Find the closest fractional inch size (1/8 to 1/128 in) within a millimeter tolerance, and list every fraction that fits with its error and margins.

Enter 0 for no allowance below nominal.

Leave blank to use the same allowance as below (± tolerance). Enter 0 for none.

Optional settings

Fractional Inch Tolerance Formula

For nominal length N, allowance below nominal a and allowance above nominal b, all in millimeters:

L = N − a; U = N + b

Choose an increment of 1/D inch, where D is 8, 16, 32, 64 or 128. The permitted integer ticks run from:

kfirst = ceil(LD/25.4); klast = floor(UD/25.4)

The count is max(0, klast − kfirst + 1). Each tick k represents k/D inches = 25.4k/D mm. Both bounds are included. NIST defines one inch as exactly 25.4 mm.

How to Use the Calculator

  1. Enter the nominal length and the allowance below it. Leave the upper allowance blank for the same ± value, or enter it separately; enter 0 for no allowance.
  2. Choose the fractional increment and select Calculate.
  3. Open the details to compare every matching size. A finer increment can produce more matches.

Inputs must be between 0 and 1,000,000 mm, with up to six decimal places. The lower allowance cannot exceed nominal length. Ranges containing more than 200 sizes are rejected; narrow the allowances or choose a coarser increment.

Worked Example

For 25 mm with 0.5 mm below and 0.5 mm above, the range is 24.5–25.5 mm. At 1/64 inch, ticks 62–64 fit:

  • 31/32 in: 24.60625 mm; error −0.39375 mm.
  • 63/64 in: 25.003125 mm; error +0.003125 mm.
  • 1 in: 25.4 mm; error +0.4 mm.

The closest is 63/64 inch. Its margins are 0.503125 mm above the lower bound and 0.496875 mm below the upper bound.

One-sided allowance: At 1/16 inch, 25 mm with 0 below and 0.5 mm above admits only 1 inch (25.4 mm), within 25–25.5 mm.

No match: At 1/8 inch, 1 mm with 0.01 mm below and above gives 0.99–1.01 mm; neither neighboring size, 0 or 3.175 mm, fits.

Frequently Asked Questions

What do error and margins mean?

Signed error is converted length minus nominal length. The two margins show how far a matching size lies inside each bound; zero means it lies exactly on that bound.

What if no size fits, or two sizes are equally close?

No matches is a valid result: the range contains no multiple of the selected increment. Equal-distance ties select the larger permitted size.

Does a matching number guarantee physical fit?

No. This tool compares exact numerical lengths; it does not account for measurement uncertainty or physical fit.

Sources

NIST: SI Units — Length, inch-to-millimeter definition.