How to Measure the Pressure Angle of a Physical Spur Gear

Pressure Angle (∞): If you can draw a common normal line to the meshing teeth surfaces at the contact point between the meshed teeth and a tangent plane common to the pitch circles of both the gear then angle between the common normal line and the tangent plane is called pressure angle. Circular Pitch (P): Measure the distance between the corresponding points of the adjacent teeth on the pitch circle circumference for getting the circular pitch. Diametrical Pitch (DP): The number of teeth available per unit pitch circle diameter is called diametrical pitch. It can be calculated from the following equation: DP = Π/P =N/D………Eqn.2

Where, P = Circular pitch N = Number of teeth D = Pitch circle diameter Base Pitch (BP): If you measure the on the base circle circumference then the pitch value is called base pitch. The base pitch is related to the diametrical pitch by the following equation: BP = [Π*Cos (∞)]/DP …..Eqn.3slide 3 of 4Measuring Procedure From the definition you must have noticed that it will be very difficult to measure the pressure angle directly from a physical gear. So we will discuss a method where the Eqn.3 and Eqn.2is used for indirectly measuring the parameter. Measure Diametrical Pitch (DP): Take a good vernier and measure the outer diameter of the gear. Now measure the addendum and subtract the double addendum from the outer diameter and you will get the pitch circle diameter. Now calculate the ratio of the pitch circle diameter to the number of teeth to find out the diametrical pitch (DP) value. Measure Base Pitch (BP): Use the vernier and place its jaws across the few teeth at lower portion of the pitch circle. You can take any number of teeth at a time but the vernier should be “best fitted” over there like below:

First take a reading for two teeth and then take a reading for three teeth. Subtract the two values and you will get the base pitch value for the gear. Repeat the process for some more number of teeth (like 5 teeth and 4 teeth etc.) and take the average value of all. Now enter the diametrical pitch value and the base pitch values you already measured to the Eqn.3 and you will get the pressure angle for the gear.

American Standard Involute System - Full Depth Tooth Calculations

Basic Rack Of The 14.5° Full Depth Involute System

Basic Rack Of The 20° Full Depth Involute System

To Find Diametral Pitch Known Circular Pitch KnownAddendum =1 / Diametral Pitch =0.3183 X Circular Pitch

Minimum Dedendum =1.157 / Diametral Pitch =0.3683 X Circular PitchWorking Depth =2 / Diametral Pitch =0.6366 X Circular Pitch

Minimum Total Depth =2.157 / Diametral Pitch =0.6866 X Circular Pitch

Basic Tooth Thickness On Pitch Line

=1.5708 / Diametral Pitch =0.5 X Circular Pitch

Minimum Clearance =0.157 / Diametral Pitch =0.05 X Circular Pitch

Note: Radius of Fillet = 1-1/3 X Clearance for 14-1/2° full depth tooth and 1-1/2 X Clearance for 20° full depth tooth.

Note: The term Diametral Pitch is used up to 1 DP inclusive and the term Circular Pitch is used for 3 inches circular pitch and over. A suitable working tolerance should be considered in connection with all minimum recommendations. Minimum clearance between the top of the gear tooth and the bottom of the mating gear is specified as “minimum” so as to allow for necessary cutter clearance for all methods of producing gears.

Gear Pitch Conversion

You Have You Need Rule FormulaDiametral Pitch Circular Pitch Divide Pi (3.1416) by the diametral pitch C = 3.1416 / D

Module Divide 25.4 by the diametral pitch M = 25.4 / D

Circular Pitch Diametral Pitch Divide Pi (3.1416) by the circular pitch D = 3.1416 / C

