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Inch Fraction Converter

Turn millimeters, centimeters or decimal inches into the nearest tape-measure fraction of an inch, or a fraction back into decimal inches and millimeters.

Level: Grades 5–6

  • Common Core standard 5.NF.B.3Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem.
  • Common Core standard 6.RP.A.3.dUse ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.
Printable worksheet

Inch Fraction Converter

Inputs
Convert

Result

Nearest 1/16 inch

1 3/8 in

1.378 in rounds to 1 3/8 in at 1/16 in (off by 0.075 mm).

That fraction as a decimal
1.375 in
Exact decimal inches
1.377953 in
Exact millimeters
35 mm
Rounding error
-0.075 mm

See the step-by-step solution ↓

Step-by-step solution

  1. Convert to inches: 1 in = 25.4 mm exactly

    3525.4=1.377953 in

  2. Count how many 1/16ths of an inch fit: multiply the inches by 16 and round to the nearest whole number, which picks the nearest mark

    1.377953×16=22.0472=rounded:22

  3. Split off the whole inches and reduce the fraction to lowest terms

    2216=1 3/8 in

  4. Find the rounding error: the rounded mark minus the exact length, so you know how close the mark is

    1.375−1.377953=−0.002953 in= = −0.075 mm

Test yourself

20 quick questions built from this calculator's formula: work out results, predict what happens when an input changes, and work backward from an answer. Every answer comes with the working.

What this calculator does

Turn any length into the nearest mark on your tape measure, or a tape-measure fraction into a decimal. In the US, tape measures, rulers and many drawings mark inches in halves, quarters, eighths and sixteenths. Calipers, spec sheets and metric plans give decimals or millimeters instead. Going from one to the other means finding the nearest mark on the tape. That's a rounding question: how many sixteenths (or thirty-seconds) of an inch is the length closest to?

Enter a measurement in millimeters, centimeters, feet or decimal inches. The calculator converts it exactly to inches, using 25.4 mm per inch. Then it rounds to the nearest fraction you choose, from 1/2 to 1/64 inch. It reduces the fraction to its simplest form. It also tells you how far the rounded mark is from the true length. In the other direction, it turns a fraction such as 2 5/16 into decimal inches, millimeters and centimeters.

Where it's used

Why this math matters outside the classroom:

  • Woodworking plans. A woodworker converts a 35 mm dimension to 1.378 in and marks it at 1 3/8 in on a tape measure.
  • Drill bit sizes. Machinists convert a 7/32 in drill bit to 0.21875 in, or 5.556 mm, to compare it with a metric bit.
  • Fractions as division. Students find 5/16 as 5 ÷ 16 = 0.3125 to compare tape-measure marks with decimal measurements.
  • Home repairs. A homeowner reads a 3/8 in socket as 9.525 mm and sees that a 10 mm socket is the nearest metric size.
  • Sewing and crafts. Quilters round a 6 mm seam allowance to the nearest 1/8 in and get 1/4 in.

Grade level and standards: Grades 5–6; Common Core State Standards for Mathematics 5.NF.B.3, 6.RP.A.3.d. © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

How to use it

  1. Choose the direction: a decimal or metric length to a fraction, or a fraction to a decimal.
  2. For a length, enter the number and pick its unit. Then choose the smallest fraction you want to read, usually 1/16 inch for a tape measure.
  3. For a fraction, type it with a space between the whole inches and the fraction, such as 1 3/8.
  4. Read the fraction or decimal. Check the rounding error to see whether a finer fraction is worth using.

What the inputs mean

Round to the nearest
Most tape measures mark 1/16 inch. Machinist rulers go to 1/32 or 1/64. Rounding to a bigger fraction gives a mark that's easier to find, but a bigger error.
Inches as a fraction
Fractions don't need to be simplified, and the top number can be bigger than the bottom one. 6/16, 12/8 and 1-3/8 all work, and the simplified form is shown.

Formula and method

inches = millimeters ÷ 25.4   (= centimeters ÷ 2.54 = feet × 12)
count = round(inches × denominator)
fraction = count ÷ denominator, written as whole inches + remainder ÷ denominator, reduced
error = fraction − exact inches;  error (mm) = error × 25.4
decimal = whole + numerator ÷ denominator;  mm = decimal × 25.4

In a fraction such as 3/8, the bottom number (8) is the denominator: how many equal parts the inch is split into. The top number (3) is the numerator: how many of those parts you have. Count is how many of the small parts fit in your length, and the remainder is what's left after the whole inches.

Multiplying by the denominator counts how many small divisions fit in the length. Rounding then picks the nearest tick mark, and an exact halfway value goes up. To reduce 6/16 to 3/8, the calculator divides the top and bottom by the largest number that goes into both.

The inch has been defined as exactly 25.4 mm since 1959, so the metric conversions are exact. Only the rounding to a fraction adds any error.

Worked example

A metric plan calls for a 35 mm hole spacing. What is that to the nearest 1/16 inch?

  1. 35 ÷ 25.4 = 1.377953 in.
  2. 1.377953 × 16 = 22.047, which rounds to 22 sixteenths.
  3. 22/16 = 1 6/16 = 1 3/8 in.
  4. Error: 1.375 − 1.377953 = −0.002953 in, about −0.075 mm.

Result: 35 mm is 1 3/8 in to the nearest sixteenth, about 0.075 mm short of the true length.

Understanding the result

A negative error means the fraction is a little shorter than the real length. A positive one means it's longer. An error of a few hundredths of a millimeter is far smaller than a tape measure can show.

If the error matters, for example when parts must fit together, choose a finer fraction. Or work in decimals or millimeters instead.

Assumptions and limitations

  • The international inch of exactly 25.4 mm.
  • Halfway values round up to the larger mark.
  • Lengths are not converted to feet and inches, so 18 in stays as 18 in.
  • Negative lengths aren't accepted.
  • A fraction is only as precise as the original measurement.

Frequently asked questions

How do I convert millimeters to a fraction of an inch?

Divide by 25.4 to get decimal inches. Multiply by 16 (or the bottom number you want), round to a whole number, and put it over 16. Then simplify: 22/16 becomes 1 3/8.

What is 1/16 inch in millimeters?

Exactly 25.4 ÷ 16 = 1.5875 mm. So rounding to the nearest sixteenth can be off by up to half that, about 0.79 mm.

Why does my result come out as a whole number?

When the length is within half a division of a whole inch, the fraction rounds away. For example, 0.99 in is 15.84 sixteenths. That rounds to 16/16, or 1 inch.

Which precision should I use?

Use 1/16 for carpentry and general tape-measure work. Use 1/32 or 1/64 for machining and fine woodworking. For rough framing or landscaping, 1/8 or 1/4 is plenty.

How this calculator is checked

Method: Exact international inch (25.4 mm); rounding to the nearest 1/n inch with halves rounded up and fractions reduced by the greatest common divisor. The calculation is covered by automated tests with known reference values and edge cases. Last updated 2026-10-18. Found a problem? Tell us.

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