Machinery's Handbook, 31st Edition
2228 Spur Gearing Circular Pitch in Gears—Pitch Diameters, Outside Diameters, and Root Diameters For any particular circular pitch and number of teeth, use the table as shown in the example to find the pitch diameter, outside diameter, and root diameter. Example: Pitch diameter for 57 teeth of 6-inch circular pitch = 10 × pitch diameter given under factor for 5 teeth plus pitch diameter given under factor for 7 teeth. (10 × 9.5493) + 13.3690 = 108.862 inches. Outside diameter of gear equals pitch diameter plus outside diameter factor from next-to-last column in table = 108.862 + 3.8197 = 112.682 inches. Root diameter of gear equals pitch diameter minus root diameter factor from last column in table = 108.862 − 4.4194 = 104.443 inches. Factor for Number of Teeth 1 2 3 4 5 6 7 8 9 6 1.9099 3.8197 5.7296 7.6394 9.5493 11.4591 13.3690 15.2788 17.1887 3.8197 4.4194 5 1 ∕ 2 1.7507 3.5014 5.2521 7.0028 8.7535 10.5042 12.2549 14.0056 15.7563 3.5014 4.0511 5 1.5915 3.1831 4.7746 6.3662 7.9577 9.5493 11.1408 12.7324 14.3239 3.1831 3.6828 4 1 ∕ 2 1.4324 2.8648 4.2972 5.7296 7.1620 8.5943 10.0267 11.4591 12.8915 2.8648 3.3146 4 1.2732 2.5465 3.8197 5.0929 6.3662 7.6394 8.9127 10.1859 11.4591 2.5465 2.9463 3 1 ∕ 2 1.1141 2.2282 3.3422 4.4563 5.5704 6.6845 7.7986 8.9127 10.0267 2.2282 2.5780 3 0.9549 1.9099 2.8648 3.8197 4.7746 5.7296 6.6845 7.6394 8.5943 1.9099 2.2097 2 1 ∕ 2 0.7958 1.5915 2.3873 3.1831 3.9789 4.7746 5.5704 6.3662 7.1620 1.5915 1.8414 2 0.6366 1.2732 1.9099 2.5465 3.1831 3.8197 4.4563 5.0929 5.7296 1.2732 1.4731 1 7 ∕ 8 0.5968 1.1937 1.7905 2.3873 2.9841 3.5810 4.1778 4.7746 5.3715 1.1937 1.3811 1 3 ∕ 4 0.5570 1.1141 1.6711 2.2282 2.7852 3.3422 3.8993 4.4563 5.0134 1.1141 1.2890 1 5 ∕ 8 0.5173 1.0345 1.5518 2.0690 2.5863 3.1035 3.6208 4.1380 4.6553 1.0345 1.1969 1 1 ∕ 2 0.4775 0.9549 1.4324 1.9099 2.3873 2.8648 3.3422 3.8197 4.2972 0.9549 1.1049 1 7 ∕ 16 0.4576 0.9151 1.3727 1.8303 2.2878 2.7454 3.2030 3.6606 4.1181 0.9151 1.0588 1 3 ∕ 8 0.4377 0.8754 1.3130 1.7507 2.1884 2.6261 3.0637 3.5014 3.9391 0.8754 1.0128 1 5 ∕ 16 0.4178 0.8356 1.2533 1.6711 2.0889 2.5067 2.9245 3.3422 3.7600 0.8356 0.9667 1 1 ∕ 4 0.3979 0.7958 1.1937 1.5915 1.9894 2.3873 2.7852 3.1831 3.5810 0.7958 0.9207 1 3 ∕ 16 0.3780 0.7560 1.1340 1.5120 1.8900 2.2680 2.6459 3.0239 3.4019 0.7560 0.8747 1 1 ∕ 8 0.3581 0.7162 1.0743 1.4324 1.7905 2.1486 2.5067 2.8648 3.2229 0.7162 0.8286 1 1 ∕ 16 0.3382 0.6764 1.0146 1.3528 1.6910 2.0292 2.3674 2.7056 3.0438 0.6764 0.7826 1 0.3183 0.6366 0.9549 1.2732 1.5915 1.9099 2.2282 2.5465 2.8648 0.6366 0.7366 15 ∕ 16 0.2984 0.5968 0.8952 1.1937 1.4921 1.7905 2.0889 2.3873 2.6857 0.5968 0.6905 7 ∕ 8 0.2785 0.5570 0.8356 1.1141 1.3926 1.6711 1.9496 2.2282 2.5067 0.5570 O.6445 13 ∕ 16 0.2586 0.5173 0.7759 1.0345 1.2931 1.5518 1.8104 2.0690 2.3276 0.5173 0.5985 3 ∕ 4 0.2387 0.4475 0.7162 0.9549 1.1937 1.4324 1.6711 1.9099 2.1486 0.4775 0.5524 11 ∕ 16 0.2188 0.4377 0.6565 0.8754 1.0942 1.3130 1.5319 1.7507 1.9695 0.4377 0.5064 2 ∕ 3 0.2122 0.4244 0.6366 0.8488 1.0610 1.2732 1.4854 1.6977 1.9099 0.4244 0.4910 5 ∕ 8 0.1989 0.3979 0.5968 0.7958 0.9947 1.1937 1.3926 1.5915 1.7905 0.3979 0.4604 9 ∕ 16 0.1790 0.3581 0.5371 0.7162 0.8952 1.0743 1.2533 1.4324 1.6114 0.3581 0.4143 1 ∕ 2 0.1592 0.3183 0.4775 0.6366 0.7958 0.9549 1.1141 1.2732 1.4324 0.3183 0.3683 7 ∕ 16 0.1393 0.2785 0.4178 0.5570 0.6963 0.8356 0.9748 1.1141 1.2533 0.2785 0.3222 3 ∕ 8 0.1194 0.2387 0.3581 0.4775 0.5968 0.7162 0.8356 0.9549 1.0743 0.2387 0.2762 1 ∕ 3 0.1061 0.2122 0.3183 0.4244 0.5305 0.6366 0.7427 0.8488 0.9549 0.2122 0.2455 5 ∕ 16 0.0995 0.1989 0.2984 0.3979 0.4974 0.5968 0.6963 0.7958 0.8952 0.1989 0.2302 1 ∕ 4 0.0796 0.1592 0.2387 0.3183 0.3979 0.4775 0.5570 0.6366 0.7162 0.1592 0.1841 3 ∕ 16 0.0597 0.1194 0.1790 0.2387 0.2984 0.3581 0.4178 0.4775 0.5371 0.1194 0.1381 1 ∕ 8 0.0398 0.0796 0.1194 0.1592 0.1989 0.2387 0.2785 0.3183 0.3581 0.0796 0.0921 1 ∕ 16 0.0199 0.0398 0.0597 0.0796 0.0995 0.1194 0.1393 0.1592 0.1790 0.0398 0.0460 These changes in outside diameters of pinion and gear do not change the velocity ratio or the procedures in cutting the teeth on a hobbing machine or generating type of shaper or planer. Data in Table 7 on page 2225 are taken from ANSI Standard B6.1-1968, reaffirmed 1974, and show for 20-degree and 25-degree full-depth standard tooth forms, respectively, the addendums and tooth thicknesses for long addendum pinions and their mating short addendum gears when the number of teeth in the pinion is as given. Similar data for Pitch Diameter Corresponding to Factor for Number of Teeth
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