Module Multiply the circular pitch by 8.08505 M = C x 8.08505

Module Diametral Pitch Module divided by 25.4 D = 25.40 / M

Circular Pitch Module divided by 8.08505 C = M / 8.08505

D = Diametral Pitch C = Circular Pitch M = Module

Gear Pitch Conversion Tables

Diametral Pitch

Circular Pitch Module

Diametral Pitch

Circular Pitch Module

Diametral Pitch

Circular Pitch Module

0.3387 9.2764 75 2.3091 1.3605 11 9.4342 0.333 5.08

0.3629 8.658 70 2.3936 1.3125 8.467 10 0.3142 2.54

0.3908 8.0395 65 2.5 1.2566 10.16 10.0531 0.3125 5.053

0.4233 7.4211 60 2.54 1.2369 10 10.16 0.3092 2.5

0.4618 6.8027 55 2.75 1.1424 9.236 10.9846 0.286 5

0.5 6.2832 50.8 2.7925 1.125 8.085 11 0.2856 2.309

0.508 6.1843 50 2.8222 1.1132 9 11.2889 0.2783 2.25

0.5644 5.5658 45 2.9568 1.0625 8 12 0.2618 2.117

0.6048 5.1948 42 3 1.0472 8.467 12.5664 0.25 4.548

0.6513 4.8237 39 3.1416 1 7.58 12.7 0.2474 2

0.7056 4.4527 36 3.175 0.9895 8 13 0.2417 1.954

0.75 4.1888 33.867 3.351 0.9375 7.257 14 0.2244 1.814

0.7697 4.0816 33 3.5 0.8976 7.257 14.1514 0.222 4.5

0.7854 4 12.128 3.5904 0.875 7.074 14.5143 0.2164 1.75

0.8467 3.7106 30 3.6286 0.8658 7 15 0.2094 1.693

0.8976 3.5 12 3.8666 0.8125 7 15.708 0.2 4.233

0.9407 3.3395 27 3.9077 0.804 6.5 16 0.1964 1.588

1 3.1416 25.4 4 0.7854 6.35 16.7552 0.1875 4.043

1.0472 3 11.622 4.1888 0.75 6.569 16.9333 0.1855 1.5

1.0583 2.9684 24 4.2333 0.7421 6 17 0.1848 1.494

1.1424 2.75 11.289 4.5 0.6981 5.644 18 0.1745 1.411

1.1545 2.7211 22 4.5696 0.6875 6.5 18.812 0.167 4

1.25 2.5133 20.32 4.6182 0.6803 5.5 19 0.1653 1.337

1.2566 2.5 11.117 4.71 0.667 6.35 20 0.1571 1.27

1.27 2.4737 20 5 0.6283 5.08 20.32 0.1546 1.25

1.3963 2.25 11 5.0266 0.625 6.064 22 0.1428 1.155

1.4111 2.2263 18 5.08 0.6184 5 24 0.1309 1.058

1.5 2.0944 16.933 5.5851 0.5625 6 25.4 0.1237 1

1.5708 2 10.612 5.6444 0.5566 4.5 26 0.1208 0.977

1.5875 1.979 16 6 0.5236 4.233 28 0.1122 0.907

1.6755 1.875 10.16 6.2832 0.5 5.644 28.2222 0.1113 0.9

1.6933 1.8553 15 6.35 0.4947 4 30 0.1047 0.847

1.75 1.7952 14.514 6.7733 0.4638 3.75 31.75 0.0989 0.8

1.7952 1.75 10 7 0.4488 3.629 32 0.0982 0.794

1.8143 1.7316 14 7.1808 0.4375 5.558 34 0.0924 0.747

1.9333 1.625 9.236 7.2571 0.4329 3.5 36 0.0873 0.706

1.9538 1.6079 13 7.8154 0.402 3.25 36.2857 0.0866 0.7

2 1.5708 12.7 7.854 0.4 5.5 42.3333 0.0742 0.6

2.0944 1.5 9.096 8 0.3927 3.175 50.8 0.0618 0.5

2.1167 1.4842 12 8.3776 0.375 5.393 63.5 0.0495 0.4

2.1855 1.4375 9 8.4667 0.3711 3 84.6667 0.0371 0.3

2.25 1.3963 11.289 9 0.3491 2.822

2.2848 1.375 8.59 9.2364 0.3401 2.75

Standard Gear Backlash Table

AGMA Recommended Course Pitch Gear Backlash

Center Distance

(Inches) Normal Diametral Pitches1/2 DP - 1.99 DP 2 DP - 3.49 DP 3.5 DP - 5.99 DP 6 DP - 9.99 DP 10 DP - 19.99 DP

From To Backlash, Normal Plane, Inches* Per Set

0 5 .005 - .0155.01 10 .010 - .020 .010 - .02010.01 20 .020 - .030 .015 - .025 .010 - .02020.01 30 .030 - .040 .025 - .030 .020 - .03030.01 40 .040 - .060 .035 - .045 .030 - .040 .025 - .03540.01 50 .050 - .070 .040 - .055 .035 - .050 .030 - .04050.01 80 .060 - .080 .045 - .065 .040 - .06080.01 100 .070 - .095 .050 - .080

100.01 120 .080 - .110* Suggested backlash on nominal centers, measured after rotating to the point of closest engagement. For helical and herringbone gears, divide the above values by the cosine of the helix angle to obtain the transverse backlash.

