# How do I add inches and fractions?

Adds or subtracts lengths in inches and fractions of an inch, or multiplies or divides one by a number, exactly, and shows the result to the nearest 1/8, 1/16, 1/32 or 1/64 inch, in feet and inches, as a decimal, and in centimetres and millimetres.

- Page: https://www.acalculator.org/construction/inch-calculator
- JSON spec: https://www.acalculator.org/construction/inch-calculator.json
- Version: f92220fa6386

## Default answer

Example with the default inputs (First length (in) 5 3/8, Operation +, Second length (in) 2 3/4, Round to 1/16 in): The result is 8 1/8 in, which is 8 1/8 in to the nearest step (8 1/8 in).

## Inputs

| Key | Label | Description |
| --- | --- | --- |
| a | First length (in) | The first length in inches: a whole number, a fraction or both, like 5 3/8. |
| op | Operation | Add or subtract a second length, or multiply or divide the first by a number. |
| b | Second length (in) | The length to add or subtract, in inches. |
| n | Number | The number to multiply or divide the first length by, like 3 or 1/2. |
| den | Round to | The fraction of an inch to round the result to, as on a tape measure. |

## Outputs

| Key | Label | Description |
| --- | --- | --- |
| rounded | Result, to the nearest fraction | The result in inches, rounded to the nearest 1/8, 1/16, 1/32 or 1/64 inch (halves away from zero). |
| feetInches | In feet and inches | The rounded result as feet and inches. |
| exact | Exact result (in) | The result in inches as an exact fraction in lowest terms. |
| decimal | Decimal inches | The exact result as a decimal, rounded to 4 decimal places. |
| cm | Centimetres | The exact result × 2.54, rounded to 3 decimal places. |
| mm | Millimetres | The exact result × 25.4, rounded to 2 decimal places. |

## Method

Result = a + b, a − b, a × n or a ÷ n in exact fractions of an inch; rounded = the nearest multiple of 1/8, 1/16, 1/32 or 1/64 inch; cm = inches × 2.54.

## Assumptions

- Every number is exact: 5 3/8 is 43/8, and 0.3 is 3/10. The result is an exact fraction before rounding.
- Rounding goes to the nearest step of the chosen fraction; a result exactly halfway between two steps rounds away from zero.
- 1 inch is 2.54 cm exactly, and 1 foot is 12 inches.

## Worked examples

1. a = 5 3/8, op = add, b = 2 3/4, den = 16 gives exact = 8 1/8, rounded = 8 1/8, feetInches = 8 1/8 in, decimal = 8.125, cm = 20.6375, mm = 206.375. Source: NIST Handbook 44, Appendix C (1 in = 2.54 cm).
2. a = 5, op = divide, n = 3, den = 16 gives exact = 1 2/3, rounded = 1 11/16, decimal = 1.666667.
3. a = 10, op = subtract, b = 3 5/16, den = 16 gives exact = 6 11/16, rounded = 6 11/16, decimal = 6.6875.
4. a = 7 1/2, op = divide, n = 3, den = 16 gives exact = 2 1/2, rounded = 2 1/2, decimal = 2.5.
5. a = 1/32, op = add, b = 0, den = 16 gives exact = 1/32, rounded = 1/16, feetInches = 1/16 in.
6. a = 30 1/2, op = add, b = 11 3/4, den = 16 gives exact = 42 1/4, feetInches = 3 ft 6 1/4 in, cm = 107.315. Source: NIST Handbook 44, Appendix C (1 ft = 12 in, 1 in = 2.54 cm).

## FAQ

### How do I add inches with fractions?

Add the whole inches and the fractions separately, with a common bottom number. 5 3/8 + 2 3/4: the fractions are 3/8 + 6/8 = 9/8 = 1 1/8, and the whole inches are 5 + 2 = 7, so the total is 8 1/8 in.

### How do I subtract fractions of an inch?

Write both lengths over the same bottom number and subtract. 10 − 3 5/16 = 160/16 − 53/16 = 107/16 = 6 11/16 in. Borrow an inch as 16/16 when the top fraction is smaller.

### How do I divide a length into equal parts?

Pick ÷ and type the number of parts. A 7 1/2 in board cut into 3 equal pieces gives 2 1/2 in each. When the answer is not a tape-measure fraction, such as 5 ÷ 3 = 1 2/3 in, the calculator also rounds it to the nearest 1/16 in: 1 11/16 in. (Each saw cut also takes the width of the blade.)

### What is 1/16 of an inch as a decimal?

0.0625 in, which is 1.5875 mm. The marks on a US tape measure are usually in 1/16 in steps: 1/8 = 0.125, 1/4 = 0.25, 3/8 = 0.375, 1/2 = 0.5, 5/8 = 0.625, 3/4 = 0.75 and 7/8 = 0.875.

### How do I convert inches to feet and inches?

Divide by 12: the whole number is the feet and the rest is inches. 42 1/4 in is 3 ft (36 in) and 6 1/4 in. The calculator shows the rounded result this way.

### How many centimetres are in an inch?

Exactly 2.54 cm, or 25.4 mm, by the international definition of the inch. So 8 1/8 in is 8.125 × 2.54 = 20.6375 cm.

## Sources

- OpenStax, Prealgebra 2e, §4.5 Multiply and Divide Mixed Numbers and §4.6 Add and Subtract Mixed Numbers. https://openstax.org/books/prealgebra-2e/pages/4-6-add-and-subtract-mixed-numbers
- NIST Handbook 44 (2024), Appendix C, General Tables of Units of Measurement: 1 in = 2.54 cm exactly; 1 ft = 12 in. https://www.nist.gov/pml/owm/nist-handbook-44-current-edition