What is feet-and-inches arithmetic?
Feet and inches is a base-12 system wearing a base-10 disguise. Twelve inches carry into one foot, so 7" + 8" comes out as 1' 3" — not 15", and definitely not 1.5'. Put a tape measure's fractions on top and a single sum can involve three bases at once: sixteenths for the fraction, twelve for the carry, ten for anything you typed as a decimal. That is the whole reason this arithmetic feels harder than it looks.
It matters most where material gets cut once. Framing a wall, ripping trim, sizing a countertop, spacing fence posts, ordering blinds. Building plans in the US and the UK are still written in feet and inches, the supplier's spec sheet is often in millimeters, and the same drawing has to serve both.
One thing worth pinning down before any of it: 8' 5" is not 8.5 feet. 8.5 feet is 8' 6". 8' 5" is 8.4167 feet. A decimal foot splits into ten parts; a real foot splits into twelve. Surveyors, engineers and spreadsheets use the first. Tapes, plans and carpenters use the second. Quietly swapping one for the other is the most common way a measurement goes wrong on paper. A feet and inches calculator earns its keep by holding both readings at once, so the number you hand the framer and the number you hand the spreadsheet are the same number.
How to use the Feet and Inches Calculator
Two measurements, one operation, one answer. There's no Calculate button in the Feet and Inches Calculator — the result updates as you type.
- Type measurement A. Feet on the left, inches on the right. The inches box reads fractions the way a carpenter writes them, so 3 1/2, 3-1/2 and 3.5 all mean the same thing.
- If you're holding a whole reading like 5' 3 1/2", paste it into the feet box. It splits itself across the two boxes when you tab away.
- Pick the operation: +, −, × or ÷. Plus is selected when the page opens.
- Type measurement B. For plus and minus it's a second feet-and-inches reading. For times it's a plain number — three lengths of the same trim. For divided by, you choose whether you're dividing by a length or by a number.
- Choose what you round to. Sixteenths is the default, because that's what most tapes mark. Drop to eighths for rough framing, go to sixty-fourths or decimal inches for machining.
- Read the answer. Underneath it you get total inches, decimal feet, meters and centimeters, each with its own copy button.
That's the whole flow. Open it, do the sum, close the tab.
The math behind adding feet and inches
Whether you're adding, subtracting, multiplying or dividing, the Feet and Inches Calculator runs the same three moves: convert both measurements to total inches, do the arithmetic once, convert back.
total inches = (feet × 12) + inches
Do the sum in total inches, then: feet = ⌊total ÷ 12⌋, inches = total − (feet × 12)
Working one all the way through. Add 5' 3 1/2" and 3' 6":
- 5' 3 1/2" → (5 × 12) + 3.5 = 63.5 inches
- 3' 6" → (3 × 12) + 6 = 42 inches
- 63.5 + 42 = 105.5 inches
- 105.5 ÷ 12 = 8, remainder 9.5 → 8' 9 1/2"
The same 105.5 inches is also 8.7917 decimal feet, 2.6797 meters and 267.97 centimeters. Every one of those readings is derived from the same stored value, so they can't drift apart by a rounding step. The metric numbers aren't approximations either — one inch has been defined as exactly 25.4 millimeters since the international agreement of 1959.
Subtraction works identically and is allowed to go negative. 3' minus 4' 6" is −1' 6", which is −18 inches: you are a foot and a half short. That minus sign is the answer to "does this piece fit," and hiding it would throw away the only part you needed.
Common sums, and what rounding does to them
Five sums a tape measure actually produces, with the readings that come back with each one:
| The sum | Answer | Total inches | Meters |
|---|---|---|---|
| 5' 3 1/2" + 3' 6" | 8' 9 1/2" | 105.5 in | 2.6797 m |
| 8' − 1' 7 3/8" | 6' 4 5/8" | 76.625 in | 1.9463 m |
| 5' 3" × 3 | 15' 9" | 189 in | 4.8006 m |
| 2' 7 1/2" × 4 | 10' 6" | 126 in | 3.2004 m |
| 3' − 4' 6" | −1' 6" | −18 in | −0.4572 m |
Notice the third and fourth rows. Multiplying here means multiplying by a plain number — three lengths of the same trim, four identical shelf sides. Length times length is an area, measured in square feet, so it belongs on a different page.
Rounding is where most measurement calculators quietly lie to you. Split a 10-foot board seven ways and each piece is 17.142857… inches, a number that exists on no tape ever made. Here's the same division at every fraction the tool offers:
| Round to | 10' ÷ 7 | Good for |
|---|---|---|
| 1/2" | ≈ 1' 5" | Rough estimates, site talk |
| 1/4" | ≈ 1' 5 1/4" | Framing, decking |
| 1/8" | ≈ 1' 5 1/8" | General carpentry |
| 1/16" | ≈ 1' 5 1/8" | The default — what most tapes mark |
| 1/32" | ≈ 1' 5 5/32" | Trim, cabinetry |
| 1/64" | ≈ 1' 5 9/64" | Fine joinery |
| Decimal | ≈ 1' 5.1429" | Machining, CNC |
Two details in that table are worth the price of admission. The ≈ is there on purpose: the exact answer doesn't land on any of those marks, and the tool says so rather than printing a clean-looking number you can't find on your tape. And the 1/8" and 1/16" rows agree — 17.142857 rounds to the same sixteenth either way — which tells you the extra precision bought you nothing for that particular cut.
