Find every fractional inch size within a millimeter tolerance range. Compare each size’s conversion, error and remaining margins, and identify the closest permitted size.

Use a decimal point and up to 6 decimal places. Enter 0 for no allowance.

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 separate lower and upper allowances. 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.