**Why Circles Are Better Than Squares – An Introduction to Geometric Tolerancing**

**By: Polly Britton**

**Project Engineer, Product Design**

*8th February 2017*

**Tolerances save on costs**

A tolerance on a technical drawing describes the boundary between what is acceptable in a part and what is not. When a part is made with even one measurement out of tolerance it has to be reworked or scrapped, at cost to the manufacturer. Additionally, an accurate manufacturing process is usually more expensive than the less accurate alternative. Therefore, great savings can be made to component prices by designing tolerances to be as lenient as they can be without impairing the function of a part. One easy way to do this is using circles instead of squares in your tolerances, as illustrated by the following example:**The square way**

A simple way to define a tolerance for a hole’s centre position looks like this:

There is nothing incorrect about this tolerance, but it is probably not a good description of what deviation is allowable. Consider the shape of the tolerance zone for the hole’s centre, shown in orange:

The problem with a square tolerance zone is illustrated above. The green and red dots represent two possible centre positions. Although both dots are an equal distance (√2 or 1.41) from the “true” centre position, a hole centred on the green dot would pass a quality inspection and the red dot would fail. For most applications the red and green centres are equally acceptable, so how can you communicate this in your technical drawing?**The circle way**

This is a drawing of the same hole, with a geometric tolerance.

The two “10” dimensions have become “true dimensions”, as depicted by the boxes around the numbers, and the two datum edges they are measured from have been marked “A” and “B”. The annotation pointing at the circle means something like “The position of the centre can lie anywhere within a diameter 2.83 (that’s 2 x √2) circle of the true centre, with respect to A and B.” This defines the tolerance zone shown below, and allows the centre of the hole to be at both the red and green positions.**Which is better?**

Using geometric tolerancing to describe a circular tolerance zone may not allow you access to cheaper manufacturing methods, but it may reduce the number of scrapped and re-worked parts without having to loosen the tolerance at all. In fact, a circular tolerance zone will be 57.1% bigger in area than a square zone would have been. This additional allowance could make quite an impact when added up over many holes in one part, when just one non-conformance means scrappage.

I would not insist that geometric tolerancing is essential for every application. There are many cases where it would just be a waste of time to define reference datums (or “data” if you prefer) and struggle with your CAD package’s tolerance tools, especially if the intended audience of your drawing is not trained in geometric tolerances. Even if you never have and never will use a geometric tolerance, I hope this has helped you think about what tolerances can say about your part.

#### Further Reading