Inspection and GD&T
True position calculator
Position = 2 x sqrt(dX^2 + dY^2). Enter nominal and measured X and Y, the position tolerance and, if the frame calls MMC, the hole sizes.
Technical review pending. Formulas and values are cited. This notice comes down after a machinist review.
Position (diametral)
in
Position = 2 x sqrt(dX^2 + dY^2) = 2 x sqrt(0.0035^2 + (-0.0038)^2) = 0.0103 in
dX = Xm - Xn = 2.5035 - 2.5000 = 0.0035 in; dY = Ym - Yn = 1.2462 - 1.2500 = -0.0038 in. Radial offset 0.0052 in. Position 0.0103 in (0.262 mm).
Total allowed tolerance
in
Allowed = T + (Actual - MMC) = 0.0100 + (0.5020 - 0.5000) = 0.0120 in
Bonus 0.0020 in added to the stated 0.0100 in.
Pass or fail
0.0103 in is within 0.0120 in
Margin 0.0017 in to spare.
Source: ASME Y14.5-2018 (dimensioning and tolerancing), position tolerance with a diameter tolerance zone
Inch results show 4 places; metric results show 0.001 mm because position tolerances are that fine.
How it works
Position = 2 x sqrt(dX^2 + dY^2); Allowed = T + (Actual - MMC)
| Symbol | Meaning | Unit |
|---|---|---|
| dX, dY | Measured location minus nominal (basic) location, from the datums the frame calls | in or mm |
| Xm, Ym | Measured location | in or mm |
| Xn, Yn | Nominal (basic) location from the drawing | in or mm |
| Position | Diameter of the zone, centered on true position, that the feature axis falls in | in or mm |
| T | Stated position tolerance in the feature control frame | in or mm |
| MMC | Maximum material condition size: smallest hole or largest pin | in or mm |
| RFS | Regardless of feature size: no modifier, no bonus, a fixed zone | none |
| Actual | Measured size of the feature (for a pin, bonus = MMC - Actual) | in or mm |
| Allowed | Stated tolerance plus bonus; the part passes when Position is at or under it | in or mm |
Worked example: RFS, fails
Hole at nominal X 2.5000 in, Y 1.2500 in; measured X 2.5035 in, Y 1.2462 in. Position tolerance Ø 0.010 in, no modifier (RFS).
- dX = 2.5035 - 2.5000 = 0.0035 in; dY = 1.2462 - 1.2500 = -0.0038 in.
- Square and add: 0.00001225 + 0.00001444 = 0.00002669 sq in.
- Square root: sqrt(0.00002669) = 0.00517 in radial.
- Double it: 2 x 0.00517 = 0.0103 in position.
- Compare: 0.0103 in is over 0.010 in by 0.0003 in.
Result: position 0.0103 in (0.262 mm). Fails at RFS by 0.0003 in.
Worked example: same hole at MMC, passes
The frame now calls MMC. The hole is 0.500 +0.004/-0.000 in, so the MMC size is 0.5000 in; it measures 0.5020 in.
- Bonus = actual - MMC = 0.5020 - 0.5000 = 0.0020 in.
- Allowed = 0.010 + 0.0020 = 0.0120 in.
- Compare: 0.0103 in is within 0.0120 in, with 0.0120 - 0.0103 = 0.0017 in to spare.
Result: allowed 0.0120 in, position 0.0103 in. Passes by 0.0017 in.
RFS or MMC
RFS gives a fixed zone: the stated tolerance is all you get at any size. MMC adds bonus as the hole departs from its MMC size, so a hole cut toward the top of its size limit can sit farther off location and still pass.
Shop notes
- Position is diametral, twice the radial error. Never compare the radial offset to a diametral tolerance.
- Cross-check: dX 0.004 in and dY 0.003 in give 2 x sqrt(0.000016 + 0.000009) = 2 x 0.005 = 0.010 in.
- Metric check: dX 0.05 mm and dY -0.03 mm give 2 x sqrt(0.0025 + 0.0009) = 2 x 0.0583 = 0.117 mm.
- The math assumes the part is set up on the datums in the order the frame lists them. Datum shift is not included.
- Check size before position. A hole outside its size limits is rejected on size, and bonus from an out-of-size hole means nothing.
- Treat the result as a starting point for inspection, not a CMM report.
FAQ
How much bonus tolerance do you get at MMC?
Actual hole size minus MMC size, added to the stated tolerance. A 0.5020 in hole with an MMC size of 0.5000 in gets 0.0020 in of bonus, so a 0.010 in position tolerance at MMC allows 0.0120 in.
Can you enter dX and dY directly instead of coordinates?
Yes. Set "Enter location as" to X and Y deviation and type the offsets, measured minus nominal; negative values are fine. A dX of 0.0035 in and a dY of -0.0038 in give the same 0.0103 in position as the coordinates 2.5035, 1.2462 in against a nominal of 2.5000, 1.2500 in.
What does the margin number mean?
Allowed tolerance minus position. With 0.0120 in allowed at MMC and a position of 0.0103 in, the margin is 0.0017 in to spare. A negative margin reads as "over by": the same hole at RFS is over 0.010 in by 0.0003 in.
Do you double the X and Y error?
No. Combine them first, then double: 2 x sqrt(dX^2 + dY^2). A dX of 0.004 in and a dY of 0.003 in give 2 x 0.005 = 0.010 in, not 0.014 in.
How is bonus figured for a pin?
For a pin or shaft at MMC, bonus = MMC size - actual size, because the MMC size is the largest pin. Pick "Pin or shaft" in the calculator and it flips the subtraction.
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