Understanding and Using the Fractional Inch Measurement

Polegada Fracionária - Fractional Inch - Pulgadas Fraccional
Use of vernier caliper in fractional inch - measuring and interpretating

The fractional inch use and measurement

In metalworking workshops from countries that have adopted the International System, as Brazil, country of professor Stefanelli, in general, the easiest way to produce parts that were designed in fractional inch is to convert the measurements in inch to millimeter . After all, machines were designed to work in the international system.

However, it is not uncommon to have in our hands a tool in inch and a part or tool for measuring. What do you do? Pretend you’re having a convulsion doesn’t solve your problem, so, keep on this page and see how easy it is!


The fraction is a way of representing a part of a whole. It is a portion of a unit which was divided into equal parts. A well known example is a pizza sliced into eight pieces or the fractional inch.

Divisão são da polegada em metades levando à polegada fracionária

figure 1 – representation of a mixed fraction and its corresponding fractional

Generally, the fraction is represented by a pair of numbers aligned in the vertical and separator by a line divider. The number over the line is the ‘numerator‘ and the underneath is the ‘denominator‘. The example in figure 1 represents an ‘mixed fraction’, which is greater than the unit, in this case, the quantity of wholes is represented to the left of the dividing line (think in a entire pizza more than five pieces).

The denominator express in how many parts the whole is divided. In the example of Figure 1 it was divided into eight parts. The numerator express how many shares will be considered (five). In this example, we consider a ‘full’ unit and another five pieces of which was divided into eight (one and five-eighths).

It is also possible to represent a whole number in fraction form. 8/8, 2/2, 1/1, 128/128 are expressions of the unit (number one – 1). See, in Figure 1, the distance between 0 and 1 is a whole that is divided into eight eighths. Thus:

1 = 2/2 = 4/4 = 8/8 = 16/16 = 32/32 = 64/64 = 128/128 … (called as apparent fraction). It is not recommended, or elegant, to express the whole number this way.

See that 1 5/8 it’s equal to 1 + 5/8 = 8/8 + 5/8 = 13/8 (keeping the denominator and summing the numerator ).

13/8 it’s what we call of ‘improper fraction’ (the value of the numerator is bigger than the denominator). Keeping the fraction like this is a kind of trap armed against you. Always express it in the mixed form (1 5/8).

The fraction must be expressed in its simplest possible form or irreducible. We know that 4/8 it’s the same of 1/2 and we must express the fraction in the form of 1/2 . No intention to make someone decorate this: if both the numerator and denominator are even numbers it is possible to simplify. The same if both are divisible by three, five … and so on.

Fractional Inch

A inch is fractioned in two halves that, in its turn, also are divided in its halves and so on successively. This is the progression that the division of fractions of inch results: 1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, 1/128 , where each new term represents half of the previous one. (It’s important to memorize this numerical progression)

Divisão são da polegada em metades levando à polegada fracionária

figure 2 – inch divided in 16 fractions

It is somewhat counter-intuitive, but a greater number in the denominator decreases the size of the fraction. One way to understand this is to note that the inch is divided into a larger number of parts. This way, if you want to reduce the fraction of the inch, go on multiplying the denominator by two (1, 1/2, 1/4, 1/8, 1/16, 1/32, 1/64, 1/128) among other ways.

Sum of fractions

When the sum of fractions (the sum of the value of the vernier to the scale, for example) has an even numerator, go on dividing both by two until only an odd number remains – irreducible fraction (see the importance of memorizing that progression?). Example: 1/8 + 3/8 = 4/8 = 2/4 = 1/2.

Tip: when summing two even numbers or two odd numbers the result will always be an even number. When summing a even number to an odd one the result will always be an odd number.

Another caution is that we can only sum fractions whose denominators are equal. It’s not possible to sum 1/2 with 1/16, except if we convert fractions to the same denominator. In this way 1/2 = 2/4 = 4/8 = 8/16 that plus 1/16 results in 9/16. Go on multiplying by two the numerator and denominator until the denominator will be equal to the other.

Dividing by half

Dividing a fraction by half (to determine the radius, for example) is also quite simple. If it is a mixed fraction (1 5/8, for example) to convert into an improper fraction (13/8) and multiply the denominator by two (half of 1 5/8, which is equivalent to 13/8, and is 13/16), if the fraction is ‘not improper’ only multiply directly the denominator by two (half of 3/4 is 3/8; half of 63/64 is 63/128)…

Tip : if in the mixed fraction the whole number is an even number , it’s not necessary to convert it to a improper fraction, just divide the whole number by two too.
(example: half of 2.1/4 is 1.1/8; half of 4.5/8 is 2.5/16)

Measuring fractions

And finally, for those who work with decimal system and have the habit to count the marks from left to right. It’s not how you do with fractions. We must ‘look’ to the whole fraction and locate your half (the mark is usually slightly larger than the adjacent) and repeat this process until you reach the measure, summing the fractions. The practice leads to perfection. However, usually we are under pressure.


Uso da polegada fracionária

figure 3 – measurement of an object in fractional inch – answer: 5/8″

Tip : count the number traits of a full inch to the other (usually 32 or 64 – remember that you are not counting traits , but the distance between them ). If they’re 16-Figure 3 – each distance is equal to 1/16″ count how many marks there are to an measure that interests to you, (the tenth-figure 3) see that the fraction is 10/16, ten is even number, simplify dividing both by two until there is an odd number in numerator. The answer is 5/8, figure 3.

That’s it. Practice your fractional inch measurement skills:

Then, interact with the topic:
Use of the Fractional Inch Caliper – Measuring and Interpreting

Eduardo Stefanelli

Engenheiro por profissão, professor por vocação