True Position Calculator

The true position formula in 2D is TP = 2 × √(X² + Y²), where X and Y are the deviations from the nominal position. In 3D mode, the formula is TP = 2 × √(X² + Y² + Z²). The result is a diametral value that describes the size of the circular tolerance zone needed to contain the feature center.

The formula is multiplied by 2 because true position is expressed as a diameter, not a radius. The square root of X² + Y² gives you the radial distance from the nominal center to the measured center. Multiplying by 2 converts that radius into a diameter, which matches how the tolerance zone is defined on engineering drawings.

An internal feature is a hole or slot cut into a part. An external feature is a pin, boss, or stud that sticks out from a part. The choice matters because it changes how MMC and LMC are calculated. For a hole, MMC is the smallest size. For a pin, MMC is the largest size.

Enter it as a positive number. The calculator already knows it is a minus tolerance. For example, if your drawing says −0.0050, just type 0.0050 in the Tolerance − field.

This warning means your measured feature size falls outside the allowed size range. The measured diameter is either smaller than the MMC size or larger than the LMC size (or vice versa for pins). The feature fails the size check regardless of its position. The part does not meet the drawing requirements.

Use whatever your drawing specifies. Look at the feature control frame on the print. If you see a circled M symbol, use MMC. If you see a circled L, use LMC. If there is no symbol, use RFS. Most drawings for mating features like bolt holes use MMC because it allows bonus tolerance.

X and Y deviations come from your inspection equipment such as a CMM (coordinate measuring machine). They are the difference between the nominal position shown on the drawing and the actual measured center of the feature. If your CMM report shows actual coordinates, subtract the nominal X from the actual X to get the X deviation, and do the same for Y.

Yes. A negative deviation means the feature center is offset in the negative direction from its nominal position. The calculator handles negative values correctly. The sign does not affect the true position result because the values are squared in the formula.

The gauge shows what percentage of your total allowed tolerance is used up by the actual true position. A low percentage (green) means the feature is well within spec. A high percentage (red) means it is close to failing. Anything over 100% means the feature fails the position check.

Bonus tolerance at MMC equals the measured feature size minus the MMC size for internal features (holes). For external features (pins), it equals the MMC size minus the measured size. The further the actual size is from MMC, the more bonus tolerance you get. If the feature is exactly at MMC, the bonus is zero.

Virtual condition is the worst-case boundary of a feature. For a hole at MMC, it equals the MMC size minus the position tolerance. It tells you the smallest effective opening a mating pin must fit through. Engineers use it to make sure parts will always assemble, even in the worst case.

Use 3D mode when your feature has a measurable deviation along the Z axis in addition to X and Y. This is common for features on angled surfaces, deep holes that may tilt, or when your inspection data includes all three axes. Most standard position checks on flat surfaces only need 2D mode.

The calculator works with any unit as long as you use the same unit for every field. If your drawing is in inches, enter all values in inches. If it is in millimeters, use millimeters everywhere. The math is the same regardless of units.

The position plot shows a top-down view of your tolerance zone. The circles represent the allowed tolerance boundary. The red dot shows where the measured feature center actually landed. If the dot is inside the circle, the feature passes. If it is outside, the feature fails.

Yes. Bonus tolerance increases the allowed zone, but if the feature is too far from its nominal position, it can still fail even with the extra tolerance. The true position must be less than or equal to the listed tolerance plus the bonus tolerance to pass.

True position controls the location of a feature center relative to datum reference features. Concentricity controls how well the median points of a feature align with a datum axis. True position is much easier to measure and is used far more often in manufacturing. Concentricity is rarely specified on modern drawings because it is difficult and expensive to inspect.

Remaining tolerance is the difference between your total allowed tolerance and your actual true position. A positive number means the feature passes and tells you how much room you have left. A negative number means the feature has exceeded its allowed tolerance and fails.

A feature control frame has the position symbol (a circled crosshair), followed by the tolerance value (with a diameter symbol), an optional modifier (circled M or L), and one or more datum references. Enter the tolerance value in the Listed Position Tolerance field and select the matching modifier in this calculator.