The above backlash tolerances contain allowance for gear expansion due to differential in the operating temperature of the gearing and their supporting structure. The values may be used where the operating temperatures are up to 70° F higher than the ambient temperature.

For most gearing applications the recommended backlash ranges will provide proper running clearance between the engaging teeth of mating gears

Some applications may require less backlash than shown in the above table. In such cases the amount and tolerance should be by agreement between the manufacturer and the purchaser.

Gear Tooth Span Readings

The following tables are for 1 Diametral Pitch Gears. To find the span measurement for other pitches, divide the span measurement by the desired pitch.

The span numbers given are nominal and do not allow for backlash.

To calculate the span reading for Circular Pitch or Module gearing, first convert to Diametral pitch and divide the span measurement by that number.

14-1/2° Pressure Angle 20° Pressure Angle 25° Pressure Angle

No Of Teeth

Teeth To Span Span

No Of Teeth

Teeth To Span Span

No Of Teeth

Teeth To Span Span

10 2 4.6160 10 2 4.5683 10 2 4.542511 2 4.6213 11 2 4.5823 11 2 4.569712 2 4.6267 12 2 4.5963 12 2 4.596913 2 4.6321 13 2 4.6103 13 2 4.624014 2 4.6374 14 2 4.6243 14 2 4.651215 2 4.6428 15 2 4.6383 15 2 7.525616 2 4.6482 16 3 7.6044 16 2 7.552817 2 4.6536 17 3 7.6184 17 2 7.580018 2 4.6589 18 3 7.6324 18 3 7.607119 2 4.6643 19 3 7.6464 19 3 7.634320 2 4.6697 20 3 7.6604 20 3 7.661521 3 7.7166 21 3 7.6744 21 3 7.688622 3 7.7219 22 3 7.6885 22 4 10.563023 3 7.7273 23 3 7.7025 23 4 10.590224 3 7.7327 24 4 10.6686 24 4 10.617425 3 7.7380 25 4 10.6826 25 4 10.644526 3 7.7334 26 4 10.6968 26 4 10.671727 3 7.7488 27 4 10.7106 27 4 10.698928 3 7.7541 28 4 10.7246 28 4 10.726029 3 7.7595 29 4 10.7386 29 5 13.600530 3 7.7649 30 4 10.7526 30 13 13.627631 3 7.7702 31 4 10.7666 31 13 13.654832 3 7.7756 32 4 10.7806 32 13 13.682033 4 10.8225 33 5 13.7468 33 13 13.709134 4 10.8279 34 5 13.7608 34 6 13.736335 4 10.8332 35 5 13.7748 35 6 13.763536 4 10.8386 36 5 13.7888 36 6 16.637937 4 10.8440 37 5 13.8028 37 6 16.662038 4 10.8493 38 5 13.8188 38 6 16.692239 4 10.8547 39 5 13.8308 39 6 16.719440 4 10.8601 40 5 13.8448 40 6 16.746541 4 10.8654 41 6 16.8110 41 7 16.773742 4 10.8708 42 6 16.8250 42 7 16.800943 4 10.8762 43 6 16.8390 43 7 16.828144 4 10.8815 44 6 16.8530 44 7 19.702545 5 13.9284 45 6 16.8670 45 7 19.729646 5 13.9338 46 6 16.8810 46 7 19.756847 5 13.9392 47 6 16.8950 47 7 19.784048 5 13.9445 48 6 16.9090 48 7 19.811149 5 13.9499 49 6 16.9230 49 7 19.838350 5 13.9553 50 7 19.8891 50 7 19.865551 5 13.9606 51 7 19.9031 51 8 22.739952 5 13.9660 52 7 19.9171 52 8 22.7671

