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Calculator · construction

True Position Calculator (Gd&T)

Compute GD&T true position from nominal and actual coordinates using the ASME Y14.5-2018 TP formula for 2D planar or 3D spatial features.

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True Position Diameter—units

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What Is True Position in GD&T?

True position is one of the most widely used Geometric Dimensioning and Tolerancing (GD&T) controls defined by the ASME Y14.5-2018 Dimensioning and Tolerancing standard. It specifies the exact location a feature — such as a drilled hole, pin, or boss — must occupy relative to a datum reference frame. Unlike simple coordinate tolerances, true position defines a cylindrical (3D) or circular (2D) tolerance zone centered on the theoretically exact location, allowing any directional combination of deviation as long as the total positional error stays within that zone.

The True Position Formula

The true position calculator applies a Euclidean-distance formula scaled by a factor of 2 to convert radial deviation into a diametric tolerance zone value that engineers compare directly against the drawing positional tolerance callout.

2D True Position (Planar Features)

TP = 2 × √[(Xactual − Xnominal)² + (Yactual − Ynominal)²]

The 2D formula applies when the feature lies in a single plane — the most common case for drilled or tapped holes on a flat machined surface. Only X and Y deviations contribute to the result.

3D True Position (Spatial Features)

TP = 2 × √[(Xactual − Xnominal)² + (Yactual − Ynominal)² + (Zactual − Znominal)²]

The 3D formula adds the Z-axis deviation and applies to features such as spherical seats, through-holes in inclined planes, or any point in space that can deviate along all three axes simultaneously.

Why Multiply by 2?

The square-root term calculates the radial distance from the nominal center to the actual center. GD&T tolerance zones are expressed as diameters — indicated by the Ø symbol on the drawing — not radii. Multiplying by 2 converts the radial offset into the equivalent diameter of the smallest tolerance circle that encloses the actual feature center, enabling direct comparison with the drawing callout.

Variable Definitions

  • Xnominal, Ynominal, Znominal — Basic dimensions: the theoretically exact coordinates taken from the engineering drawing. Basic dimensions appear enclosed in rectangular boxes and carry no tolerance of their own; all positional tolerance is captured in the feature control frame.
  • Xactual, Yactual, Zactual — Measured coordinates obtained from a Coordinate Measuring Machine (CMM), optical comparator, vision system, or calibrated gauge on the finished part.
  • TP — The calculated true position value expressed as a diameter in mm or inches. The part conforms when TP ≤ the tolerance value stated in the feature control frame.

Step-by-Step Worked Example

A machined aluminum bracket has a tapped hole whose nominal center is X = 25.000 mm, Y = 40.000 mm. CMM inspection reports the actual center at X = 25.062 mm, Y = 39.948 mm. The drawing specifies a true position tolerance of Ø 0.200 mm.

  • ΔX = 25.062 − 25.000 = 0.062 mm
  • ΔY = 39.948 − 40.000 = −0.052 mm
  • TP = 2 × √(0.062² + 0.052²) = 2 × √(0.003844 + 0.002704) = 2 × √0.006548 = 2 × 0.08092 = 0.162 mm
  • Result: 0.162 mm < 0.200 mm — the hole passes inspection. If the tolerance were Ø 0.125 mm, the same hole would fail.

Practical Applications

  • Bolt-circle patterns — Verifying that bolt holes align with mating flanges on pipe assemblies, gearboxes, and engine blocks.
  • Press-fit pins and dowels — Confirming pin locations on PCB assemblies and precision jigs meet functional assembly requirements.
  • Aerospace structural fasteners — Ensuring hole patterns in airframe panels conform to tight positional tolerances per AS9100 quality requirements.
  • Medical device housings — Validating feature locations on implantable components where even small misalignment affects patient safety.
  • Automotive powertrain components — Checking cylinder-head bolt patterns and transmission bearing bores against design intent.

Sources & Further Reading

The formula and tolerance zone interpretation follow the definitions in the ASME Y14.5-2018 Dimensioning and Tolerancing standard. Additional background on the positional deviation formula is available at GD&T Basics — True Position and the formula application guide at Engineers Edge — True Position GD&T Formula.

Reference

Frequently asked questions

What is the true position formula in GD&T?
The true position formula is TP = 2 × √[(ΔX)² + (ΔY)²] for 2D features and TP = 2 × √[(ΔX)² + (ΔY)² + (ΔZ)²] for 3D features, where ΔX, ΔY, and ΔZ are the differences between actual measured coordinates and the nominal basic dimensions on the drawing. The factor of 2 converts the radial deviation into a diametric value for direct comparison with the Ø tolerance callout. This formula is codified in ASME Y14.5-2018.
What is a typical true position tolerance value?
Typical true position tolerances range from Ø 0.025 mm for precision aerospace or medical components to Ø 0.5 mm or more for general structural fabrication. A common benchmark for CNC-machined holes is Ø 0.1 mm to Ø 0.2 mm. Tighter tolerances demand higher-grade tooling, more frequent tool-offset verification, and CMM inspection, which raises per-part manufacturing cost substantially.
How do you measure true position without a CMM?
Without a CMM, true position can be estimated using a precision surface plate with a height gauge and sine bar, a toolmaker's microscope, or an optical comparator. Measure the X and Y coordinates of the feature center referenced from the datum surfaces, then apply the TP formula manually. For tolerances tighter than Ø 0.1 mm, CMM measurement is strongly recommended because manual methods accumulate setup and parallax errors that inflate measurement uncertainty and can lead to incorrect conformance decisions.
What is the difference between 2D and 3D true position?
2D true position evaluates deviation in the X and Y axes only, producing a circular tolerance zone in a single plane — correct for holes drilled perpendicular to a flat surface. 3D true position adds Z-axis deviation, producing a spherical tolerance zone used for features like spherical seats, angled holes, or nominal locations defined in all three coordinate dimensions. Applying the wrong mode either understates or overstates the actual geometric deviation of the feature.
What happens when a part fails true position inspection?
When the calculated TP value exceeds the tolerance stated in the feature control frame, the part is nonconforming. Disposition options include rework — such as reaming or re-machining the feature if sufficient material remains — use-as-is approval via a Material Review Board if functional analysis confirms the deviation is acceptable, or scrapping the part entirely. Repeated failures on the same feature typically point to a fixture alignment issue, progressive tool wear, or an incorrect datum setup that requires formal corrective action.
How does true position differ from plus/minus coordinate tolerance?
Plus/minus coordinate tolerances create a square or rectangular zone — for example, ±0.1 mm in X and ±0.1 mm in Y defines a 0.2 mm × 0.2 mm square. True position defines a circular zone of diameter Ø. A Ø 0.2 mm circular zone contains roughly 57% of the area of the equivalent square zone, making it more restrictive in the diagonal directions while better reflecting the actual functional requirement of most round features such as bolts or pins that seat symmetrically.