Why does the answer show a rounding error?

A tape measure is divided into sixteenths, so any result that does not land on one has to be rounded to be readable. Adding two tape measurements usually lands exactly; converting from millimeters almost never does. 1 cm is 25/64 in on a fine rule and 3/8 in on a framing tape, and the second is 0.4 mm short. Every calculator rounds here; this one tells you by how much and in which direction.

What is 2 ft times 3 ft?

Six square feet, not 72 feet. Multiplying two lengths produces an area, and the unit changes with it. Multiplying a length by a plain number keeps it a length: three pieces of 2 ft 6 in is 7 ft 6 in. This calculator separates the two, and prints the area on its own line whenever both fields hold real measurements.

Which of these numbers are exact?

The millimeter and centimeter figures are exact when the input was in inches, because the inch has been defined as exactly 25.4 mm since the 1959 international yard and pound agreement. Going the other way is not exact: most millimeter values fall between two sixteenths, so the inch fraction is a rounded reading and the error line shows the size of the compromise.

Does this handle the US survey foot?

No, and almost nothing you measure needs it. The international foot used here is exactly 0.3048 m; the US survey foot, retired for new work at the end of 2022, was larger by a factor of 1.000002 — about 3 mm over a mile. It matters on a plat or a state plane coordinate, not on a cut list.

Feet and Inches Calculator

With first measurement 30 inch, second measurement 36 inch, feet and inches comes to 5' 6" — result. It is reached in 7 steps, the last of which is 0 * 30 + 1 * (30 + 36) + 0 * (30 - 36) + 0 * (30 * 3) + 0 * (30 / (3 + 1 - 0)), and each one is printed on the page with its numbers filled in. The formula is the one published by NIST Special Publication 811, App. B.6, not an approximation fitted to it.

Convert to feet and inches, or add, subtract, multiply and divide feet-and-inches measurements, with the rounding error shown beside the fraction.

Formula and sources checked 17 August 2026 · How we check

Operation Add, First measurement 30 inch, Second measurement 36 inch

5' 6"

Result for the example below. Editing a field recomputes the calculator below; this figure holds the answer the page was loaded with.

It is written into the HTML rather than drawn by a script, so a search engine reading this page without running JavaScript still finds an answer.

OperationFirst measurementAccepts 2' 6", 2ft 6in, 30, or 30 1/2.Second measurementThe measurement to add or subtract.

Result

5' 6"

Exact result: 0 * 30 + 1 * (30 + 36) + 0 * (30 - 36) + 0 * (30 * 3) + 0 * (30 / (3 + 1 - 0))66 in
Rounded to the nearest 1/16: round(66 * 16) / 1666 in
Rounding error: 66 - 660 in
Rounding error in millimeters: 0 * 25.40 mm
Exact result in decimal feet: 66 / 125.5 ft
Exact result in millimeters: 66 * 25.41,676.4 mm
If you multiply these two lengths: area: (1 + 0) * 30 * 36 / 1447.5 sq ft

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Worked example

Adding 2' 6" to 3' 0" gives 5' 6". Both inputs land exactly on a sixteenth, so the rounding error is zero — which is the point of printing it: when it is not zero, you can see it.

How to work it out yourself

1.Read each measurement off the tape as feet and inches. Type it the way you read it: 2' 6", 2ft 6in and 30 all mean the same thing here.
2.Pick the operation. Multiply and divide take a plain count, not a second measurement, because three pieces of 2' 6" is a length and 2' 6" times 3' 0" is not.
3.Read the answer as feet and inches. The rounding error underneath tells you how far the printed fraction sits from the exact value.
4.If you were multiplying two lengths to get an area, use the area line instead. Feet times feet is square feet, never feet.

The formula

Exact result0 * 30 + 1 * (30 + 36) + 0 * (30 - 36) + 0 * (30 * 3) + 0 * (30 / (3 + 1 - 0))
Rounded to the nearest 1/16round(66 * 16) / 16
Rounding error66 - 66
Rounding error in millimeters0 * 25.4
Exact result in decimal feet66 / 12
Exact result in millimeters66 * 25.4
If you multiply these two lengths: area(1 + 0) * 30 * 36 / 144

Source: NIST Special Publication 811, App. B.6 — the inch is exactly 25.4 mm, NIST Office of Weights and Measures — international yard and pound agreement, effective 1 July 1959

Questions people actually ask

Why does the answer show a rounding error?: A tape measure is divided into sixteenths, so any result that does not land on one has to be rounded to be readable. Adding two tape measurements usually lands exactly; converting from millimeters almost never does. 1 cm is 25/64 in on a fine rule and 3/8 in on a framing tape, and the second is 0.4 mm short. Every calculator rounds here; this one tells you by how much and in which direction.
What is 2 ft times 3 ft?: Six square feet, not 72 feet. Multiplying two lengths produces an area, and the unit changes with it. Multiplying a length by a plain number keeps it a length: three pieces of 2 ft 6 in is 7 ft 6 in. This calculator separates the two, and prints the area on its own line whenever both fields hold real measurements.
Which of these numbers are exact?: The millimeter and centimeter figures are exact when the input was in inches, because the inch has been defined as exactly 25.4 mm since the 1959 international yard and pound agreement. Going the other way is not exact: most millimeter values fall between two sixteenths, so the inch fraction is a rounded reading and the error line shows the size of the compromise.
Does this handle the US survey foot?: No, and almost nothing you measure needs it. The international foot used here is exactly 0.3048 m; the US survey foot, retired for new work at the end of 2022, was larger by a factor of 1.000002 — about 3 mm over a mile. It matters on a plat or a state plane coordinate, not on a cut list.

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