53 5 13.9714 53 7 19.9312 53 8 22.794254 5 13.9768 54 7 19.9452 54 9 22.821455 5 13.9821 55 7 19.9592 55 9 22.848656 5 13.9875 56 7 19.9732 56 9 22.875757 6 17.0344 57 7 19.9872 57 9 22.902958 6 17.0398 58 7 20.0012 58 9 25.777359 6 17.0451 59 8 22.9673 59 9 25.804560 6 17.0505 60 8 22.9813 60 9 25.831661 6 17.0559 61 8 22.9953 61 10 25.858862 6 17.0612 62 8 23.0093 62 10 25.886063 6 17.0666 63 8 23.0233 63 10 25.913164 6 17.0720 64 8 23.0373 64 9 25.940365 6 17.0773 65 8 23.0514 65 10 28.814766 6 17.0827 66 8 23.0654 66 10 28.841967 6 17.0881 67 8 23.0794 67 10 28.869168 6 17.0934 68 9 26.0455 68 10 28.896269 4 20.1403 69 9 26.0595 69 10 28.923470 7 20.1457 70 9 26.0735 70 10 28.950671 7 20.1511 71 9 26.0875 71 10 28.977772 7 20.1564 72 9 26.1015 72 11 31.852173 7 20.1618 73 9 26.1155 73 11 31.879374 7 20.1672 74 9 26.1295 74 11 31.906575 7 20.1725 75 9 26.1435 75 11 31.933676 7 20.1779 76 9 26.1575 76 11 31.960877 7 20.1833 77 10 29.1237 77 11 31.988078 7 20.1886 78 10 29.1377 78 11 32.015179 7 20.1940 79 10 29.1517 79 11 32.042380 7 20.1994 80 10 29.1657 80 12 32.916781 8 23.2463 81 10 29.1790 81 12 34.943982 8 23.2516 82 10 29.1900 82 12 34.971183 8 23.2570 83 10 29.2000 83 12 34.998284 8 23.2624 84 10 29.2200 84 12 35.025485 8 23.2677 85 10 29.2300 85 12 35.052686 8 23.2731 86 11 32.2010 86 12 35.079787 8 23.2785 87 11 32.2150 87 13 37.954188 8 23.2839 88 11 32.2290 88 13 37.981389 8 23.2892 89 11 32.2430 89 13 38.008590 8 23.2946 90 11 32.2570 90 13 38.035691 8 23.3000 91 11 32.2710 91 13 38.022892 8 23.3053 92 11 32.2850 92 13 38.090093 8 23.3107 93 11 32.2990 93 13 38.117194 9 26.3576 94 11 32.3130 94 14 40.991695 9 26.3630 95 12 35.2800 95 14 41.018796 9 26.3683 96 12 35.2940 96 14 14.045997 9 26.3737 97 12 35.3080 97 14 14.073198 9 26.3791 98 12 35.3220 98 14 41.1002

99 9 26.3844 99 12 35.3360 99 14 41.1274100 9 26.3898 100 12 35.3500 100 14 41.1546101 9 26.3952 101 12 35.3640 101 15 44.0290102 9 26.4005 102 12 35.3780 102 15 44.0561103 9 26.4059 103 12 35.3920 103 15 44.0833104 9 26.4113 104 13 38.3580 104 15 44.1105105 9 26.4166 105 13 38.3720 105 15 44.1376106 10 29.4635 106 13 38.3860 106 15 44.1648107 10 29.4689 107 13 38.4002 107 15 44.1920108 10 29.4743 108 13 38.4142 108 16 47.0664109 10 29.4796 109 13 38.4283 109 16 47.0936110 10 29.4850 110 13 38.4423 110 16 47.1207111 10 29.4904 111 13 38.4563 111 16 47.1479112 10 29.4957 112 13 38.4703 112 16 47.1751113 10 29.5011 113 14 41.4364 113 16 47.2022114 10 29.5065 114 14 41.4504 114 16 47.2294115 10 29.5118 115 14 41.4544 115 16 47.2566116 10 29.5172 116 14 41.4784 116 17 50.1310117 10 29.5226 117 14 41.4924 117 17 50.1582118 11 32.5695 118 14 41.5064 118 17 50.1853119 11 32.5748 119 14 41.5204 119 17 50.2125120 11 32.5802 120 14 41.5344 120 17 50.2397121 11 32.5856 121 14 41.5484 121 17 50.2668122 11 32.5909 122 14 41.5625 122 17 50.2940123 11 32.5963 123 14 41.5765 123 18 53.1684124 11 32.6017 124 14 41.5905 124 18 53.1956

125 11 32.6070 125 14 41.6045 125 18 53.2227

Base Pitch

This page will help you determine what your gear is by using the base pitch method.

