Question 1

What is the module of a gear?

Accepted Answer

The module m (in millimetres) is the pitch diameter divided by the number of teeth: m = d / z. It sets the size of the teeth, so two spur gears can only mesh if they share the same module and pressure angle. The pitch diameter is then simply d = m × z.

Question 2

How do I find the pitch, tip and root diameters from the module?

Accepted Answer

For a standard full-depth spur gear the pitch diameter is d = m·z, the tip (outside) diameter is da = m·(z + 2) because the addendum equals one module, and the root diameter is df = m·(z − 2.5) because the dedendum is 1.25 m. For example m = 2 mm and z = 20 give d = 40, da = 44 and df = 35 mm.

Question 3

How do I calculate the centre distance between two gears?

Accepted Answer

For two standard spur gears of the same module m the centre distance is a = m × (z1 + z2) / 2, which is just the average of the two pitch diameters. With m = 2 mm, z1 = 20 and z2 = 40 the centre distance is 2 × 60 / 2 = 60 mm.

Question 4

What is the base circle diameter and why does the pressure angle matter?

Accepted Answer

The base circle is the circle from which the involute tooth profile is generated: db = d × cos α, where α is the pressure angle (20° for most modern gears, sometimes 14.5°). A larger pressure angle gives a stronger tooth root but more separating force. The base diameter is needed to lay out the involute or to compute the base pitch.

Question 5

Why do gears below about 17 teeth get undercut?

Accepted Answer

When a standard 20° full-depth pinion has fewer than about 17 teeth the generating tool removes material from the root and undercuts the tooth, weakening it. The usual fixes are a profile shift (addendum modification) or a higher pressure angle. This calculator shows theoretical standard dimensions only, so flag small tooth counts for a shifted-gear design.

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