True Position Calculator (X/Y Deviation to Diameter Position)
Position is reported as a diameter, not a radius or a pair of X and Y numbers. This calculator takes the X and Y deviations from a CMM or height gauge, converts them into the diametral position value, adds any MMC bonus, and tells you whether the feature is in tolerance.
Your numbers
Measured X minus basic X. Keep the sign.
Measured Y minus basic Y. Keep the sign.
Smallest hole limit or largest pin limit.
Your results
Assumes a cylindrical zone referenced to the datum reference frame used to measure dx and dy. Check size and form limits separately.
Send CMM results straight to your quality records
Optional: a short review of how inspection results flow from CMM files into your ERP.
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How to use it
Enter the deviation of the measured centre from the basic X and Y location, keeping signs, then enter the stated position tolerance from the feature control frame. Pick hole or pin, choose MMC or RFS, and enter the MMC size limit and the measured actual size. For a 8.00 to 8.10 hole at MMC, the MMC limit is 8.00. A hole measured at 8.05 gains 0.05 mm of bonus. The result shows true position, the allowed zone including bonus, the margin and a pass or fail flag.
The formula
True position equals twice the square root of dx squared plus dy squared. The doubling is because the zone is a diameter: a centre that sits 0.072 mm from true position needs a 0.144 mm diameter zone. Bonus tolerance for a hole at MMC is actual size minus MMC size, and for a pin it is MMC size minus actual size. Bonus can never be negative, and it only applies if the frame carries the MMC (or LMC) modifier. Under RFS the allowed zone is just the stated tolerance.
Worked example
Default inputs: dx 0.06, dy -0.04, tolerance 0.2, hole at MMC 8.00, actual 8.05. Position is 2 times the square root of 0.0052, which is 0.144 mm. Bonus is 0.05, so the allowed zone is 0.25 mm. The margin is 0.106 mm and 58 percent of the zone is used, a pass. Without the bonus the margin would be 0.056, still a pass but much tighter. Try an actual size of 8.00 and an X deviation of 0.1 to see the same part fail.
- Report the position value, not just pass or fail
- Record actual size next to position so bonus can be audited
- Round only at the end, never before the square root
Common mistakes
Common errors are reporting a radius instead of a diameter, forgetting the bonus on an MMC callout, applying bonus when the frame has no modifier, and using the wrong MMC limit for a pin versus a hole. Another is measuring with a datum order different from the drawing, which changes dx and dy even though the part has not moved. Datum shift from a datum feature modifier is not included here.
Frequently Asked Questions
How do you calculate true position from X and Y?
Take the deviation of the measured centre from the basic location in each axis, square them, add them, take the square root, then multiply by two. The result is the diameter of the smallest circle centred on the true position that contains the measured centre.
Why do you multiply by 2 in the position formula?
The deviation is a radial distance, but a position tolerance is stated as a diameter zone. The measured centre can sit anywhere within a circle, so the equivalent zone diameter is twice the radial offset.
What is bonus tolerance?
Bonus tolerance is extra position tolerance gained when a feature of size is away from its MMC or LMC limit, applied only when the feature control frame carries that modifier. A hole larger than its minimum size has more clearance, so the location can drift further without hurting assembly.
Can true position be negative?
No. True position is always a positive diameter because it comes from a square root. The signs of dx and dy matter only for direction and for corrective offsets on the machine, not for the pass or fail value.
If position results are keyed into spreadsheets before they reach your ERP quality records, we can help automate capture from CMM output into your inspection results.
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