A dividing head turns one tedious calculation — how far to crank for each of N equal divisions — into a repeatable plate-and-arm setting. This calculator does the arithmetic for a standard 40:1 head and finds an index plate that hits your division exactly.
How it works
The 40:1 worm gear means 40 crank turns equal one spindle revolution, so each of N divisions needs:
crank turns per division = 40 / N
= whole turns + (remainder / N)The whole-turns part is straightforward. The fractional part must be expressed as a whole number of holes on an available circle: the tool reduces the fraction and searches standard hole circles for one whose hole count is a multiple of the denominator, then scales the numerator to give the holes to advance.
Standard hole circles
The tool searches the common Brown & Sharpe plates (15, 16, 17, 18, 19, 20, 21, 23, 27, 29, 31, 33, 37, 39, 41, 43, 47, 49) and Cincinnati plates (24, 25, 28, 30, 34, 38, 42, 48, 51, 54, 57, 58, 62, 66) for an exact match. Set the sector arms to the computed number of holes and swing to the next arm after each cut.
Worked example — 24 divisions
For 24 divisions: 40 ÷ 24 = 1 remainder 16, so 1 full turn plus a fraction of 16/24 = 2/3 of a turn.
Search for a hole circle divisible by 3: the 15-hole Brown & Sharpe circle works. Scale the numerator: (2/3) × 15 = 10 holes.
Setting: 1 full turn + 10 holes on the 15-hole circle.
Set the sector arms to span 10 holes (counting gaps, not holes) and advance by that span after each cut. After 24 cuts you complete one full spindle revolution.
Another example — 18 divisions
40 ÷ 18 = 2 remainder 4, so 2 full turns plus 4/18 = 2/9 of a turn.
Search for a circle divisible by 9: the 27-hole circle works. Scale: (2/9) × 27 = 6 holes.
Setting: 2 full turns + 6 holes on the 27-hole circle.
When simple indexing cannot solve the division
Some division counts — particularly large primes like 53, 59, 61, and 67 — cannot be achieved exactly by simple indexing on either Brown & Sharpe or Cincinnati plates because no standard circle count is a multiple of those numbers’ denominators. In those cases, the tool reports that differential indexing (using change gears to offset the plate rotation) is required. Attempting to approximate an unsolvable division leads to cumulative angular error across the workpiece, which the tool avoids by flagging rather than guessing.
Tips for accurate work
- Count holes (gaps) between positions, not the holes themselves — the first hole you start in does not count.
- Lock the index crank firmly in the final hole before taking each cut; a loose crank is the most common source of misdivision.
- After setting sector arms, verify the span by counting across a section of the plate before the workpiece is in the machine.
- For large division counts where the crank barely moves each step, consider whether compound or differential indexing would give a larger, easier-to-read arm span.