True Position Calculator

What Is True Position?

True position is a geometric tolerance that defines the allowable variation of a feature's location from its theoretically exact position. It is commonly used in mechanical engineering and manufacturing to specify the acceptable deviation of a hole, pin, or other feature from its nominal (design) location. Unlike simple coordinate tolerances (±X, ±Y), true position uses a diametrical tolerance zone, which provides a more accurate and functional representation of allowable error.

The true position calculation follows the formula: True Position = 2 × √(ΔX² + ΔY²), where ΔX and ΔY are the deviations from the nominal coordinates in the X and Y axes respectively. The result is a diameter value that represents the total positional error of the measured feature.

How the True Position Calculator Works

This calculator determines the true position of a feature based on your measured coordinates and the nominal (design) location. The calculation process involves three steps:

1. Calculate deviations – Subtract the nominal X and Y coordinates from the measured X and Y coordinates to find the deviation in each axis.
2. Compute radial distance – Apply the Pythagorean theorem to find the straight-line distance from the nominal center to the measured point.
3. Double the radial distance – Multiply the radial distance by 2 to obtain the diametrical true position value.

The calculator also compares the result against any specified tolerance to determine whether the feature passes or fails inspection.

How to Use the True Position Calculator

1. Enter nominal coordinates – Input the design X and Y coordinates for the feature's intended location.
2. Enter measured coordinates – Input the actual X and Y coordinates obtained from inspection or measurement.
3. Set tolerance (optional) – Enter the allowable true position tolerance to automatically check pass/fail status.
4. Review results – The calculator displays the true position value, the radial deviation, and whether the feature is within tolerance.

Example Calculation

Scenario: A hole is designed with nominal coordinates of X = 50.000 mm, Y = 30.000 mm. After measurement, the actual coordinates are X = 50.120 mm, Y = 30.085 mm. The tolerance is 0.250 mm.

Step 1: Calculate deviations
ΔX = 50.120 − 50.000 = 0.120 mm
ΔY = 30.085 − 30.000 = 0.085 mm

Step 2: Compute radial distance
Radial distance = √(0.120² + 0.085²) = √(0.0144 + 0.007225) = √0.021625 = 0.147 mm

Step 3: Calculate true position
True Position = 2 × 0.147 = 0.294 mm

Result: The true position of 0.294 mm exceeds the tolerance of 0.250 mm, so the feature fails inspection.

Understanding the Results

The true position value represents the diameter of a circle centered at the nominal location that contains the measured point. A smaller value indicates better positional accuracy. Key points to understand:

• Pass/Fail status – If the calculated true position is less than or equal to the tolerance, the feature passes. If it exceeds the tolerance, the feature fails.
• Radial deviation – This is the straight-line distance from nominal to measured location. It is half the true position value.
• Coordinate deviations – Individual ΔX and ΔY values help identify which axis contributes more to the positional error.

Common Mistakes When Using True Position

• Confusing radial deviation with true position – The true position is the diameter, not the radius. A radial deviation of 0.1 mm equals a true position of 0.2 mm.
• Using absolute coordinate tolerances instead – A ±0.1 mm coordinate tolerance creates a square tolerance zone, while true position uses a circular zone. The circular zone allows approximately 57% more variation for the same linear tolerance.
• Forgetting to include material condition modifiers – In GD&T, true position tolerances often include Maximum Material Condition (MMC) or Least Material Condition (LMC) modifiers that affect the allowable tolerance based on the feature's actual size.
• Ignoring the Z-axis for 3D features – For features with depth, true position may need to account for angular deviation in addition to X and Y displacement.

Limitations and Considerations

This calculator provides a basic true position calculation based on X and Y coordinates. It does not account for:

• Material condition modifiers – MMC, LMC, and RFS (Regardless of Feature Size) are not included in this basic calculation.
• Datum reference frames – Complex GD&T callouts may reference multiple datums that affect how true position is evaluated.
• 3D positional tolerance – Features with significant depth or angular requirements may need additional calculations.
• Bonus tolerance – When MMC is specified, the allowable tolerance increases as the feature size deviates from MMC. This calculator does not compute bonus tolerance.

Practical Applications

True position calculations are used across manufacturing and quality control:

• CNC machining – Verifying hole locations on machined parts against engineering drawings.
• Quality inspection – Using CMM (Coordinate Measuring Machine) data to validate part conformance.
• Assembly fitment – Ensuring that mating features align correctly during assembly.
• PCB manufacturing – Checking component placement accuracy on printed circuit boards.
• Fixture design – Validating that jigs and fixtures position parts within required tolerances.