Changing the rounding always re-rounds the exact answer, never the previously rounded one. Round to a half, then switch to sixty-fourths, and you get the true value at sixty-fourths — not 1' 5" dressed up with more digits.
Edge cases and limitations
A few behaviors that trip people up on other feet and inches calculators:
More than twelve inches is fine. Type 5' 18" and you get 6' 6". Adding stock lengths in your head often leaves you with something untidy like that, and refusing the entry helps nobody. Improper fractions carry the same way: 3 5/4 becomes 4 1/4.
Dividing a length by a length gives a count. 12' ÷ 16" is 9 times — how many 16-inch spacings fit in a 12-foot wall. It isn't 9 feet and it isn't 9 inches, so the unit conversions and the rounding control disappear for that case: there's nothing to convert and no fraction to round. When the count isn't whole, the fractional part is your leftover piece. 16' 8" ÷ 24" is 8.3333 times — eight full 24-inch bays and a third of one left at the end.
What it won't do. It won't multiply two lengths into square feet, it won't handle angles or diagonals, and it won't calculate board feet, which needs a thickness. It also doesn't know what you're building — if a cut list has to allow for a saw kerf, a reveal or an expansion gap, that allowance is yours to add. And nothing you type is checked against reality: measure twice regardless.
Related measurement tools
If the answer you want isn't a length, one of these probably is the right page. Length times length is an area — the square footage calculator takes room dimensions in feet and inches and answers in square feet, which is what you order flooring and paint by. Buying rough lumber priced by volume? The board foot calculator handles thickness × width × length.
For straight unit changes with nothing to add up, the single-purpose converters are quicker: feet to inches, inches to feet, feet to centimeters and feet to meters. And if you're stuck on the fraction rather than the measurement — adding 3/8 to 5/16 by hand — the fraction calculator does that part on its own and simplifies the result.
Frequently asked questions
How many studs do I need at 16 inches on center?
Divide the wall length by the spacing, then add one. A 12-foot wall at 16" on center is 12' ÷ 16" = 9 times, so 9 spacings — which means 10 studs, because you need one at each end. The same "add one" rule applies to fence posts, balusters and shelf brackets. If the division doesn't come out whole, round the count up and expect a short bay at the end.
How do I split a board into equal pieces?
Set the operation to ÷, choose "a number" as the divisor, and type how many pieces you want. A 10-foot board in seven pieces is about 1' 5 1/8" each at sixteenths — dividing feet and inches by a plain number always gives a length back. One warning the arithmetic can't give you: every cut eats roughly 1/8" of material, so seven pieces means six kerfs and about 3/4" of board that becomes sawdust. Cut from one end and measure each piece fresh rather than marking all seven at once.
Why does my answer start with ≈?
Because the exact value falls between two marks on your tape, and the tool would rather tell you than pretend. 10' ÷ 7 is 17.142857… inches; at sixteenths the nearest mark is 1' 5 1/8". You'll also see a line naming the fraction it rounded to. If you'd rather have the full precision, switch the rounding control to Decimal and you'll get 1' 5.1429".
Can I type the foot and inch marks?
Yes — paste a whole reading like 5' 3 1/2" into the feet box and it splits across the two boxes when you tab away. Forms like 5 ft 3 1/2 in and 5-3 work too. One deliberate exception: 3-1/2 typed into a feet box stays as three and a half feet, because in a feet box that's far more likely to be what you meant than three feet and half an inch.
Why not just multiply two measurements to get square feet?
Because the units change. Feet times feet is square feet, and an answer in square feet can't be displayed as feet and inches without being wrong. Calculators that switch you from length to area mid-sum are how people end up ordering flooring for the wrong room. Here, × means times a plain number. For area, the square footage calculator is the page you want.
Does it work on a phone on site, and what does it cost?
It's built for exactly that. The page is static, the calculator fits a 360-pixel screen without scrolling past the answer, and the arithmetic runs in your browser — so it keeps working on one bar of signal. There's no sign-up, no trial countdown and no ad wedged between the inputs and the result. Most construction calculators for feet and inches are either a paid app, or a feature buried three taps inside a per-seat subscription that also wants to do your invoicing and your time tracking, with the basics gated behind a trial clock. This is just the calculator. It's free to use, and 10% of every dollar Microapp earns goes to charity, off the top, audited quarterly.