How to Convert Decimal Feet to Feet, Inches and Sixteenths
Why this matters
Laser measures, site plans, survey stakes and a lot of estimating software speak decimal feet. Tape measures, saws and the crew speak feet, inches and fractions. Every time a number crosses that line someone converts it, and the most common conversion is no conversion at all: 12.37 ft gets read as "12 feet 3.7 inches" or "12 feet 3 and a bit", and the piece comes out about three quarters of an inch short. A tenth of a foot is not an inch, and the decimal part of a foot is not inches.
The conversion is two multiplications. This card lays them out, gives the anchors that let you sanity check a conversion in your head, and covers the reverse direction for when the tape reading has to go into a calculator or a plan. Reading the tape itself and the fraction table live in 'Tape Measure Reading + Fractions Reference'.
The conversion, worked for 12.37 ft
DECIMAL FEET -> FEET, INCHES, SIXTEENTHS
reading: 12.37 ft
1. whole feet: 12 ft (set aside)
decimal part: 0.37 ft
2. to inches: 0.37 ft x 12 in/ft = 4.44 in
whole inches: 4 in (set aside)
decimal part: 0.44 in
3. to 16ths: 0.44 in x 16 = 7.04 sixteenths
round: 7/16 in (7.04 -> 7)
answer: 12 ft 4-7/16 in
check back: 7/16 = 0.4375 in
4.4375 in / 12 = 0.3698 ft
12 + 0.3698 = 12.3698 ft -> 12.37
Three things in that layout do the work.
The whole numbers are set aside at each stage and never multiplied. Only the decimal part of the feet goes times 12, and only the decimal part of the inches goes times 16. Multiplying the whole 12.37 by 12 gives 148.44 in, which is correct but is a different answer format (total inches); it is fine if you want it, but do not then treat 148 as feet and inches.
Rounding happens once, at the last line. 7.04 rounds to 7 sixteenths. Rounding 4.44 in to 4.4 or 4.5 before the second multiplication moves the answer: 0.4 x 16 = 6.4 sixteenths, which rounds to 6/16, and 0.5 x 16 = 8 sixteenths. Either early rounding misses the true 7/16 by a sixteenth. Carry the digits until the end.
The check runs the other direction. Converting the answer back to decimal feet and landing on the reading you started with is the only proof that you did not drop a step.
Step 1: Note what the reading's last digit is worth
Before converting, look at how many decimal places the reading carries. A reading to two decimal places of a foot resolves 0.01 ft, which is 0.12 in, a little less than 1/8 in. A reading to three places resolves 0.001 ft, about 0.012 in, finer than a sixteenth.
Why it matters: converting 12.37 ft to the nearest sixteenth looks more precise than the reading was. The true length is anywhere from about 12.365 to 12.375 ft, which is 12 ft 4-3/8 in to 12 ft 4-1/2 in. Calling it 4-7/16 is the honest middle, but it is not a reading good to a sixteenth. When the cut has to be good to a sixteenth, set the laser to show three decimals, or to inches and fractions directly if it can, or take the tape to it. See related: Measurement Resolution and Honest Rounding.
What breaks if you skip it: a two-decimal reading converted to sixteenths and then cut to the sixteenth gives a crew false confidence in a number that was only ever good to about an eighth.
Step 2: Split off the whole feet
Write the whole feet down and work only with the decimal. 12.37 ft becomes 12 ft and 0.37 ft. For a reading under a foot (0.83 ft), the whole feet are zero; write the 0 so the line does not get skipped.
Step 3: Decimal feet times 12 gives inches
0.37 x 12 = 4.44 in. The whole number is inches (4); the decimal (0.44) is a fraction of an inch still to convert.
Anchors to check this line in your head:
- 0.1 ft = 1.2 in, and 0.37 ft is 3.7 tenths, so 3.7 x 1.2 = 4.44 in. Same answer by a different route.
- 0.25 ft = 3 in, 0.5 ft = 6 in, 0.75 ft = 9 in. 0.37 sits between 0.25 and 0.5, so the inches sit between 3 and 6.
- 0.083 ft is about 1 in (1 / 12 = 0.0833).
If your inches answer is bigger than 11.99, something went wrong: no decimal part of a foot is 12 in or more.
Step 4: Decimal inches times 16 gives sixteenths, then round
0.44 x 16 = 7.04, so 7/16 in. Round to the nearest whole sixteenth, not down. Rounding down every time (truncating) is a common slip, and it only shows up when the decimal lands past the half:
Second reading, 8.64 ft. 0.64 ft x 12 = 7.68 in. 0.68 in x 16 = 10.88 sixteenths. Rounded, that is 11/16 in, so 8 ft 7-11/16 in. Truncated it would be 10/16 = 5/8 in, and the piece would be cut a sixteenth short. Check back: 11/16 = 0.6875 in, 7.6875 in / 12 = 0.6406 ft, so 8.6406 ft, which reads 8.64.
Reduce the fraction for the crew: 2/16 = 1/8, 4/16 = 1/4, 8/16 = 1/2, 12/16 = 3/4, and so on. A crew reading "10/16" off a cut list will get it right most of the time and wrong some of the time; "5/8" they will get right.
