Gear Span Measurement Calculator (Measurement Over Pins)
Span measurement over pins for an external spur gear, with the involute contact angle solved from the DIN 3960 relation, separate formulas for odd and even tooth counts, and the profile shift applied to both the tooth thickness and the tip diameter. The pin contact is checked against the tip pressure angle so an invalid measurement is flagged rather than reported as a number.
How to use this calculator
- Enter the module, tooth count, pressure angle and profile shift coefficient from the gear drawing.
- Enter the addendum coefficient, which is 1.0 for a standard full depth tooth and 0.8 for a stub tooth.
- Enter the diameter of the pins or balls being used, around 1.68 times the module for a 20 degree gear.
- Read the span over pins, the pressure angle at the pin contact, and the tip pressure angle, and confirm the contact sits below the tip so the pin is on the usable involute.
Frequently asked questions
Why measure over pins rather than across the teeth with a caliper?
A pin sits against the true involute flanks, so the span is a direct reading of tooth thickness rather than a chord across a curved surface. It is also far more repeatable: a micrometer over two pins has a definite contact geometry, whereas a caliper over a tooth chord depends on where the operator places the jaws and on the tip chamfer. The span over pins is the standard production measurement for this reason.
Why does the tooth count parity change the formula?
With an even tooth count there are tooth gaps opposite each other, so the span is measured straight across the axis and the pins sit at the same angular position. With an odd count one side is a gap and the other is a tooth, so the pins are half a tooth pitch apart in angle, which puts a cosine of half a pitch into the formula. Using the even formula on an odd gear gives a span that is wrong by a small but consistent amount.
How do I choose the pin diameter?
Around 1.68 times the module works well for a 20 degree gear, about 1.92 m for 14.5 degrees and 1.44 m for 25 degrees. The pin also has to be a size the gap can accept: too small and it reaches past the start of the usable involute into the undercut, too large and it touches the tip land instead of the flank. Both limits move with the tooth count and the profile shift, so check the pin range for the specific gear.
How does profile shift affect the measurement?
It enters twice, once through the tooth thickness, which grows by twice the shift times the tangent of the pressure angle, and once through the tip diameter, which grows by twice the shift directly. Both must be applied with the same sign. A gear cut with shift and measured against a zero shift drawing will read consistently wrong on every tooth in a way that looks like a tooth thickness error rather than a setup error.