Why is the constant 40?

Standard dividing heads use a 40 to 1 worm-and-wheel ratio, so 40 turns of the index crank rotate the spindle one full revolution. To cut N equal divisions you advance the crank 40 divided by N turns for each division.

How is the hole circle chosen?

The fractional part of 40/N must be expressed as a whole number of holes on an available circle. The tool searches standard Brown & Sharpe and Cincinnati hole circles for one whose hole count is a multiple of the fraction's denominator, then scales the numerator to match.

What is the sector arm for?

The sector arms are set to span the number of holes you advance each division so you do not have to count holes every time. Set the arms to the computed spaces, and after each cut swing the crank to the next arm position.

What if no plate gives an exact division?

Some prime divisions above 50, such as 53 or 59, cannot be done by simple indexing on standard plates and require differential indexing with change gears or angular approximation. The tool reports when a division is not achievable by simple indexing.

Do the holes counted include the starting hole?

No. The count is the number of spaces, or gaps, to advance, not holes touched. Advancing 9 holes on a 15-hole circle means moving past 9 gaps from your current hole, which the sector arms enforce automatically.

Dividing Head Calculator

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.

Example and tips

For 24 divisions, 40 / 24 = 1 and 16/24 = 1 turn plus 2/3 of a turn. On a 15-hole circle, 2/3 of 15 is 10 holes, so the setting is 1 full turn plus 10 holes on the 15-circle. Some primes above 50 — 53, 59, 61 — have no exact simple-indexing solution and need differential indexing; the tool flags those cases rather than returning a wrong approximation.