Use eighths when that is all the job needs. Multiply the decimal inches by 8 instead of 16. 0.44 x 8 = 3.52, which rounds to 4/8 = 1/2 in. So for rough framing 12.37 ft is 12 ft 4-1/2 in.
Step 5: Carry when the fraction rounds up to a whole
Occasionally the sixteenths round to 16/16. That is a whole inch, and it carries into the inches, which can in turn carry into the feet.
Third reading, 3.999 ft. 0.999 x 12 = 11.988 in. 0.988 x 16 = 15.81 sixteenths, which rounds to 16/16 = 1 in. 11 in + 1 in = 12 in, which is 1 ft. So the answer is 4 ft 0 in, not "3 ft 11-16/16 in". Writing the carried form keeps somebody from hooking a tape on 3 ft and hunting for a mark that does not exist.
Step 6: Convert back to check, and for the reverse job
The reverse is the same chain run backward: fraction to decimal inches, inches to decimal feet, add the whole feet.
Taped 7 ft 9-5/8 in, needed in decimal feet for a plan or a calculator:
- 5/8 in = 5 / 8 = 0.625 in
- 9 in + 0.625 in = 9.625 in
- 9.625 in / 12 in per ft = 0.8021 ft
- 7 ft + 0.8021 ft = 7.8021 ft, written 7.80 ft to two places or 7.802 ft to three
Keep three decimal places when the reverse result will be converted again later or used to compute something else. 1/16 in is 0.0052 ft, so two decimal places cannot hold a sixteenth; rounding 7.8021 to 7.80 and converting back gives 7 ft 9-5/8 in only by luck (0.80 x 12 = 9.60 in, and 0.60 x 16 = 9.6 sixteenths, which rounds to 10/16 = 5/8). Run 7 ft 9-9/16 in the same way and the luck runs out: 9.5625 in / 12 = 0.7969 ft, two places makes it 7.80 ft, and 7.80 converts back to 9-5/8 in. A sixteenth has moved just by passing through two decimal places.
Where the readings come from, and what each one hides
Laser distance meters can usually display decimal feet, feet-inches-fractions, or inches. If the meter can show fractions, use that for cutting and skip the conversion entirely. If it shows decimal feet, check how many places; many models drop to fewer decimal places over long distances or in some modes. Also check which end of the meter it is measuring from (front edge, back edge or a fold-out tab), which is a bigger error than any conversion.
Site and civil plans are commonly dimensioned in decimal feet, read off an engineer's scale (divided into tenths). Architectural plans are dimensioned in feet and inches. A dimension like 24.50 on a site plan is 24 ft 6 in; on an architectural drawing you would see 24'-6". See related: Architectural and Engineering Scales on One Ruler.
Survey stakes and grade marks are written in decimal feet, often to two places (a cut of 0.42 ft at a stake is 5.04 in, call it 5 in). Grading work rarely needs better than an eighth of an inch, so two places are fine there.
Estimating software and spreadsheets store lengths in decimal feet or decimal inches and display whatever the template formats them as. A cut list exported from one of these often arrives in decimal inches (52.375 in); that only needs the second multiplication: 0.375 x 16 = 6, so 52-6/16 = 52-3/8 in.
The quick estimate, and how far off it is
The rule of thumb that 0.01 ft is about 1/8 in is a useful way to sanity check a conversion, and it runs slightly long: 0.01 ft is 0.12 in, and 1/8 in is 0.125 in, about 4 percent more. Over a few hundredths it does not matter. Over a whole decimal part it does: 0.37 ft by the rule is 37 eighths, which is 4-5/8 in, against the true 4-7/16 in. That is 3/16 in long. Use the rule to catch a wrong answer, never to produce the cut dimension.
The slip the anchors catch: if someone writes 12.37 ft as 12 ft 3-11/16 in (treating .37 as 3.7 inches and then converting the .7), the 0.1 ft = 1.2 in anchor shows it immediately. 0.37 ft has to be more than 3.7 in, because every tenth of a foot is more than an inch. The miss is 4-7/16 minus 3-11/16 in, which is 3/4 in short.
Write both forms on the cut list
When a measurement taken in decimal feet becomes a cut, put both forms on the line: "12.37 ft = 12 ft 4-7/16 in". The person cutting reads the fraction. The person who checks the job later, or re-orders material from the plan, reads the decimal, and can redo your conversion in thirty seconds if the piece does not fit. A cut list with only the converted fraction hides the conversion, so a wrong one cannot be traced back to the reading; a cut list with only the decimal sends the conversion to the saw, which is the worst place to do arithmetic.
How to know you got it right
- The back-conversion lands on the reading you started with, to the same number of decimal places.
- The inches answer is between 0 and 11 and the fraction is between 0 and 15/16 (anything 16/16 or 12 in has been carried).
- The 0.1 ft = 1.2 in anchor puts the inches in the right neighborhood.
- The fraction on the cut list is reduced, and it does not claim more precision than the reading carried.
References
- See related: Tape Measure Reading + Fractions Reference
- See related: Trade Math and Imperial Fractions Reference
- See related: Measurement Resolution and Honest Rounding
- See related: Architectural and Engineering Scales on One Ruler
- See related: Write the Calculation Down: the Field Math Habit