5' 6 3/8" ≈ 5.531 ft
Right Triangle Calculator in Feet and Inches
Type sides the way you read them off a tape measure and get every side back to the nearest 1/16 in, plus decimal feet and both angles.
Solve a right triangle in feet and inches
Measurements on a job site come in feet, inches and fractions, but the math needs plain numbers. This calculator
does the conversion both ways. Type any two of the legs, the hypotenuse and the angles, with lengths written as
you read them, such as 5' 6 3/8". It solves the triangle with the same solver as the
right triangle calculator and gives every side as a tape reading to the nearest 1/16 in, with
decimal feet next to it.
Under each length you type, the calculator shows how it read it, so a typo can't slip through. It starts with a 9 ft by 12 ft layout.
Results
- Leg a
- 12 ft 12 ft
- Leg b
- 9 ft 9 ft
- Hypotenuse c
- 15 ft 15 ft
- Angle α
- ≈ 53.13°
- Angle β
- ≈ 36.87°
≈ marks a rounded value: feet and inches to the nearest 1/16 in, decimal feet to 0.001 ft, angles to 0.01°.
How it’s worked out
The working is in decimal feet and keeps extra decimal places, so you can check it by hand. Only the answers above are rounded to the nearest 1/16 in.
- Apply the Pythagorean theoremc = √(a² + b²)c = √(12² + 9²)= 15 ft
- Find angle αα = arctan(a / b)α = arctan(12 / 9)≈ 53.1301°
- Find angle ββ = 90° − αβ = 90° − 53.130102°≈ 36.8699°
How to type feet and inches
Use ' or ft after the feet and " or in after the inches.
Fractions can follow the whole inches after a space or a hyphen, and the curly quotes a phone keyboard types work
too. Each of these is read as the same length:
| You type | Read as | Notes |
|---|---|---|
5' 6 3/8" | 5 ft 6 3/8 in (≈ 5.531 ft) | Feet and inch marks |
5'-6 3/8" | 5 ft 6 3/8 in (≈ 5.531 ft) | As written on building plans |
5 ft 6 3/8 in | 5 ft 6 3/8 in (≈ 5.531 ft) | Words or abbreviations |
5' 6 3/8 | 5 ft 6 3/8 in (≈ 5.531 ft) | After the feet, a bare number is inches |
66 3/8" | 5 ft 6 3/8 in (≈ 5.531 ft) | Inches only |
5.53125 | 5 ft 6 3/8 in (≈ 5.531 ft) | A plain number is decimal feet |
5’ 6⅜” | 5 ft 6 3/8 in (≈ 5.531 ft) | Phone keyboard quotes and fractions |
Angles are plain degrees, such as 36.87. A bare pair like 5 6 isn't accepted, because
it could mean 5 ft 6 in or 56 in; add the marks so there's no doubt.
Worked example: the diagonal of a 9 ft by 12 ft layout
Say you're laying out a 9 ft by 12 ft shed floor. Before the corners are fixed, you want the diagonal: the
distance from one corner to the opposite one. Two sides and that diagonal make a right triangle with the diagonal
as its hypotenuse, so c = √(12² + 9²) = √(144 + 81) = √225 = 15 ft. That's exactly 15 ft, because
9-12-15 is the 3-4-5 triangle three times over. Both diagonals should read 15 ft once the corners are square,
and the angles at the corners of each triangle are about 53.13° and 36.87°. The calculator above is set up with
this layout.
Lumber rarely lands on whole feet, though. Say the frame came out 12 ft 0 1/4 in by 9 ft 0 3/8 in. Here's the diagonal worked out by hand, the way the calculator does it:
-
Turn each side into decimal feet by dividing the inches by 12:
12' 1/4" = 12 + 0.25 ÷ 12 ≈ 12.0208 ftand9' 3/8" = 9 + 0.375 ÷ 12 = 9.03125 ft. - Apply the Pythagorean theorem:
c = √(12.0208² + 9.03125²) ≈ √226.0639 ≈ 15.0354 ft. -
Keep the 15 whole feet and turn the 0.0354 ft that's left into inches:
0.0354 × 12 ≈ 0.425 in, so no whole inches. -
Turn the part of an inch into sixteenths:
0.425 × 16 = 6.8, which rounds to 7. The diagonals should read 15 ft 0 7/16 in.
