# The Mysterious Plus/Plus Tolerance

Here’s an interesting tolerance question: Have you ever seen a plus/plus tolerance? (or minus/minus?) The ASME standard does not mention this, so a purist would say that it is illegal (see paragraphs 2.2 and 2.3 of the Y14.5 standard). But I’ve seen examples such as a hole dimensioned with:

The real problem is that, with a casual glance, you might not realize that a part made at the “nominal” size of 1.25 is a bad part! (The size limits are 1.252 – 1.255.) So the obvious question is: Why did the engineer (or designer) choose this odd method of expressing a tolerance?

The most likely answer is because there is some desired fit with a mating feature. Depending on the assembly, they may want a press fit, transition fit, or clearance fit. So if the example given above is a hole, then a pin in the mating part may be dimensioned with a minus/minus tolerance. In this way we can say that the pin and hole each have a nominal size of 1.250 inches, but the respective tolerances will ensure that there is always a little looseness (clearance fit).

In the metric system, an entire method of coding different limits and fits has been developed. A nominal size would be given, along with a letter and number. For example, 16D8 corresponds to a hole with a nominal size of 16 mm, but with actual limits of 16.050 to 16.077 mm (I had to look this up in a table!). The “16D8” is usually not understood in American design usage, so if a design is being converted from another country to an American program, the engineer usually translates it into an odd-looking “plus/plus” tolerance:

(Similarly, external features use a lowercase letter, so a corresponding hole might be 16d8, which corresponds to 15.923 to 15.950 mm.)

For more information on the code letters and numbers for this ISO usage, consult a Machinery’s Handbook or the ANSI standard for “Preferred Metric Limits and Fits,” ANSI B4.2-1978.

# 5 Comments

1. I notice that sometimes, with inch tolerances, there is no zero in front of the decimal point. But it seems that the zero is always there for metric tolerances. Is this a rule?

2. Yes, according to the ASME Y14.5 standard, the metric system shows a preceding zero for numbers less than 1, but the zero is omitted for English unit numbers less than 1. Of course the meaning is not affected, but this has been the custom so I would say that everyone should stick with that convention. Thanks for your comment!

3. Unfortunately I just learned of this tolerancing method the hard way. Now I have some parts machined to the nominal dimension that have been returned by the customer for rework. Believe me when I say that I wont make that mistake again.

4. Will you please tell me how to calculate cp and cpk value for such tolerancing? Also tell whether this is unilateral or bilateral tolerance.

• I don’t think it would be any different than calculating Cp or Cpk for a regular “equal bilateral” tolerance. We must realize that the 1.250 in the example above might be the “nominal” size (so the plus/plus tolerance can be called unilateral), but 1.250 is not intended to be a target value for manufacturing. The statistical distribution for manufacturing would ideally be centered around the middle of the acceptable range.