true Position Calculator

true position works like measuring how far a dart landed from the bullseye, but with a manufacturing twist. Instead of just finding the distance from center, true position doubles that distance to represent the full diameter of the tolerance zone. This matters because GD&T specifications define tolerance zones as diameters, not radii.

The calculation squares both X and Y deviations, adds them, takes the square root (creating the hypotenuse of a right triangle), then multiplies by 2. This geometric approach creates a circular tolerance zone that often allows more manufacturing variation than traditional ± tolerances while maintaining the same functional requirements.

True position assumes your measurements are taken from the same datum references used on the engineering drawing. If your measurement setup uses different reference points, the calculation becomes meaningless. Most quality failures in true position stem from datum reference errors, not actual manufacturing deviations.

Use true position when your drawing shows a position tolerance symbol (⌖) with a diameter tolerance. This applies to holes, pins, slots, and any feature where location matters more than individual X and Y dimensions. true position is mandatory for parts that mate with other components.

Avoid true position for features with bilateral tolerances (±) on the drawing. Those require separate X and Y tolerance checks, not circular zone verification. Also skip true position for form tolerances like straightness or flatness - those need different measurement approaches.

True position is most valuable in high-volume manufacturing where you need to verify many identical features quickly. Single prototypes or one-off parts often use simpler coordinate measurement instead of formal GD&T verification.

The most common mistake is confusing radius with diameter. Some calculators show the distance from nominal position (radius) instead of true position (diameter). Always verify your calculator multiplies by 2 - the true position should always be exactly double the distance from center.

Measurement datum errors cause more rejection than actual manufacturing problems. If your fixture or measurement setup references different surfaces than the drawing specifies, your true position calculation will be wrong even if the part is perfect. Always verify your measurement datum matches the drawing datum before calculating.

Another frequent error is mixing measurement units. If your nominal coordinates are in inches but measurements are in millimeters, the calculation produces meaningless results. Some shops have scrapped good parts because someone entered 25mm as 25 inches in the calculation.

The true position formula is: TP = 2 × √((X_measured - X_nominal)² + (Y_measured - Y_nominal)²). The factor of 2 converts from radius to diameter since GD&T tolerance zones are specified as diameters.

For example: if a hole should be at (25.000, 15.000) but measures at (25.100, 15.050), the calculation is: TP = 2 × √((25.100-25.000)² + (15.050-15.000)²) = 2 × √(0.100² + 0.050²) = 2 × √(0.0100 + 0.0025) = 2 × √0.0125 = 2 × 0.1118 = 0.224mm.

The formula fails when measurements have different units than nominal values, or when datum references don't match between measurement and design. Edge case: if both deviations are zero, true position equals exactly zero (perfect position). Maximum true position approaches infinity as deviations increase, but practical manufacturing limits typically keep values under 10× the tolerance.

The ASME Y14.5 standard specifies that true position applies at Maximum Material Condition (MMC) unless otherwise noted. This means a smaller hole gets more positional tolerance, while a larger hole gets less. Most basic calculators ignore this MMC modifier, potentially rejecting good parts or accepting bad ones.