To add fractional inches, rewrite both measurements in sixteenths, add the numerators, and regroup the result as a mixed number. So 3 5/8 + 2 7/16 = 5 17/16 = 6 1/16 in. Subtracting works the same way and borrows one unit when the fraction on top is smaller than the one below.
This guide works with measurements you have already read. If you are still unsure which mark is which, start with how to read fractional inches on a ruler. If you need the value in millimeters, the fractional inches to millimeters converter does that step. And for fractions that are not shop measurements, use the adding fractions calculator.
| If you have | Do this | Where to see it |
|---|---|---|
| Two measurements with different parts | Convert to sixteenths and add | Worked example |
| A subtraction with the smaller fraction on top | Borrow one unit | Subtracting and borrowing |
| Feet and inches | Add each column and regroup in 12s | Adding feet and inches |
| A saw split | Subtract the cuts first | Dividing a board and subtracting the kerf |
Start with the first row: converting measurements to sixteenths is the base for all the other operations.
A quick estimate prevents big mistakes. The first measurement is over 3.5 and the second is almost 2.5, so the sum has to land a little above 6.
Table of sixteenths and common sums
The table lists the fifteen sixteenth marks within one inch, with their simplified form and terminating decimal. The middle column is the one you use when adding, because it gives the number of sixteenths in each mark.
| Simplified fraction | Sixteenths | Decimal (in) |
|---|---|---|
| 1/16 | 1 | 0.0625 |
| 1/8 | 2 | 0.125 |
| 3/16 | 3 | 0.1875 |
| 1/4 | 4 | 0.25 |
| 5/16 | 5 | 0.3125 |
| 3/8 | 6 | 0.375 |
| 7/16 | 7 | 0.4375 |
| 1/2 | 8 | 0.5 |
| 9/16 | 9 | 0.5625 |
| 5/8 | 10 | 0.625 |
| 11/16 | 11 | 0.6875 |
| 3/4 | 12 | 0.75 |
| 13/16 | 13 | 0.8125 |
| 7/8 | 14 | 0.875 |
| 15/16 | 15 | 0.9375 |
When a sum goes past 16 sixteenths, take out a whole inch and keep the rest as a fraction. So 24 sixteenths is 1 inch and 8 sixteenths, which is 1 1/2 in after simplifying. A sum of two marks, such as 9/16 + 3/16 = 12/16, is solved with the middle column and simplified with the one on the left.
Worked example: two pieces added together
Two pieces measure 3 5/8 in and 2 7/16 in. How long are they together?
- Convert to improper fractions. Multiply the whole number by the denominator and add the numerator, which gives 29/8 and 39/16.
- Choose the common denominator. 8 divides into 16, so 16 works.
- Convert to sixteenths. 29/8 = 58/16, because you multiply top and bottom by 2. The 39/16 is already in sixteenths.
- Add the numerators. 58 + 39 = 97, so the result is 97/16. The denominators are not added.
- Go back to a mixed number. 97 ÷ 16 is 6 with 1 left over, so the mixed number is 6 1/16.
Result: 6 1/16 in.
Check: 3.625 + 2.4375 = 6.0625.
Subtracting and borrowing
Subtraction starts like addition, with a common denominator. The difference appears when the fraction on top is smaller than the one below. In 5 1/4 − 2 3/8, rewritten in eighths, the top has 2 and the bottom has 3, so you cannot subtract directly.
So you take one unit from the 5 and write it as 8/8, which leaves 4 10/8. Now you subtract column by column, and the result is 2 7/8 in.
Borrowing is only needed when the fraction on top is the smaller one. If it is the other way around, subtract directly in sixteenths without touching the whole numbers.
Adding feet and inches
A foot is 12 inches. To add mixed measurements, add the inches and the feet separately, and regroup in 12s at the end. With 5 ft 7 3/4 in and 2 ft 8 1/2 in, the inches go past 12, so 1 ft is added to the feet and the rest stays in inches. The feet give 5 + 2 + 1 = 8, and the total is 8 ft 4 1/4 in.
To check, convert everything to inches with decimals. The total is 100.25 in, and 100.25 ÷ 12 is 8 ft with 4.25 in left over, the same result. If the inches do not reach 12, there is nothing to regroup.
Dividing a board and subtracting the kerf
The saw removes material with every cut. That width is called the kerf, and it depends on the blade. Suppose a kerf of 1/8 in. When you divide a board, the number of cuts is the number of pieces minus one, so 4 pieces take 3 cuts.
A 48 in board is divided into 4 equal pieces. You lose 3/8 in, so the usable length is 47 5/8 in, which is 381/8. Each piece measures 381/8 ÷ 4 = 381/32 = 11 29/32 in.
That measurement does not fall on a sixteenth mark. The neighboring marks are 11 15/16 above and 11 7/8 below. When dividing a board, you round down so you do not exceed the usable length, so each piece is marked at the lower mark. Since 11 29/32 sits exactly halfway between the two marks, it is a tie, and the usable length decides the direction.
Rounding down costs 1/32 in per piece. The four pieces add up to 47 1/2 in, which leaves an eighth of an inch of the board, a margin you can use for sanding. If you rounded up, the four pieces would add up to 47.75 in, more than the usable length, and the last piece would come up short.
The calculation is exact on the numbers as written. The ruler and the actual cut have their own tolerance, so measure the kerf of your blade before dividing.
Practice what you learned
The three calculations use the same steps as the guide: convert to sixteenths, operate, and simplify. Solve them by hand first and then check each result in the calculator.
Three calculations to do by hand
- Add 2 5/16 in and 1 3/4 in.
- Subtract 6 1/8 in − 2 5/16 in.
- Add 3 ft 9 1/2 in and 1 ft 5 3/4 in.
Show the answers
- 4 1/16 in. The 3/4 is 12/16 and the sum gives 17/16.
- 3 13/16 in. You have to borrow, because 2/16 is smaller than 5/16.
- 5 ft 3 1/4 in. The inches go past 12 and are regrouped into one foot.
Which guide to use next
If the problem is matching parts of different sizes in general, the guide on why you do not add denominators explains the reason with other examples. To see the common denominator and the reduced result for each operation, use the subtracting fractions calculator. The mixed numbers calculator accepts the whole and fractional parts separately, and the round to fraction calculator takes a shop result to the nearest ruler mark.
Sources
English Wikipedia, article Inch. It states that the inch is defined as exactly 25.4 mm and that subdivisions of an inch are typically written as fractions with odd numerators, such as 2+3/8 (accessed October 17, 2026). This guide uses that definition for the millimeter equivalence and the odd-numerator notation for writing the results.