# ANSI Drill Bit Size for M2.5 Screw Hole

## using slide rule for ratio calculation

For a DIY project, I need to drill mounting holes for M2.5 (metric) screws. I happen to own ANSI (imperial) drill bits set only, which comes in 1/64 inch increments.

Fortunately, there is a screw gauge template in the box, which allows me to trial fit the M2.5 screw one-by-one, until finding the closest drill bit size.

I’d like to find a better way to do this, with the help of a slide rule.

First, from this link (https://engineersbible.com/clearance-hole-metric/), we know that a M2.5 screw can fit in 2.7mm to 3.1mm screw hole. We need to drill a hole in that size range.

Secondly, the conversion between **mm** and **inch** gives us the direct formula:

**screw hole size (mm)/25.4 = N / 64**

**N** can only take integer values.

Since slide rule is very good at ratio calculation, here is how to do it:

- put the cursor on
**2.54**of D scale; we will use this hairline to read C scale in the coming steps

2. Now slide C scale, use 6.4 on D scale to match integer N (for example, N = 8) on C scale

3. Now you can read the C scale above 2.54 to get the screw hole size, 3.18 in this case.

Mathematically, the ratio calculation you just performed is:

**3.18/25.4 = 8/64**

25.4 and 64 are two known constants in the denominator, whereas 8 gets “mapped” to 3.18.

So a drill bit of 8/64 = 1/8 can certainly give a snug fit. To get a tighter fit, now try to move 7 on C scale above 6.4 (Note the sequence of smaller size drill bits are 7/64, 6/64, 5/64, …)

This time, you read 2.78, which can still fit. On the other hand, if you keep going to the next number, you will find 6/64 being too small.

To make matters a little more complicated, ANSI drill bits also come with gauge numbers such as #31, #32, #33, etc. These don’t follow any math formulas, you have to look them up in a table. This table lists both ANSI and metric drill bits sizes: https://www.custompartnet.com/drill-size-chart

“So just use the table, why bother with the slide rule,” you might ask.

The beauty of slide rule is that it turns the 4 numbers in a ratio equation “dynamic”. In this case, sliding a different integer number over 6.4 gives immediate “response” of the screw hole size over 2.54. And you can see the continuous change of values, as the calculation is being performed.

In a sense, slide rule visualizes the ratio calculation very nicely.