CNC / machinist calculator
Measurement Over Pins Calculator (Gears and Splines)
Measuring over pins is how you check tooth thickness on a gear or involute spline without a special gauge: drop a pin or ball into opposite tooth spaces and measure across them. This calculator gives the target dimension over pins for an external part or between pins for an internal one, handles the even and odd tooth-count cases, and suggests the ideal pin diameter to use. It works at 20 degrees for standard gears and at 30 degrees for DIN 5480 and DIN 5482 involute splines.
How it works
A pin resting in a tooth space touches the two involute flanks at a contact diameter set by the pin size, the module, the tooth count and the pressure angle. The calculator solves the involute equation for that contact pressure angle, finds the diameter to the pin centres, and then adds the pin for an external part or subtracts it for an internal one. With an even number of teeth the pins sit exactly opposite; with an odd number they sit in the nearest opposite spaces, and the geometry is corrected by the cosine of ninety degrees over the tooth count.
Pin size matters. The ideal pin contacts the flank near the reference diameter, which for a standard 20 degree gear is roughly 1.7 times the module. In practice you pick the nearest standard pin or ball and recompute, which is why the calculator both suggests the ideal size and takes whatever pin you actually have.
For a gear this dimension, together with the span measurement, pins down the tooth thickness. For an involute spline the same involute math gives the nominal geometry, but the standardized measuring-ball diameter, the profile shift and the tabulated inspection limits are defined by the spline standard, not by this calculator - see the coverage note below.
Worked example
A module 2, 20-tooth, 20-degree external gear over 3.5 mm pins measures 44.9293 mm (1.7689 in). The ideal pin for this gear is 3.449 mm, so a 3.5 mm standard pin sits close and contacts near the pitch line.
Frequently asked questions
What is measurement over pins?
It is an inspection method where pins or balls are placed in opposite tooth spaces and the distance across them is measured. Because the pins touch the involute flanks at a fixed geometry, the reading is a repeatable check of tooth thickness for gears and splines.
How does the even or odd tooth count change it?
With an even number of teeth the pins sit exactly opposite and you measure straight across. With an odd number there is no exactly-opposite space, so the pins go in the nearest opposite spaces and the geometry is corrected by the cosine of ninety degrees divided by the tooth count.
What pin or ball diameter should I use?
Use one that contacts the flank near the reference diameter, roughly 1.7 times the module for a 20 degree gear. The calculator suggests this ideal size; pick the nearest standard pin or ball you own and enter it, and the measurement updates for the pin you actually use.
Does this cover DIN 5480 and DIN 5482 splines?
It computes the nominal over-balls geometry at the 30 degree spline pressure angle. It does not supply the DIN standardized ball diameter, the DIN profile shift, or the tabulated inspection dimensions and tolerance classes, which come from DIN 5480-1 and DIN 5480-2. Enter your ball size and profile shift from the standard.
Can I use diametral pitch gears?
Yes. Choose diametral pitch and enter the DP; the calculator converts to module as 25.4 divided by the DP, computes the measurement in millimetres, and also reports it in inches.
Related calculators
Coverage
Implements Involute over-pins measurement (general; DIN 5480/5482 for splines): External and internal involute gears and splines, Any pressure angle (20 for gears, 30 for DIN splines), even and odd teeth, Module or diametral pitch, with profile shift, plus ideal pin suggestion. Deliberately not offered yet:
- DIN 5480/5482 standardized measuring-ball diameter, profile shift and inspection tables - these are tabulated in DIN 5480-1/-2 and are not derived here; the tool gives nominal geometry for a user-supplied ball and shift (revisit: if the DIN 5480 ball-diameter and inspection tables are licensed and transcribed)
- Tooth-thickness allowance and tolerance classes - the measurement is the nominal value; the minus-allowance for backlash or fit comes from the gear or spline tolerance class
Sources
- Over-pin (ball) measurement (KHK Gears)
- Dimension over pins, balls and wires (zakgear.com, Dr. Stepan V. Lunin)
- Determining tooth thickness, over pins, part III (Gear Solutions)
Every formula on this page is shown and sourced. See how we verify.
These calculators are for planning and as a starting point. Recommended speeds and feeds are published starting values that vary with your specific tool, coating, machine rigidity, workholding and coolant. Always start conservative, listen to the cut, and follow your tool maker data sheet.