In the calculator, type 12' 1/4" for leg a and 9' 3/8" for leg b. It shows the same
15 ft 0 7/16 in, with 15.035 ft in decimal feet, and angles of
53.08° and 36.92°. If the two diagonals you measure don't
match, the corners aren't square yet; the 3-4-5 rule calculator tells you
how far off they are and which way to push.
Reading sixteenths on a tape measure
US tapes split the inch into binary fractions: halves, quarters, eighths and sixteenths. Every split gets a shorter line, so you can tell a mark's fraction from its length alone. Count the sixteenths from the last whole inch, then reduce the fraction if you can.
A sixteenth of an inch is 1.5875 mm, since an inch is exactly 25.4 mm. Rounding to the nearest sixteenth means a reading is never more than 1/32 in, about 0.8 mm, from the exact length. That's the rounding the calculator uses for every tape reading it shows. To mark a cut on a decimal length by hand, use the conversion in the FAQ below.
Feet and inches FAQ
Why are the answers rounded to the nearest 1/16 inch?
Because 1/16 in is the smallest mark on most tape measures, so it is the finest length you can mark and cut to. Rounding to it moves a length by 1/32 in at most, which is under a millimeter. A steel tape that meets NIST Handbook 44 is allowed to be off by up to 1/16 in over lengths of 7 to 30 ft, so a finer answer would not make the cut any more accurate. The decimal feet and the working keep more digits if you need them.
How do I read the 1/16-inch marks on a tape measure?
Each inch is split in half, then in half again, and the length of a line tells you which split it belongs to. The longest line inside the inch is 1/2, the next longest are 1/4 and 3/4, then come the eighths, and the shortest lines are the sixteenths. To read a mark, count the shortest steps from the last whole inch and reduce the fraction: 10 sixteenths is 5/8, 12 is 3/4, and 7 stays 7/16. Some tapes add 1/32 marks along the first few inches for fine work.
How do I turn decimal feet into feet, inches and sixteenths?
Keep the whole feet, multiply what is left by 12 to get inches, then multiply the leftover part of an inch by 16 and round to the nearest whole number of sixteenths. For 10.79 ft: keep 10 ft, then 0.79 × 12 = 9.48 in. Keep 9 in, then 0.48 × 16 = 7.68, which rounds to 8 sixteenths, or 1/2. So 10.79 ft is 10 ft 9 1/2 in. If the sixteenths round up to 16, add one inch instead.
Does rounding to 1/16 inch make the answer less accurate?
Only by the rounding itself, which is never more than 1/32 in. The calculator works with the exact lengths you type and rounds only the final answers, so small errors don’t pile up from step to step. Rounding as you go is different: round each side to a sixteenth before squaring it, and the hypotenuse can land a mark away from the true answer. If you reuse an answer, for example as a side of the next triangle, type its decimal feet rather than the rounded tape reading.
Why does the hook on the end of my tape measure move?
It is meant to. The hook slides by its own thickness so both kinds of measurement start from true zero: hooked over an edge, the pull draws it out, and pushed against a wall, it slides in. Either way, the hook’s thickness is accounted for. If it gets bent or its rivets are tightened, every reading is off by about that thickness. For a reading that has to be exact, measure from the 1 in line instead and take 1 in off the result.
To size a brace for a gate or frame, use the diagonal brace calculator. See the full right triangle FAQ for more general questions.
Cite this page
To cite this calculator in schoolwork or a report, you can use this reference (APA style):
Right Triangle Calculators. (2026, November 10). Feet and inches calculator. https://righttrianglecalculators.com/right-triangle-calculator-feet-inches
References
The formulas and definitions on this page match these standard references.
- Weisstein, Eric W. “Pythagorean Theorem.” MathWorld, Wolfram Research.
- “NIST Guide to the SI, Appendix B.8: Factors for Units Listed Alphabetically.” NIST Special Publication 811, National Institute of Standards and Technology.
- “Handbook 44 (2026), Section 5.52: Linear Measures.” NIST Handbook 44, National Institute of Standards and Technology.
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