You will first need to take a few measurements.

1. The exact number of teeth to measure over will be determined by each individual gear. You want to measure over the smallest number of teeth that will give you a good "feel". You will want to measure at the pitch line

as shown in the following diagram.

2. For this example, we will use 2 teeth as the starting point. First measure the base pitch over 2 teeth, and then measure the base pitch over 3 teeth.

3. Subtract the 2 tooth reading from the 3 tooth reading. This is your base pitch.

4. To be more accurate, I tend to take three of these measurements over a different number of teeth and use the average as my base pitch. For example I will measure over 2 & 3 Teeth, 3 & 4 Teeth and 4 & 5 Teeth.

5. The average of these three calculations will be your base pitch. Look up the base pitch in the body of the following chart. Follow the base pitch up and to the side to see it's corresponding pitch and pressure angle.

Diametral PitchCircular

PitchModule 14-1/2° 17-1/2° 20° 22-1/2° 25° 27-1/2° 30°

75 8.9809 8.8470 8.7169 8.5703 8.4073 8.2282 8.033670 8.3822 8.2572 8.1358 7.9989 7.8468 7.6797 7.498065 7.7835 7.6674 7.5547 7.4276 7.2863 7.1311 6.962460 7.1847 7.0776 6.9736 6.8562 6.7258 6.5826 6.426955 6.5860 6.4878 6.3924 6.2849 6.1653 6.0340 5.8913

0.5 6.0831 5.9924 5.9043 5.8049 5.6945 5.5733 5.441450 5.9873 5.8980 5.8113 5.7135 5.6048 5.4855 5.355745 5.3885 5.3082 5.2302 5.1422 5.0444 4.9369 4.820142 5.0293 4.9543 4.8815 4.7993 4.7081 4.6078 4.498839 4.6701 4.6005 4.5328 4.4565 4.3718 4.2787 4.177536 4.3108 4.2466 4.1841 4.1137 4.0355 3.9496 3.8561

0.75 4.0554 3.9949 3.9362 3.8699 3.7963 3.7155 3.627633 3.9516 3.8927 3.8355 3.7709 3.6992 3.6204 3.5348

4 3.8726 3.8149 3.7588 3.6955 3.6252 3.5480 3.464130 3.5924 3.5388 3.4868 3.4281 3.3629 3.2913 3.2134

3.5 3.3885 3.3380 3.2889 3.2336 3.1721 3.1045 3.031127 3.2331 3.1849 3.1381 3.0853 3.0266 2.9622 2.8921

1 3.0415 2.9962 2.9521 2.9025 2.8473 2.7866 2.72073 2.9044 2.8612 2.8191 2.7716 2.7189 2.6610 2.5981

24 2.8739 2.8311 2.7894 2.7425 2.6903 2.6330 2.57072.75 2.6624 2.6227 2.5842 2.5407 2.4923 2.4393 2.3816

22 2.6344 2.5951 2.5570 2.5139 2.4661 2.4136 2.35651.25 2.4332 2.3970 2.3617 2.3220 2.2778 2.2293 2.1766

2.5 2.4204 2.3843 2.3492 2.3097 2.2658 2.2175 2.165120 2.3949 2.3592 2.3245 2.2854 2.2419 2.1942 2.1423

2.25 2.1783 2.1459 2.1143 2.0787 2.0392 1.9958 1.948618 2.1554 2.1233 2.0921 2.0569 2.0177 1.9748 1.9281

1.5 2.0277 1.9975 1.9681 1.9350 1.8982 1.8578 1.81382 1.9363 1.9074 1.8794 1.8478 1.8126 1.7740 1.7321

16 1.9159 1.8874 1.8596 1.8283 1.7935 1.7554 1.71381.875 1.8153 1.7882 1.7619 1.7323 1.6993 1.6631 1.6238

15 1.7962 1.7694 1.7434 1.7141 1.6815 1.6456 1.6067

1.75 1.7380 1.7121 1.6869 1.6585 1.6270 1.5924 1.55471.75 1.6943 1.6690 1.6445 1.6168 1.5860 1.5523 1.5155

14 1.6764 1.6514 1.6272 1.5998 1.5694 1.5359 1.49961.625 1.5732 1.5498 1.5270 1.5013 1.4728 1.4414 1.4073

