How to Add and Subtract Feet and Inches

Adding two lengths sounds trivial until the units bite: inches roll over at 12, fractions need a common denominator, and one slip turns a tidy cut into firewood. Here's the method that always works — and why most people reach for an app once they've done it by hand a few times.

The rule: line up like with like

Feet add to feet, inches to inches, fractions to fractions. The only twist is the carrying:

• If the inches add up to 12 or more, subtract 12 and carry 1 to the feet.
• If the fractions add up to a whole inch or more, carry that whole inch over.

Adding, worked through

Say you're joining two runs of trim: 5' 8-3/4" and 2' 7-1/2".

1. Fractions: 3/4 + 1/2 = 3/4 + 2/4 = 5/4 = 1-1/4″. Write down 1/4, carry 1 inch.
2. Inches: 8 + 7 + 1 (carried) = 16. That's over 12, so write 4 and carry 1 foot.
3. Feet: 5 + 2 + 1 (carried) = 8.

Result: 8' 4-1/4". The two carries — fraction-to-inch and inch-to-foot — are exactly where hand math goes wrong.

Subtracting means borrowing

Subtraction is the same idea in reverse. To take 1' 9-1/2" off a 4' 3-1/4" board, the top number is "smaller" in both inches and fractions, so you borrow:

1. Fractions: you can't take 1/2 from 1/4, so borrow 1 inch (16/16): 1/4 becomes 20/16... easier as 1-1/4″ minus 1/2″ after borrowing. Borrow 1 inch from the 3, leaving 2 inches and making the fraction 1-1/4″. Now 1-1/4 − 1/2 = 3/4.
2. Inches: you're now subtracting 9 from 2, so borrow 1 foot (12 inches): 2 becomes 14. 14 − 9 = 5.
3. Feet: 3 (after borrowing) − 1 = 2.

Result: 2' 5-3/4". If that felt like a lot of bookkeeping for one cut, you're not wrong.

The common-denominator trap: you can only add or subtract fractions once they share a denominator. 3/8 and 1/2 don't combine until you rewrite 1/2 as 4/8. Sixteenths are a safe common ground for any tape-measure fraction.

Why decimals don't rescue you

A lot of people try to dodge fractions by converting to decimals on a phone calculator: 8-3/4″ becomes 8.75, add it up, convert back. It works until you hit a fraction like 5/16″ = 0.3125, round it to 0.31, and quietly lose 1/64″ on every step. Over a multi-cut layout those rounding errors stack up. We dug into this in why your phone's calculator can't do tape-measure math.

The faster way

This is precisely the chore Totient was built for. You enter 5' 8-3/4" and 2' 7-1/2" the way you'd read them off the tape, press add, and get 8' 4-1/4" — fractions reduced, feet carried, no decimals in sight. Do it by hand to understand it; use the app so a tired afternoon doesn't cost you a board.

Next up, it helps to be fluent moving between units entirely — see converting inches, feet and yards.