Gear Design Equations and Formula
Circular Pitches and Equivalent Diametral Pitches Table

Gear Design and Selection Application

  Spur Gear design formula for geometry, pitch, tooth clearance and critical functional data.

Calculate When Defined Formula
Diametral Pitch (P) Pitch Diameter (PD) and the Number of Teeth (N) P = N / PD
Diametral Pitch (P) Circular Pitch (p) P = 3.1416/p
Diametral Pitch (P) Outside Diameter (OD) and the Number of Teeth (N) P = (N+2)/OD
Pitch Diameter (PD) . Number of teeth (N) and the Diametral Pitch (P) PD = N/DP
Outside Diameter (OD) Number of teeth (N) and the Diametral Pitch (P) OD = (N+2)/DP
Number of Teeth (N). Pitch Diameter (D) and the Diametral Pitch (P) N = PD * DP
Addendum (a) . Diametral Pitch (P) a = 1/DP
Dedendum (d) Whole Depth and Addendum d = hw - a
Tooth Thickness (t) at the Pitch Diameter Diametral Pitch (P) t = 1.5708/P
Working Depth (WD). Addendum WD = 2(a)
Center Distance (C) Normal Diametral Pitch (P) and the Number of Teeth in Both Gears C = (N1+N2)/2P
Center Distance (C) Pitch Diameters of both gears C = (PD1+PD2)/2
Circular Pitch (p) Diametral Pitch (P) p = 3.1416 / P
Whole Depth (hw) for 20 Pitch & finer . Diametral Pitch (P) hw = 2.2/P + .002
Whole Depth (hw) for Coarser than 20 Pitch . Diametral Pitch (P) hw = 2.157/P

Helical Gear

Calculate When Defined Formula
Normal D.P. (Pn) Tranverse D.P.(P) and the Helix Angle (A) Pn= P / cos A
Normal D.P. (Pn) Number of teeth (N) and the Helix Angle (A) Pn= N / (D X cos A)
Pitch Diameter (D) Number of teeth (N), the Normal Diametral Pitch and the Helix Angle (A) D = N / (Pn X cos A)
Outside Diameter (OD) Pitch Diameter (D) and the Addendum (a) OD = D + (2 X a)
Outside Diameter (OD) Normal Diametral Pitch (P) and the Pitch Diameter (D) OD = D + 2/Pn
Helix Angle (A) for Parallel Shaft Drive Number of Teeth (N), Pitch Diameter (D) and the Diametral Pitch (P) Cos A = N / (Pn X D)
Addendum (a) Normal Diametral Pitch (Pn) a = 1 / Pn
Lead (L) Pitch Diameter (D) and Pitch Helix Angle L = (pi*D) / Tan

Circular Pitches and Equivalent Diametral Pitches Table

Circular Pitch
Diametral Pitch
Module
Arc Thickness
of Tooth on Pitch Line
Addendum
Working Depth
of Tooth
Dedendum or Depth
of Space Below Pitch Line
Whole Depth
of Tooth
4 0.7854 32.3402 2.0000 1.2732 2.5464 1.4732 2.7464
3 - 1/2 0.8976 28.2581 1.7500 1.1140 2.2281 1.2890 2.4031
3 1.0472 24.2552 1.5000 0.9549 1.9098 1.1049 2.0598
2 - 3/4 1.1424 22.2339 1.3750 0.8753 1.7506 1.0128 1.8881
2 - 1/2 1.2566 20.2117 1.2500 0.7957 1.5915 0.9207 1.7165
2 - 1/4 1.3963 18.1913 1.1250 0.7162 1.4323 0.8287 1.5448
2 1.5708 16.1701 1.0000 0.6366 1.2732 0.7366 1.3732
1 - 7/8 1.6755 15.1595 0.9375 0.5968 1.1937 0.6906 1.2874
1 - 3/4 1.7952 14.1488 0.8750 0.5570 1.1141 0.6445 1.2016
1 - 5/8 1.9333 13.1382 0.8125 0.5173 1.0345 0.5985 1.1158
1 - 1/2 2.0944 12.1276 0.7500 0.4775 0.9549 0.5525 1.0299
1 - 7/16 2.1855 11.6223 0.7187 0.4576 0.9151 0.5294 0.9870
1 - 3/8 2.2848 11.1169 0.6875 0.4377 0.8754 0.5064 0.9441
1 - 5/16 2.3936 10.6116 0.6562 0.4178 0.8356 0.4834 0.9012
1 - 1/4 2.5133 10.1062 0.6250 0.3979 0.7958 0.4604 0.8583
1 - 3/16 2.6456 9.6010 0.5937 0.3780 0.7560 0.4374 0.8154
1 - 1/8 2.7925 9.0958 0.5625 0.3581 0.7162 0.4143 0.7724
1 - 1/16 2.9568 8.5904 0.5312 0.3382 0.6764 0.3913 0.7295
1 3.1416 8.0851 0.5000 0.3183 0.6366 0.3683 0.6866
15/16 3.3510 7.5798 0.4687 0.2984 0.5968 0.3453 0.6437
7/8 3.5904 7.0744 0.4375 0.2785 0.5570 0.3223 0.6007
13/16 3.8666 6.5692 0.4062 0.2586 0.5173 0.2993 0.5579
3/4 4.1888 6.0639 0.3750 0.2387 0.4775 0.2762 0.5150
11/16 4.5696 5.5586 0.3437 0.2189 0.4377 0.2532 0.4720
2/3 4.7124 5.3903 0.3333 0.2122 0.4244 0.2455 0.4577
5/8 5.0265 5.0532 0.3125 0.1989 0.3979 0.2301 0.4291
9/16 5.5851 4.5479 0.2812 0.1790 0.3581 0.2071 0.3862
1/2 6.2832 4.0426 0.2500 0.1592 0.3183 0.1842 0.3433
7/16 7.1808 3.5373 0.2187 0.1393 0.2785 0.1611 0.3003
2/5 7.8540 3.2340 0.2000 0.1273 0.2546 0.1473 0.2746
3/8 8.3776 3.0319 0.1875 0.1194 0.2387 0.1381 0.2575
1/3 9.4248 2.6947 0.1666 0.1061 0.2122 0.1228 0.2289
5/16 10.0531 2.5266 0.1562 0.0995 0.1989 0.1151 0.2146
2/7 10.9956 2.3100 0.1429 0.0909 0.1819 0.1052 0.1962
1/4 12.5664 2.0213 0.1250 0.0796 0.1591 0.0921 0.1716
2/9 14.1372 1.7967 0.1111 0.0707 0.1415 0.0818 0.1526
1/5 15.7080 1.6170 0.1000 0.0637 0.1273 0.0737 0.1373
3/16 16.7552 1.5160 0.0937 0.0597 0.1194 0.0690 0.1287
1/6 18.8496 .5053 0.0833 0.0531 0.1061 0.0614 0.1144

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