How do I add inches and fractions?
Type lengths in inches and fractions of an inch, like 5 3/8, and pick an operation. The inch calculator works the answer out exactly, then rounds it to the nearest 1/8, 1/16, 1/32 or 1/64 inch, as on a tape measure.
- Result, to the nearest fraction
- 8 1/8
The result is 8 1/8 in, which is 8 1/8 in to the nearest step (8 1/8 in).
- In feet and inches
- 8 1/8 in
- Exact result (in)
- 8 1/8
- Decimal inches
- 8.125
- Centimetres
- 20.638
- Millimetres
- 206.38
Result, to the nearest fraction: 8 1/8. The result is 8 1/8 in, which is 8 1/8 in to the nearest step (8 1/8 in).
How to calculate
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.
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).
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.
- 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
Each example is checked against the calculator on every build.
- First length (in) 5 3/8, Operation +, Second length (in) 2 3/4, Round to 1/16 in gives Exact result (in) 8 1/8, Result, to the nearest fraction 8 1/8, In feet and inches 8 1/8 in, Decimal inches 8.125, Centimetres 20.6375, Millimetres 206.375.Source: NIST Handbook 44, Appendix C (1 in = 2.54 cm)
- First length (in) 5, Operation ÷, Number 3, Round to 1/16 in gives Exact result (in) 1 2/3, Result, to the nearest fraction 1 11/16, Decimal inches 1.666667.
- First length (in) 10, Operation −, Second length (in) 3 5/16, Round to 1/16 in gives Exact result (in) 6 11/16, Result, to the nearest fraction 6 11/16, Decimal inches 6.6875.
- First length (in) 7 1/2, Operation ÷, Number 3, Round to 1/16 in gives Exact result (in) 2 1/2, Result, to the nearest fraction 2 1/2, Decimal inches 2.5.
- First length (in) 1/32, Operation +, Second length (in) 0, Round to 1/16 in gives Exact result (in) 1/32, Result, to the nearest fraction 1/16, In feet and inches 1/16 in.
- First length (in) 30 1/2, Operation +, Second length (in) 11 3/4, Round to 1/16 in gives Exact result (in) 42 1/4, In feet and inches 3 ft 6 1/4 in, Centimetres 107.315.Source: NIST Handbook 44, Appendix C (1 ft = 12 in, 1 in = 2.54 cm)
How it works
Each length is an exact fraction of an inch: 5 3/8 is 43/8, and a decimal such as 2.3 is 23/10. The calculator does the operation in exact fractions:
- + and −: first length ± second length
- × and ÷: first length × or ÷ a number (a whole number, a fraction, or both, like 1 1/2)
Then it shows the result six ways:
- Exact result: the fraction in lowest terms, as a mixed number (1 2/3, −1 1/4).
- Result to the nearest fraction: the nearest multiple of the step you pick (1/8, 1/16, 1/32 or 1/64 inch), as a mixed number in lowest terms. A result exactly halfway between two steps rounds away from zero: 1/32 to the nearest 1/16 is 1/16.
- Feet and inches: the rounded result as whole feet (12 in each) and the inches left, such as "3 ft 6 1/4 in". A zero part is left out ("8 1/8 in", "3 ft"); zero is "0 in"; a negative length has a minus sign in front.
- Decimal inches: the exact result to at most 4 decimals; centimetres (× 2.54) to at most 3 decimals; millimetres (× 25.4) to at most 2. Each is rounded half up from the exact value, with trailing zeros left off.
No answer. Dividing by 0 shows "You cannot divide by 0." A result beyond 1,000,000,000 inches either way shows "The result is more than 1,000,000,000 inches; use smaller numbers."
Assumptions
- The inputs are exact: what you type is the length, with no measuring error.
- 1 in = 2.54 cm exactly (the international inch).
- Nothing is taken off for saw cuts.
Worked examples by hand
5 3/8 + 2 3/4. 43/8 + 22/8 = 65/8 = 8 1/8 in = 8.125 in = 20.6375 cm (206.375 mm).
10 − 3 5/16. 160/16 − 53/16 = 107/16 = 6 11/16 in = 6.6875 in.
7 1/2 ÷ 3. 15/2 ÷ 3 = 15/6 = 2 1/2 in.
5 ÷ 3. 5/3 = 1 2/3 in exactly. To the nearest 1/16: 5/3 × 16 = 26.67, which rounds to 27, so 1 11/16 in.
1/32 to the nearest 1/16. 1/32 × 16 = 0.5, exactly halfway, so it rounds up to 1 step: 1/16 in.
30 1/2 + 11 3/4. 122/4 + 47/4 = 169/4 = 42 1/4 in, which is 3 ft 6 1/4 in or 107.315 cm.
Other questions people ask
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.