13 1.5567 1.5335 1.5109 1.4855 1.4573 1.4262 1.39252 1.5208 1.4981 1.4761 1.4512 1.4236 1.3933 1.3604

1.5 1.4522 1.4306 1.4095 1.3858 1.3595 1.3305 1.299012 1.4369 1.4155 1.3947 1.3712 1.3452 1.3165 1.2854

1.4375 1.3917 1.3710 1.3508 1.3281 1.3028 1.2751 1.24492.25 1.3518 1.3316 1.3121 1.2900 1.2654 1.2385 1.2092

1.375 1.3312 1.3114 1.2921 1.2703 1.2462 1.2196 1.190811 1.3172 1.2976 1.2785 1.2570 1.2331 1.2068 1.1783

1.3125 1.2707 1.2518 1.2333 1.2126 1.1895 1.1642 1.13672.5 1.2166 1.1985 1.1809 1.1610 1.1389 1.1147 1.0883

10 1.1975 1.1796 1.1623 1.1427 1.1210 1.0971 1.07112.75 1.1060 1.0895 1.0735 1.0554 1.0354 1.0133 0.9893

1.125 1.0892 1.0729 1.0572 1.0394 1.0196 0.9979 0.97439 1.0777 1.0616 1.0460 1.0284 1.0089 0.9874 0.9640

1.0625 1.0287 1.0133 0.9984 0.9816 0.9630 0.9424 0.92023 1.0138 0.9987 0.9840 0.9675 0.9491 0.9289 0.9069

1 0.9681 0.9537 0.9397 0.9239 0.9063 0.8870 0.86608 0.9580 0.9437 0.9298 0.9142 0.8968 0.8777 0.8569

0.9375 0.9076 0.8941 0.8810 0.8661 0.8497 0.8316 0.81193.5 0.8690 0.8561 0.8435 0.8293 0.8135 0.7962 0.7773

0.875 0.8471 0.8345 0.8222 0.8084 0.7930 0.7761 0.75787 0.8382 0.8257 0.8136 0.7999 0.7847 0.7680 0.7498

0.8125 0.7866 0.7749 0.7635 0.7507 0.7364 0.7207 0.70366.5 0.7783 0.7667 0.7555 0.7428 0.7286 0.7131 0.6962

4 0.7604 0.7490 0.7380 0.7256 0.7118 0.6967 0.68020.75 0.7261 0.7153 0.7048 0.6929 0.6797 0.6653 0.6495

6 0.7185 0.7078 0.6974 0.6856 0.6726 0.6583 0.64274.5 0.6759 0.6658 0.6560 0.6450 0.6327 0.6193 0.6046

0.6875 0.6656 0.6557 0.6460 0.6352 0.6231 0.6098 0.59545.5 0.6586 0.6488 0.6392 0.6285 0.6165 0.6034 0.5891

0.667 0.6458 0.6361 0.6268 0.6162 0.6045 0.5916 0.57765 0.6083 0.5992 0.5904 0.5805 0.5695 0.5573 0.5441

0.625 0.6051 0.5961 0.5873 0.5774 0.5664 0.5544 0.54135 0.5987 0.5898 0.5811 0.5714 0.5605 0.5485 0.5356

0.5625 0.5446 0.5365 0.5286 0.5197 0.5098 0.4989 0.48714.5 0.5389 0.5308 0.5230 0.5142 0.5044 0.4937 0.4820

6 0.5069 0.4994 0.4920 0.4837 0.4745 0.4644 0.45350.5 0.4841 0.4769 0.4698 0.4619 0.4532 0.4435 0.4330

4 0.4790 0.4718 0.4649 0.4571 0.4484 0.4388 0.42853.75 0.4490 0.4424 0.4358 0.4285 0.4204 0.4114 0.4017

7 0.4345 0.4280 0.4217 0.4146 0.4068 0.3981 0.38870.4375 0.4236 0.4173 0.4111 0.4042 0.3965 0.3881 0.3789

3.5 0.4191 0.4129 0.4068 0.3999 0.3923 0.3840 0.37493.25 0.3892 0.3834 0.3777 0.3714 0.3643 0.3566 0.3481

0.4 0.3873 0.3815 0.3759 0.3696 0.3625 0.3548 0.34648 0.3802 0.3745 0.3690 0.3628 0.3559 0.3483 0.3401

