I have two spur gears, each of a diametrical pitch of 16. One gear has 36 teeth and the other 72. I need to know what the distance should be center line to center line of the gear set. This would be the distance between the two shafts that the gears would rotate on.

  • $\begingroup$ (D1 / 2) + (D2 / 2) either root diameter or pitch diameter or outer diameter. $\endgroup$
    – Solar Mike
    Dec 28, 2017 at 19:01
  • $\begingroup$ What you are describing is commonly called the 'Centre Distance', the formula in the answer below is correct. However, in practical applications the 'working centre distance' is often different to the nominal value calculated in this manner. $\endgroup$
    – Petrichor
    Mar 1, 2018 at 12:18

1 Answer 1


The pitch diameter $d$ of any spur gear can be calculated from the number of teeth $N$ and the diametral pitch $D_P$ (or module $m$ in metric units):

$$d = \frac{N}{D_P} \left( = Nm\right)$$

To find the (nominal) centreline distance $C$, note how the centreline distance is the sum of the pitch radii of each gear in mesh:

$$C = \frac{d_1+d_2}{2}$$

$d_1$ and $d_2$ are the pitch diameters for gears 1 and 2 respectively.

In your case, $d_1=36/16=2.25\text{in}$ and $d_2=72/16=4.5\text{in}$. Therefore, $C=\frac{2.25+4.5}{2}=3.375\text{in}.$

3.375in is the nominal value of centreline distance. (Note, however, that (provided the gears are involute gears, which is usually a fair assumption) it is possible to opt for slightly higher (and maybe lower) values of centreline distance than the nominal value without significantly impacting the smoothness of operation of the gears, provided such a change in centreline distance doesn’t cause the teeth to stop contacting or start jamming with one another.)


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