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How to Cut Spur Gears with a Dividing Head

Guide · Updated October 28, 2026

With a dividing head, a footstock and an involute gear cutter, a manual mill can cut good spur gears. This guide covers the basic numbers for standard 20° full-depth gears; gear design itself is a bigger subject.

Size the gear blank

Gear blanks are turned to the outside diameter. Prove your mic on gage blocks first. The free Gage Block Calculator builds the stack.

Step by step

Work out the gear numbers: Pitch diameter = N ÷ DP. Outside diameter = (N + 2) ÷ DP. Whole depth = 2.157 ÷ DP for coarse-pitch full-depth teeth (fine pitch, 20 DP and finer, uses 2.200 ÷ DP + 0.002 in).
Turn the blank: Turn the OD and faces on an arbor so the blank runs true.
Pick the cutter: Choose the involute cutter number for the tooth count (see the table below).
Set up the head: Mount the blank between the dividing head and footstock and indicate it true.
Center the cutter: Center the cutter on the blank centerline.
Set depth: Touch the OD, then raise the table by the whole depth, in two passes.
Index and cut: Cut a tooth, back out, index, and repeat around the blank.

Worked example: 30 teeth, 12 DP

PD = 30 ÷ 12 = 2.500 in. OD = 32 ÷ 12 = 2.667 in. Whole depth = 2.157 ÷ 12 = 0.180 in. Indexing on a 40:1 head: 40 ÷ 30 = 1-1/3 turns, so one full turn plus 6 holes on an 18-hole circle (6/18 = 1/3). Set the sector arms to span 6 spaces (7 holes counting the one the pin is in). Cutter: 30 teeth falls in the #4 range (26–34 teeth).

Brown & Sharpe involute cutter ranges

#1: 135 teeth to rack. #2: 55–134. #3: 35–54. #4: 26–34. #5: 21–25. #6: 17–20. #7: 14–16. #8: 12–13. Each cutter is exact for the lowest count in its range and close enough for the rest.

Checking the teeth

Use a gear tooth vernier at the chordal addendum, or measure over pins. A simple check is meshing with a known good gear on fixed centers: center distance = (N1 + N2) ÷ (2 × DP).

Depth on the cutter

Many cutters are stamped with D+F, the whole depth for that pitch. 2.157 ÷ DP is a minimum whole depth; if the cutter marking differs, follow the cutter.

Common problems

Wrong tooth count: lost a hole on the sector arms. Teeth lean: cutter not on center. Uneven teeth: backlash in the head, so always index in one direction. Rough finish: dull cutter or too heavy a cut.

Tips

Head: dividing head basics.
Rotary: rotary table.
Speeds: milling speeds and feeds.

FAQ

What is diametral pitch?

Teeth per inch of pitch diameter.

How do I find blank diameter?

(N + 2) ÷ DP.

How deep do I cut?

2.157 ÷ DP for coarse-pitch full-depth teeth.

Which cutter for 30 teeth?

#4, which covers 26–34.

How do I index 30 teeth?

1 turn and 6 holes on an 18-hole circle.

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