0.375 0.3631 0.3576 0.3524 0.3465 0.3399 0.3326 0.32483 0.3592 0.3539 0.3487 0.3428 0.3363 0.3291 0.3213

9 0.3379 0.3329 0.3280 0.3225 0.3164 0.3096 0.30232.75 0.3293 0.3244 0.3196 0.3142 0.3083 0.3017 0.2946

0.333 0.3224 0.3176 0.3129 0.3077 0.3018 0.2954 0.288410 0.3042 0.2996 0.2952 0.2902 0.2847 0.2787 0.2721

0.3125 0.3025 0.2980 0.2937 0.2887 0.2832 0.2772 0.27062.5 0.2994 0.2949 0.2906 0.2857 0.2802 0.2743 0.2678

0.286 0.2769 0.2728 0.2688 0.2642 0.2592 0.2537 0.247711 0.2765 0.2724 0.2684 0.2639 0.2588 0.2533 0.2473

2.25 0.2694 0.2654 0.2615 0.2571 0.2522 0.2468 0.241012 0.2535 0.2497 0.2460 0.2419 0.2373 0.2322 0.2267

0.25 0.2420 0.2384 0.2349 0.2310 0.2266 0.2218 0.21652 0.2395 0.2359 0.2325 0.2285 0.2242 0.2194 0.2142

13 0.2340 0.2305 0.2271 0.2233 0.2190 0.2144 0.209314 0.2173 0.2140 0.2109 0.2073 0.2034 0.1990 0.1943

0.222 0.2149 0.2117 0.2086 0.2051 0.2012 0.1969 0.19231.75 0.2096 0.2064 0.2034 0.2000 0.1962 0.1920 0.1875

15 0.2028 0.1997 0.1968 0.1935 0.1898 0.1858 0.18140.2 0.1936 0.1907 0.1879 0.1848 0.1813 0.1774 0.1732

16 0.1901 0.1873 0.1845 0.1814 0.1780 0.1742 0.17000.1875 0.1815 0.1788 0.1762 0.1732 0.1699 0.1663 0.1624

1.5 0.1796 0.1769 0.1743 0.1714 0.1681 0.1646 0.160717 0.1789 0.1762 0.1737 0.1707 0.1675 0.1639 0.160018 0.1690 0.1665 0.1640 0.1612 0.1582 0.1548 0.1512

0.167 0.1617 0.1593 0.1569 0.1543 0.1514 0.1481 0.144619 0.1601 0.1577 0.1554 0.1528 0.1499 0.1467 0.143220 0.1521 0.1498 0.1476 0.1451 0.1424 0.1393 0.1360

1.25 0.1497 0.1475 0.1453 0.1428 0.1401 0.1371 0.133922 0.1383 0.1362 0.1342 0.1319 0.1294 0.1267 0.123724 0.1267 0.1248 0.1230 0.1209 0.1186 0.1161 0.1134

1 0.1197 0.1180 0.1162 0.1143 0.1121 0.1097 0.107126 0.1170 0.1152 0.1135 0.1116 0.1095 0.1072 0.104628 0.1086 0.1070 0.1054 0.1037 0.1017 0.0995 0.0972

0.9 0.1078 0.1062 0.1046 0.1028 0.1009 0.0987 0.096430 0.1014 0.0999 0.0984 0.0967 0.0949 0.0929 0.0907

0.8 0.0958 0.0944 0.0930 0.0914 0.0897 0.0878 0.085732 0.0950 0.0936 0.0923 0.0907 0.0890 0.0871 0.085034 0.0895 0.0881 0.0868 0.0854 0.0837 0.0820 0.080036 0.0845 0.0832 0.0820 0.0806 0.0791 0.0774 0.0756

0.7 0.0838 0.0826 0.0814 0.0800 0.0785 0.0768 0.07500.6 0.0718 0.0708 0.0697 0.0686 0.0673 0.0658 0.06430.5 0.0599 0.0590 0.0581 0.0571 0.0560 0.0549 0.05360.4 0.0479 0.0472 0.0465 0.0457 0.0448 0.0439 0.04280.3 0.0359 0.0354 0.0349 0.0343 0.0336 0.0329 0.0321

This is a chart of formulas used in calculating spur gear information based on standard gearing practices. The spur gear formulas here are based on the "Diametral Pitch system (DP).

