0532) 5/8″ 7,9375 10,915 15,3693 14,9176 15,95930 5,0800 5 7,9796 10,973 15,4510 14,9968 16,49336 5,2500 8,2467 11,340 15,9680 15,4987 17,27876 5,5000 8,6394 11,880 16,7284 16,2367 17,46250 (5,5585) 11/16″ 8,7312 12,006 16,9063 16,4094 18,06415 5,7500 9,0321 12,420 17,4888 16,9747 18,84956 6,0000 9,4248 12,960 18,2492 17,7128 19,05000 (6,0638) 3/4″ 9,5250 13,098 18,4432 17,9011 19,63495 6,2500 9,8175 13,500 19,0095 18,4508 19,94911 6,3500 4 9,9746 13,716 19,3137 18,7460 20,42035 6,5000 10,2102 14,040 19,7699 19,1889 20,63750 (6,5691) 13/16″ 10,3187 14,189 19,9801 19,3929 21,20575 6,7500 10,6029 14,580 20,5303 19,9269 21,99115 7,0000 10,9956 15,120 21,2907 20,6649 22,22500 (7,0744) 7/8″ 11,1125 15,281 21,5171 20,8847 22,79899 7,2571 31/2″ 11,3995 15,675 22,0728 21,4240 23,56194 7,5000 11,7810 16,200 22,8114 22,1410 23,81250 (7,5798) 15/16″ 11,9062 16,372 23,0540 22,3764 25,13274 8,0000 12,5664 17,280 24,3322 23,6170 25,40000 8,0851 1 12,7000 17,464 24,5909 23,8682 26,59882 8,4667 3 13,2994 18,288 25,7516 24,9947 26,70353 8,5000 13,3518 18,360 25,8530 25,0931 28,27433 9,0000 14,1372 19,440 27,3737 26,5692 28,57500 (9,0957) 11/8″ 14,2875 19,647 27,6648 26,8517 29,01689 9,2364 23/4″ 14,5084 19,951 28,0926 27,2670 30,16250 9,6010 13/16″ 15,0812 20,738 29,2018 28,3435 31,41593 10,0000 15,7080 21,600 30,4153 29,5213 31,75000 (10,1063) 11/4″ 15,8750 21,830 30,7387 29,8352 31,91858 10,1600 21/2″ 15,9593 21,946 30,9019 29,9937 33,33750 (10,6117) 15/16″ 16,6687 22,921 32,2756 31,3270 34,55752 11,0000 17,2788 23,760 33,4568 32,4734 34,92500 (11,1170) 13/8″ 17,4625 24,013 33,8126 32,8188 35,46509 (11,2889) 21/4″ 17,7325 24,384 34,3354 33,3263 36,51250 (11,6223) 17/16″ 18,2562 25,104 35,3495 34,3105 37,69911 12,0000 18,8496 25,920 36,4983 35,4256 38,10000 (12,1276) 11/2″ 19,0500 26,196 36,8864 35,8023 39,26990 12,5000 19,6349 27,000 38,0191 36,9016 39,89823 12,7000 2 19,9491 27,432 38,6274 37,4921 40,84070 13,0000 20,4203 28,080 39,5398 38,3777 41,27500 (13,1382) 15/8″ 20,6375 28,379 39,9603 38,7858 43,98230 14,0000 21,9911 30,240 42,5814 41,3298
 p m DP CP S h pb a=14°30’ a=20°00’ 45,59797 (14,5143) 13/4″ 22,7990 31,351 44,1456 42,8481 47,12388 15,0000 23,5619 32,400 45,6229 44,2820 47,62500 (15,1595) 17/8″ 23,8125 32,745 46,1080 44,7529 48,69468 15,5000 24,3473 33,480 47,1436 45,7580 50,26548 16,0000 25,1327 34,560 48,6644 47,2341 50,80000 (16,1701) 2″ 25,4000 34,928 49,1819 47,7364 53,19764 16,9333 11/2″ 26,5988 36,576 51,5032 49,9894 53,40701 17,0000 26,7035 36,720 51,7059 50,1862 56,40707 17,9549 28,2035 38,783 54,6104 53,0053 59,69026 19,0000 29,8451 41,040 57,7890 56,0905 62,83185 20,0000 31,4159 43,200 60,8305 59,0426 63,50000 20,2127 21/2″ 31,7500 43,659 61,4774 59,6705 63,83716 20,3200 11/4″ 31,9186 43,891 61,8038 59,9873 69,11504 22,0000 34,5575 47,520 66,9136 64,9469 69,85000 22,2339 23/4″ 34,9250 48,025 67,6251 65,6375 75,39822 24,0000 37,6991 51,840 72,9966 70,8511 78,53982 (25,0000) 39,2699 54,000 76,0381 73,8033 79,79645 (25,4000) 1″ 39,8982 54,864 77,2547 74,9841 84,82300 27,0000 42,4115 58,320 82,1212 79,7075 87,96459 28,0000 43,9823 60,480 85,1627 82,6597 91,10618 29,0000 45,5531 62,640 88,2042 85,6118 94,24777 30,0000 47,1239 64,800 91,2458 88,5639