How to use this site

Hole calc provides a set of simple calculators to determine the diameter of a bore based on the size of three pin gages (a.k.a. plug gages or gauges) that fit into it. This three-gage method can provide a quick way to measure bore diameters when you don't have access to a GO/NOGO gage pair or other precision bore measuring method. Measurements obtained via the three-pin method should be considered approximate relative to the use of these other methods.

Three pin method step-by-step

  1. Prepare the hole to be measured. Make sure the bore is clean and dry and the edge of the hole is free from burrs.
  2. Select three clean, dry gage pins that will slide in to the bore together.
  3. If needed, replace one of the pins with a larger or smaller diameter pin in order to adjust the fit within the bore. The pins should slide in and out by hand. Each pin should contact both the other two pins and the wall of the bore without any play.
  4. Once a well fitting combination of pins is found, enter the diameter of each pin into the three pin calculator.
  5. If you want to see a result range based on gage class, select the "Tolerance" radio button. Enter the tolerance class and sign for each gage pin using the drop-down fields that appear. See the "Precautions" selection below for more information on tolerance mode.
  6. Select desired units and digits of precision from the drop-down fields.
  7. Press the "Calculate" button
  8. Your result should appear to the right of the input fields (desktop) or below (mobile). If your inputted values are invalid (not a number or mathematically impossible), an error message will appear.

Reverse mode

Hole calc also has a "reverse mode" calculator. When you enter the diameters of two pin gages and a bore, the reverse calculator will output the diameter of the remaining, third pin which will fit into that bore diameter. This can be useful if you want to determine the best combination of available pin gages to measure a target bore diameter. As with the three pin calculator, it is possible to enter values that are mathematically impossible to calculate, in which case the calculator will show an error message.

Gage size mode

The third mode provided by hole calc is a pin gage diameter calculator, based on specifications provided by ASME B89.1.5-1998. This tells you the allowable diameter range for a gage pin of a given nominal diameter, tolerance class/sign, and units of measure. ASME B89.1.5-1998 only defines tolerance classes for gages from 0.0010 in to 21.010 in (0.254 mm to 533.65 mm), so values above or below those limits will generate an error.


This calculator simply does the math for you- it does not substitute for an understanding of the metrology involved in measuring holes. A full overview of how to use pin gages and measure holes is outside the scope of this guide (this video is a good starting point). However, the following caveats should be kept in mind when attempting to do precision work using the three-pin method:

  • Every gage pin has a class indicating the tolerance of the pin diameter and are designated as plus or minus relative to the nominal size. The tolerance of each pin and resulting stack-up will affect the measurement of the hole. Hole calc has a "Tolerance" mode that will automatically calculate minimum/maximum values based on tolerance class and sign of each pin. While this can provide a high degree of numeric precision, the degree to which this reflects the actual size of the hole will depend on the precision of your measuring process.
  • As with the standard GO/NOGO method of measuring a bore, insertion pressure, surface roughness, cleanliness, (lack of) edge breaks and material will all affect how easily gages slide into the bore and therefore the choice of gages used for the final measurement.
  • The three gage method assumes the bore to be perfectly round. If the bore is oval-shaped or lobed, the three gage method will provide inconsistent results depending on the relative position of the gages within the bore.

The math

This calculator is based on Descartes' Theorem, which states that for every four mutually tangent circles, the radii of the circles satisfy a certain quadratic equation. The circles described in this theorem are also known as Soddy circles. If we assume the three pins used for the calculator measurement all touch each other as well as the larger bore they fit into, finding the diameter of the bore is a straightforward application of the quadratic equation described in Descartes' theorem.

Keep in mind that it's possible to have certain combinations of pin diameter and bore diameter that are mutually tangent without visually filling the entire space of the bore. While it's unlikely to encounter this scenario during actual measuring use, it's still a valid application of the theorem and the calculator. So if you're seeing an odd result of this nature, verify in your CAD program of choice or pen and paper before submitting a bug report or request for help.

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