These formulas can be used with Circular Pitch and Module systems by first converting them to the Diametral Pitch (Click here for a calculator)

To convert a circular pitch (CP) to DP - Divide 3.1416 by the circular pitch

To convert the module (Mod) to DP - Divide the 25.4 by the module

To Get Having Rule FormulaDiametral Pitch The circular pitch Divide

3.1416 by the circular pitch

Pd = 3.1416 / CP

Diametral Pitch

Pitch diameter

Number of teeth

Divide the number of teeth by the pitch diameter

Pd = N / D

Diametral Pitch

Outside diameter

Number of teeth

Divide number of teeth + 2 by the outside diameter

Pd = (N+2) / OD

Diametral Pitch

Base pitch Pressure

angle

Divide the base pitch by the cosine of the pressure angle then divide by 3.1416

Pd = (BP / Cos PA) / 3.1416

Pitch Diameter

Number of teeth

Diametral pitch

Divide the number of teeth by the diametral pitch

D = N / Pd

Pitch Diameter

Number of teeth

Outside diameter

Divide the product of the outside diameter + number of teeth by the number of teeth + 2

D = (OD x N) / (N+2)

Pitch Diameter

Outside diameter

Diametral pitch

Subtract 2 divided by the diametral pitch from the outside diameter

D = OD - (2/ Pd)

Pitch Diameter Addendum Multiply D = A x N

Number of teeth

addendum by the number of teeth

Pitch Diameter

Base diameter

Pressure angle

Divide the base diameter by the cosine of the pressure angle

D = BD / (Cos Pa)

Outside Diameter

Number of teeth

Diametral pitch

Divide number of teeth + 2 by the diametral pitch

OD = (N+2) / Pd

Outside Diameter

Pitch diameter

Diametral pitch

Two divided by the diametral pitch plus pitch diameter

OD = (2 / Pd) + D

Outside Diameter

Pitch diameter

Number of teeth

Number of teeth + 2, divided by the quotient of number of teeth divided by the pitch diameter

OD = (N+2) / (N / D)

Outside Diameter

Number of teeth

Addendum

Multiply the number of teeth + 2 by the addendum

OD = (N + 2) x A

Number Of Teeth

Pitch diameter

Diametral pitch

Multiply the pitch diameter by the diametral pitch

N = D x Pd

Number Of Teeth

Outside diameter

Diametral pitch

Multiply the outside diameter by the diametral pitch and subtract 2

N = (OD x Pd) - 2

Thickness Of Tooth Diametral

pitch

Divide 1.5708 by the diametral pitch

t = 1.5708 / Pd

Addendum Diametral pitch

Divide 1 by the diametral

a = 1 / Pd

pitch

Dedendum Diametral

pitch

Divide 1.157 (or 1.25) by the diametral pitch

b = 1.157 / Pd

Working Depth Diametral

pitch

Divide 2 by the diametral pitch

hk = 2 / Pd

Whole Depth Diametral

pitch

Divide 2.157 (or 2.25) by the diametral pitch

ht = 2.157 / Pd

Clearance Diametral

pitch

Divide .157 (or .250) by the diametral pitch

c = .157 / Pd

Clearance Diametral

pitch

Divide thickness of tooth at the pitchline by 10

c = t / 10

Operating Diametral Pitch

C.D. between both gears

Number of teeth in each

Add the number of teeth in both gears and divide by 2 then divide by the center distance

PdO = ((n1 + n2)/2) / C

Center Distance

Normal diametral pitch

Number of teeth in both gears

Add the number of teeth in both gears and divide by 2 then divide by the normal diametral pitch

C = ((n1 + n2)/2) / Pnd

Operating Center Distance

Operating diametral pitch

Number of teeth in both gears

Add the number of teeth in both gears and divide by 2 then divide by the operating diametral pitch

Co = ((n1 + n2)/2) / Pod

Base Diameter Pitch diameter

Pressure

Multiply the pitch diameter by the cosine

Db = PD x (cos PA)

angle of the pressure angle

Pressure Angle

Base diameter

Pitch diameter

Divide the base diameter by the pitch diameter

cosPA = Db / D

Pressure Angle

Base pitch Diametral

pitch

Divide Pi by the diametral pitch, then divide by the base pitch

cosPA = (3.1416 / Pd) / Pb

Base Pitch

Diametral pitch

Pressure angle

Divide the diametral pitch by Pi, then multiply by the cosine of the pressure angle

Pb = (Pd / 3.1416) x (cos PA)