Measurement calculator
Feet and Inches Calculator
Add, subtract, multiply, or divide measurements written in feet, inches, fractions, decimals, and metric units. I will keep the twelfths, halves, and borrowed inches organized so they do not form a committee.
Sage’s guided lesson
Feet and inches use place values, but not base ten place values
Twelve inches make a foot, while ruler fractions usually split an inch into powers of two. That means one measurement can contain base twelve and repeated halving at the same time. The cleanest approach is to convert everything to one unit, perform the arithmetic, then rebuild the result.
Three number systems are sharing one measurement
Feet, inches, and fractions each need a clear job
In 8 ft 3 1/2 in, the 8 counts groups of twelve inches, the 3 counts whole inches, and 1/2 counts part of another inch. The measurement is easy to read on a tape, but awkward to calculate until the pieces are placed in one common unit.
Convert 8 ft 3 1/2 in to total inches
8 ft × 12 in/ft = 96 in
96 in + 3 in + 1/2 in = 99.5 in
A decimal foot is a different form. The measurement 8.5 ft means 8 feet plus half a foot, so it equals 8 ft 6 in. It does not mean 8 ft 5 in.
Never assume digits after a decimal point are inches. In decimal feet, they are fractions of a twelve inch foot.
This method works even when the numbers get ugly
Convert both lengths to total inches, then calculate
Addition and subtraction become ordinary arithmetic when both measurements use the same unit. Convert each length to total inches, perform the operation, then divide the result by 12 to recover feet and remaining inches.
Worked subtraction: 8 ft 3 1/2 in minus 2 ft 7 3/8 in
8 ft 3 1/2 in = 99.5 in
2 ft 7 3/8 in = 31.375 in
99.5 − 31.375 = 68.125 in
68.125 ÷ 12 = 5 ft with 8.125 in remaining
Answer = 5 ft 8 1/8 in
Worked addition: 4 ft 10 3/4 in plus 2 ft 4 5/8 in
58.75 in + 28.625 in = 87.375 in
87.375 in = 7 ft 3 3/8 in
I know this is off topic, but this reminds me of a joke I heard when teaching this to one of my interns, why did the saw avoid the math meeting? It did not want to get into a cutting division. Yeah, I do not see the connection either, but I think it is cute. Back to the math.
You can also work directly in compound units
Borrow one foot as 12 inches; carry 12 inches back into one foot
When subtracting by hand, the top inch amount may be smaller than the bottom inch amount. Borrow one foot from the feet column and add 12 inches to the top inches. Fractions must also use a common denominator before they are subtracted.
Borrowing example
6 ft 2 1/4 in − 3 ft 8 3/4 in
Borrow 1 ft: 6 ft 2 1/4 in becomes 5 ft 14 1/4 in
14 1/4 in − 8 3/4 in = 5 1/2 in
5 ft − 3 ft = 2 ft
Answer = 2 ft 5 1/2 in
For addition, carry whenever the inch total reaches 12. If the inches add to 15 3/8, carry 12 inches into one foot and leave 3 3/8 inches behind.
After subtraction, add the answer back to the smaller measurement. You should return to the starting measurement. Inverse operations are excellent lie detectors.
Repeated pieces and equal divisions
Multiply a length by a count; divide a length by a count
In this calculator, multiplication treats the second entry as a plain number. That is useful for finding the total length of several equal pieces. Division also treats the second entry as a plain number, which is useful for splitting one total length into equal sections.
Six equal pieces, each 27 3/8 inches long
27 3/8 in = 27.375 in
27.375 × 6 = 164.25 in
164.25 in = 13 ft 8 1/4 in
Divide 8 feet into three equal sections
8 ft = 96 in
96 ÷ 3 = 32 in
32 in = 2 ft 8 in
Do not confuse a count with another length. Multiplying inches by inches produces square inches, not a longer line. This calculator deliberately uses a plain number for multiplication and division so the result remains a length.
Six pieces cut from one board usually require more than six times the finished length because the saw removes material between cuts. Use the Saw Kerf Calculator when planning stock.
Twelve is awkward in a decimal calculator, but wonderful at sharing
Why feet contain 12 inches, and why the system lasted
Body based measurements appeared in many cultures because feet, fingers, hands, arms, and paces were always available. The convenience came with a problem: bodies vary. Standards gradually replaced the literal body part while keeping familiar unit names.
Twelve has more whole number divisors than ten. It divides evenly by 2, 3, 4, and 6, which makes halves, thirds, quarters, and sixths convenient. That divisibility helped base twelve relationships remain practical in trade, construction, and layout even when the arithmetic looked strange beside decimal notation.
In medieval England, an inch was officially associated with three barleycorns laid end to end. Modern standards are far more precise. Since the international agreement adopted in 1959, one inch is exactly 25.4 millimeters and one foot is exactly 0.3048 meter.
Long before electronic calculators, people handled compound unit arithmetic with written tables, specialized rules, slide rules, and careful column calculations. The calculator is new; the problem of carrying twelve inches into a foot is not.
5.6 feet equals 5 feet 7.2 inches because 0.6 × 12 = 7.2. It does not equal 5 feet 6 inches. That mistake appears often enough to deserve its own chair at the meeting.
A correct sum can still make a poor layout
Check the datum, the tool, the fraction, and the physical process
Measurement arithmetic assumes every length refers to compatible points. If one dimension starts from the outside edge and another starts from an inside shoulder, adding them may produce a perfectly correct answer to the wrong geometric question.
Tape hooks can move by design to compensate for inside and outside measurements. Pencil lines have width. Boards are not always straight. Materials expand, shrink, compress, and bend. The calculator handles the numbers; the setup still needs judgment.
Sage’s final layout checklist
Use one clear reference edge or datum. Write the operation before entering the measurements. Match the result fraction to the ruler divisions. Include saw kerf, gaps, clearances, and trim allowances where needed. Check subtraction by adding the answer back. For repeated spacing, measure from one datum instead of stepping the tape forward repeatedly.Rounding each small section separately can create cumulative error. When equal spaces must fit inside one total distance, calculate from the total and mark positions from a common starting point.
Write down the measurement. Memory is very confident for something that changes 37 5/8 into 37 3/8 while walking across the room.
Everything measures up
The feet, inches, and fractions have agreed to one answer.
You now know why compound measurements feel unusual, how to convert them to total inches, how borrowing and carrying work, and how to multiply or divide a length without accidentally creating an area.
That earns cheese fries. I will divide the basket evenly, but I am not accepting a complaint from anyone who forgot to include the kerf.
Quick answers
Feet and inches questions
How do I add feet, inches, and fractions?
Convert both measurements to total inches, add them, then divide by 12 to return to feet and inches. You can also add in columns and carry every 12 inches into one foot.
How do I subtract when the top inches are smaller?
Borrow one foot as 12 inches and add it to the top inch value, then subtract. Converting both lengths to total inches avoids borrowing entirely.
Can I enter mixed fractions such as 7 3/8 inches?
Yes. The calculator accepts whole numbers, fractions, mixed feet and inches, yards, millimeters, centimeters, and meters.
What does multiplication do in this calculator?
The first entry is a length and the second is a plain multiplier. Use it for repeated equal pieces, such as six boards at 27 3/8 inches each.
What does division do in this calculator?
The first entry is a length and the second is a plain divisor. Use it to split a total length into equal sections.
Why is 5.6 feet not 5 feet 6 inches?
The decimal part is a fraction of one foot. 0.6 × 12 = 7.2 inches, so 5.6 feet equals 5 feet 7.2 inches.