Master the fundamentals of machinist math, fractions, decimals, speeds & feeds, and see how shop mathematics, Machinists Handbook tips, and key machinist symbols boost accuracy on the shop floor.

Machinist Math Basics: Shop Mathematics & Handy Tricks

Fractions to decimals

Machinists constantly have to do math conversions from fractions to decimals, a core part of machining math. Some of them are easy, but then some fractions are just tricky to convert in your head. To speed up the process, let’s take a look at some tricks that we can use to convert fractions to decimals.

Let’s start with one that isn’t too bad. Say you needed to know what 13/20 was in decimal form. We know that it will be just slightly over half and under ¾ by deduction, but do you know how to quickly get the answer? First, convert the denominator to 100 by multiplying 20 by five. Then multiply the numerator by five as well. This comes out to 65/100, so the decimal form is .65. All of these processes you should be able to do decently fast in your head, and they will help you along in the conversion process.

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Now, let’s try a more difficult one: 9/15. For this, you are going to want to simplify. Divide both numbers by 3, giving you ⅗. Then multiply everything by two to make the denominator 10, and you are left with 6/10 or .6.

Finally, what about a fraction that doesn’t evenly multiply, like 11/40? We’re going to apply the trick of always getting the denominator to a power of 10 again. Simply divide the fraction by 2 to get 5.5/20, and multiply everything by 5. This leaves you with 27.5/100, or a decimal of .275.

Most fractions should be able to be simplified to a power of ten, and this is the easiest way to find the decimal form in a snap.

Imperial to metric

The US still uses the imperial system of measurement, making conversions a staple of shop mathematics. For machinists in the US, this means constantly converting between metric and imperial and vice versa.

Unfortunately, there’s no easy conversion for the bulk of the metric system to imperial measurements. For this reason, most conversions will likely require a chart of some kind. However, let’s focus on perhaps the most commonly needed conversion: inches to millimeters.

The best way might just be to memorize that 1 inch is about 2.54 cm or 25.4 mm. You can then approximate things like wrench sizes and other measurements using some quick mental math. For inch fractions with a denominator of 32, a quick conversion is that 1/32 of an inch is about .8 mm. So if you have 7/32, then multiply 7 by 8 to get 5.6 mm. If you have 3/16, then multiply 6 by 8 to get 4.2 mm.

Most machinists will need an exact conversion, which means you just have to pull out your handy calculators and conversion tables or consult the Machinists Handbook. If only we used the metric system…

Speeds and feeds

Lastly, machinists need to know how to calculate speeds and feeds on the fly, so quick machining solutions are a must.We need to know things like Surface Feet per Minute (SFPM), RPMs, Chip Loads per Tooth, or the feed rate in inches per minute.

First, let’s look at ways to calculate RPM for a cutting job. We’ll need a chart for mill cutting speeds per material for this one, like the one below from Datron.

You’ll want to find the material you are cutting, select the number based on your cutting tool type, and you’ll be ready to go for the calculation. So, here’s what you’ll end up with:

SFPM (from chart) x (3.82/Tool Diameter) = RPM

To calculate the feed rate in inches per minute, we can use the RPM we just calculated combined with the manufacturer’s suggested chip load per tooth and the number of flutes. It looks like this:

RPM x Chip Load Per Tooth x Number of Flutes = Inches Per Minute

If you want to find any one of those variables, you can just rearrange the formula to equal the variable you desire. So, to solve for chip load per tooth, you could rearrange the formula to look like this:

IPM / RPM / Number of Flutes = CLPT

See, not too bad!

All of this math is essential to succeeding as a machinist. Knowing these conversion tricks and formulas by heart could save you minutes or more in a job process. Refining your math skills is one of the best ways to stay at the top of your game.