CNC / machinist calculator
True Position Calculator (GD&T)
Check a positional feature against its GD&T callout. Enter how far the feature center sits from its nominal location in X and Y and this calculator returns the diametral true position. Add the stated position tolerance and, if the callout uses maximum material condition, the feature size to get the bonus tolerance and a clear pass or fail. It is the quick inspection math for holes and pins on a position frame.
- Bonus tolerance
- —
- Total allowed
- —
—
How it works
True position describes how far a feature's actual axis is from where the print says it should be, expressed as the diameter of a tolerance zone centered on the true location. Because the error can be in any direction, the positional deviation is two times the straight-line distance from nominal, which is two times the square root of the X deviation squared plus the Y deviation squared.
Many callouts apply at maximum material condition, which grants a bonus tolerance as the feature departs from its tightest size. For a hole, the maximum material condition is the smallest allowed diameter, so a hole made larger than that earns bonus tolerance equal to how far its actual size exceeds the maximum material size. The total position tolerance available is the stated tolerance plus that bonus.
The feature passes when the measured true position is no greater than the total tolerance. This tool reports the position, the bonus, the total allowed and the verdict, which is exactly the row an inspection report needs.
Worked example
A hole 0.003 off in X and 0.004 in Y has a true position of 2 x sqrt(0.003^2 + 0.004^2) = 0.010 dia. Against a 0.014 tolerance it passes, with extra room if the hole is over its MMC size.
Frequently asked questions
How do I calculate true position?
True position is two times the square root of the X deviation squared plus the Y deviation squared. The factor of two turns the radial distance from nominal into the diameter of the cylindrical tolerance zone the callout uses.
What is bonus tolerance at MMC?
When a position is called at maximum material condition, the feature earns extra tolerance as it departs from its tightest size. For a hole that means making it larger than the smallest allowed size, and the bonus equals that size departure.
Is maximum material condition the largest or smallest hole?
For a hole it is the smallest diameter, because that leaves the most material. For a pin or shaft it is the largest diameter. Bonus tolerance accrues as the feature moves away from its maximum material size.
How do I know if the feature passes?
Compare the measured true position to the total tolerance, which is the stated tolerance plus any bonus. If the true position is less than or equal to the total, the feature is in tolerance; if it is greater, it fails.
Why is true position a diameter and not a radius?
GD&T defines the position tolerance as a cylindrical zone around the true axis, so the controlled value is the diameter of that zone. That is why the deviation is doubled, since the axis can be off in any direction within the cylinder.
Related calculators
Sources
- Geometric dimensioning and tolerancing - position (Wikipedia)
- Position tolerance and bonus (Wikipedia, GD&T)
Every formula on this page is shown and sourced. See how we verify.
These calculators are for planning and as a starting point. Recommended speeds and feeds are published starting values that vary with your specific tool, coating, machine rigidity, workholding and coolant. Always start conservative, listen to the cut, and follow your tool maker data sheet.