Dividing Head Indexing Calculator
Enter the divisions or angle, worm ratio, and index plate set to get a crank-and-hole setting. The result calls out exact simple indexing, exact compound indexing, or the nearest available simple setting with error.
Recommended indexing instructionTurn the crank 1 full turn plus 3 spaces on the 37-hole circle each step.
- Indexing method
- Simple indexing
- Crank turns per step
- 1.08
- Spindle angle per step
- 9.73
- Sector-arm setting
- Set the sector arms 3 spaces apart on the 37-hole circle.
- Alternative exact settings
- No other exact setting found on selected plates.
- Error per step
- 0
- Accumulated closure error
- 0
Count spaces between holes, not the starting hole itself.
Error values are arc-seconds; zero means the recommended setting is exact.
How to use this calculator
- Choose whether the job is defined by equal divisions or by an angular step.
- Enter the dividing-head worm ratio from the machine and select the mounted index plate set.
- Use custom circles only when the listed holes are all on the same accessible plate face.
- Read the crank turns, hole circle, sector-arm spacing, and any error before laying out the cut.
How the indexing setting is calculated
A dividing head turns the work through the worm ratio. On a 40:1 head, forty crank turns rotate the spindle one full revolution. For N equal divisions, the required crank movement is T = R / N, where R is the worm ratio. For an angular step theta, the movement is T = R x theta / 360.
The calculator separates T into whole crank turns and a fractional turn. If the fraction is zero, the instruction is just whole turns. For simple indexing, it tests each available hole circle H and checks whether fraction x H is a whole number of spaces. When it is, the sector arms are set that many spaces apart on that circle.
Some divisions cannot be reached by simple indexing on a standard plate. When compound indexing is allowed, the calculator searches pairs of circles on the same physical plate face and looks for an identity of the form T = W + a/H1 +/- b/H2. The two hole movements must be possible without changing plates. Exact compound answers are ranked by the fewest total hole spaces first, then by smaller circles.
What changes the answer
The worm ratio changes every result. A 60:1 head needs half again as much crank movement as a 40:1 head for the same spindle angle. The plate set matters just as much: a 37-hole circle makes 37 divisions straightforward on a 40:1 head, while a plate without that circle may require compound indexing or a small approximation.
If no permitted exact answer exists, the calculator rounds the simple-indexing hole count on every available circle, normalizes a full-circle carry into the whole-turn count, and reports the setting with the smallest angular error. Error per step and accumulated closure error are shown in arc-seconds so you can judge whether the approximation is acceptable for the part.
What this calculator leaves out
This tool solves angular indexing only. It does not choose gear cutters, calculate tooth form, design differential-indexing change gears, or account for worm wear, plate manufacturing error, backlash, or operator technique. Always approach the pin from the same direction, lock the spindle before cutting, and verify the actual holes on the plate in front of you.
Worked example
For 37 equal divisions on a 40:1 dividing head, the crank movement is 40 / 37 = 1 + 3/37 turns. With the Brown & Sharpe standard set selected, the calculator gives 1 full turn plus 3 spaces on the 37-hole circle. The spindle angle is 360 / 37, or about 9.73 degrees, and the error is zero.
For 51 divisions on the same head, no Brown & Sharpe simple circle gives an exact whole number of spaces. Compound indexing can still be exact because 40 / 51 = 1 + 2/17 - 6/18, so the instruction is 1 full turn, 2 spaces on the 17-hole circle forward, and 6 spaces on the 18-hole circle backward.
Common questions
Why do many dividing heads use a 40:1 ratio?
A 40:1 worm ratio gives useful crank movements for many common gear tooth counts and polygon divisions, and it keeps hand indexing manageable. Other heads and rotary tables may use 60:1, 90:1, or another ratio, so the number stamped on the machine should control the calculation.
Do I count holes or spaces when moving the crank?
Indexing instructions count spaces moved by the pin, not the starting hole. If the result says 3 spaces on a 37-hole circle, the pin leaves its current hole and enters the third hole after it in the chosen direction.
What is the difference between simple and compound indexing?
Simple indexing uses one hole circle after the whole crank turns. Compound indexing combines two hole-circle movements, either in the same direction or opposite directions, to create a fraction that is not available on one circle alone.
Can this be used with a 60:1 head or rotary table?
Yes, if the machine uses a worm and index plates in the same way. Enter the actual ratio and the actual hole circles, because changing from 40:1 to 60:1 changes the crank movement for every division.
Why are some prime-number divisions hard to index exactly?
The denominator of the required fraction has to be represented by the available hole circles, or by a compound combination of two circles on the same plate face. If the needed factors are not present, the calculator can only report a nearest simple setting unless differential indexing is used.