True Position Calculator
Plan your materials specifications project with our free true position calculator. Get precise measurements, material lists, and budgets.
Reviewed by Abdullah, Technical Content Specialist
Formula
True Position = 2 x sqrt(dX² + dY²)
Calculate the deviation in X (actual X minus nominal X) and deviation in Y (actual Y minus nominal Y). Square each deviation, sum them, take the square root to get the radial distance, and multiply by 2 to convert to the diametral true position value. Compare the result against the specified tolerance zone diameter.
Worked Examples
Example 1: Drilled Hole Position Check
Problem:A hole has a nominal position of X=25.000, Y=50.000. The actual measured position is X=25.080, Y=50.120. The true position tolerance is 0.400mm diameter.
Solution:dX = 25.080 - 25.000 = 0.080mm\ndY = 50.120 - 50.000 = 0.120mm\nTP = 2 x sqrt(0.080² + 0.120²)\nTP = 2 x sqrt(0.0064 + 0.0144)\nTP = 2 x sqrt(0.0208) = 2 x 0.1442 = 0.2884mm
Result:True position = 0.2884mm, within 0.400mm tolerance (72.1% used)
Example 2: Bolt Pattern Verification
Problem:A bolt hole at nominal X=10.000, Y=20.000 measures at X=10.150, Y=20.080. Tolerance is 0.500mm.
Solution:dX = 0.150mm, dY = 0.080mm\nTP = 2 x sqrt(0.150² + 0.080²)\nTP = 2 x sqrt(0.0225 + 0.0064)\nTP = 2 x 0.1700 = 0.3400mm
Result:True position = 0.3400mm, within 0.500mm tolerance (68.0% used)
Frequently Asked Questions
What is true position in GD&T?
True position is a GD&T (Geometric Dimensioning and Tolerancing) callout that defines the exact location where a feature should be placed relative to datum references. It uses a cylindrical or circular tolerance zone centered on the theoretically exact position. Unlike traditional coordinate tolerancing which creates a square tolerance zone, true position creates a circular zone that provides approximately 57% more usable tolerance area. The true position value is always expressed as a diameter.
How is true position calculated from X and Y deviations?
True position is calculated using the formula TP = 2 times the square root of (dX squared plus dY squared), where dX is the deviation in X from nominal and dY is the deviation in Y from nominal. The factor of 2 converts the radial distance to a diametral value, which is how true position tolerance zones are specified on engineering drawings. For example, if a hole is 0.10mm off in X and 0.15mm off in Y, the true position equals 2 times sqrt(0.01 + 0.0225) = 2 times 0.1803 = 0.3606mm.
What is the difference between true position and coordinate tolerancing?
Coordinate tolerancing creates a square tolerance zone defined by plus-minus values on X and Y dimensions. True position creates a circular (diametral) tolerance zone. The circular zone is more representative of how features actually function in assemblies. A coordinate tolerance of plus-minus 0.25mm in each axis creates a 0.50mm square zone, but the diagonal of that square is 0.707mm. True position with a 0.50mm diameter zone allows equal deviation in all directions, providing a more uniform and generous tolerance.
Can true position be applied at MMC or LMC?
Yes, true position is frequently applied at Maximum Material Condition (MMC) or Least Material Condition (LMC) using the circled M or circled L modifier. At MMC, bonus tolerance is gained as the feature departs from its maximum material size. For a hole, as it gets larger than the MMC size, additional positional tolerance becomes available. This is highly beneficial in manufacturing because it allows more positional freedom for features that are already oversized, while maintaining the functional requirement of assembly fit.
References
Reviewed by Abdullah, Technical Content Specialist · Editorial policy