True Position Calculator uses ΔX, ΔY, and 2√(ΔX²+ΔY²) to find diametric true position, compare it with allowed tolerance, and show pass/fail, margin, radial offset, and converted values.
This True Position Calculator takes measured X and Y coordinates, compares them to their basic (nominal) values, and computes the GD&T true position diametric deviation — the single number you compare against the drawing tolerance zone. Enter a position tolerance and any applicable bonus tolerance, and the calculator immediately returns the true position diameter, radial center offset, axis deviations, tolerance margin, and a clear PASS or FAIL verdict.
What the Calculator Measures
In GD&T, a position tolerance defines a cylindrical tolerance zone centred on the true (basic) position of a feature. Any measured point — typically the centre of a hole or pin — must fall within that zone to be accepted. The zone is specified as a diameter, not a radius, so all comparisons in this calculator use diametric values.
The calculator resolves two separate but related quantities from your X and Y input data:
The straight-line distance from the basic (nominal) centre point to the measured actual centre — calculated using the Pythagorean theorem applied to the X and Y deviations. This is a radial (radius) value.
The diametric tolerance zone equivalent — exactly twice the radial centre offset. This is the value the GD&T position tolerance on the drawing controls, and the value compared against total allowed tolerance to determine PASS or FAIL.
True Position Formula
All calculations are performed in the unit system selected (US Customary inches or metric millimetres). The sequence below shows how each output derives from the inputs.
ΔX = X_measured − X_basic
Signed value. Positive means the measured point is to the right of nominal; negative means to the left. Direction is preserved in the output.
ΔY = Y_measured − Y_basic
Signed value. Positive means the measured point is above nominal; negative means below. Direction is preserved in the output.
Radial Offset = √( ΔX² + ΔY² )
The Euclidean distance from the basic centre to the measured centre in the X–Y plane. Always a positive value regardless of the signs of ΔX and ΔY.
True Position = 2 × √( ΔX² + ΔY² )
Multiplied by 2 because GD&T position tolerances are specified as a diameter zone, not a radius. This is the value printed after the ⌀ symbol in a position feature control frame.
Total Allowed Tolerance = Position Tolerance + Bonus Tolerance Entered
Bonus tolerance is a manually entered value. This calculator does not derive bonus tolerance from a feature size measurement — you must calculate and enter any applicable bonus from your own measurement data.
Tolerance Used (%) = ( True Position ÷ Total Allowed Tolerance ) × 100
Expresses how much of the available tolerance zone has been consumed. Values above 100% indicate a FAIL condition.
Tolerance Margin = Total Allowed Tolerance − True Position
Positive margin means the feature is within tolerance by that diametric amount. Negative margin means the feature has exceeded the tolerance zone by that amount.
How to Use the Inputs
Each input field maps directly to a value on the engineering drawing or inspection report. Use the descriptions below to ensure you are entering data in the correct fields.
Select US Customary (inches) or Metric (mm). Switching systems resets all inputs to sensible defaults for that unit and converts all outputs accordingly. The Converted Values result card always shows the result in the opposite unit system.
The diametric position tolerance value from the feature control frame on the drawing — the number after the ⌀ symbol in the position row. This is the base tolerance before any bonus is added. Must be a positive non-zero value.
The additional tolerance earned from a material condition modifier (MMC or LMC), entered manually. You must calculate this from your feature size measurement before entering it here. If no bonus applies, leave this as 0.000. The calculator does not derive bonus automatically.
The basic (theoretically exact) X-axis coordinate of the feature from the drawing. Basic dimensions are shown in a rectangular box on the drawing and define the true position of the tolerance zone itself. They carry no tolerance of their own.
The actual measured X-axis coordinate of the feature centre from your inspection data — CMM report, digital readout, or other measurement source. Used with X Basic to calculate ΔX.
The basic (theoretically exact) Y-axis coordinate from the drawing. Same rules as X Basic — dimensioned from the applicable datums referenced in the feature control frame.
The actual measured Y-axis coordinate of the feature centre. Used with Y Basic to calculate ΔY.
Understanding the Results
The calculator returns four result cards plus a primary hero value and a PASS/FAIL verdict. Each output is explained below in the same order it appears in the calculator.
The hero result. This is the calculated GD&T true position expressed as a diametric value — the diameter of the smallest perfect circle centred on the basic position that encloses the measured point. It is this value that is directly compared to the position tolerance on the drawing.
2 × √( ΔX² + ΔY² )
Because the drawing specifies a diameter zone, the factor of 2 is not optional — it is definitional. Reporting only the radial offset (√(ΔX² + ΔY²)) without doubling would produce a value half the size of the actual GD&T true position and would give an incorrect comparison against a diametric tolerance. The calculator always reports the diametric true position in this field.
This card shows the radial centre offset — the actual Euclidean distance from the basic position to the measured position — alongside the signed X and Y axis deviations that produced it.
√( ΔX² + ΔY² ) = True Position ÷ 2
X_measured − X_basic (signed)
Y_measured − Y_basic (signed)
The ΔX and ΔY values retain their signs (positive or negative) so you can see the direction of the deviation — whether the measured feature has drifted left, right, up, or down from the nominal position. The radial offset is always positive because it is a distance. It is exactly half of the true position diameter.
The tolerance analysis card compares the calculated true position diameter against the total allowed tolerance and expresses the result as a percentage consumed.
Position Tolerance + Bonus Tolerance Entered
True Position Diameter ≤ Total Allowed Tolerance
( True Position ÷ Total Allowed Tolerance ) × 100
The calculator uses three alert states: PASS (green) when true position is within tolerance; PASS — Marginal (amber) when true position has consumed more than 80% of the available zone but has not yet exceeded it; and FAIL (red) when true position exceeds total allowed tolerance. The 80% threshold for the marginal warning is informational only — the acceptance boundary is strictly at 100% of the total allowed tolerance.
The tolerance margin is the diametric distance between the actual true position and the total allowed tolerance limit. It gives you an immediate sense of how much room remains — or how far over the limit the feature is — without doing the subtraction yourself.
Total Allowed Tolerance − True Position (positive = space remaining)
True Position − Total Allowed Tolerance (amount over the limit)
The margin is a diametric value — the same unit system as the true position result and the tolerance. It is not a radial gap; it is the full diametric width of unused tolerance zone on a passing part, or the full diametric amount by which a failing part has exceeded the zone.
This card displays the true position diameter, ΔX, and ΔY in the unit system opposite to the one selected. If you are working in inches, converted values are shown in millimetres; if you are working in metric, converted values are shown in inches. The conversion uses the exact international definition of 1 inch = 25.4 mm.
value (mm) = value (in) × 25.4
value (in) = value (mm) ÷ 25.4
The PASS/FAIL comparison is always performed in the selected unit system. The converted values card is a convenience reference only — it does not change the acceptance decision.
Worked Example
Using the default calculator values — a 0.010 in position tolerance with no bonus — the following results are produced step by step.
When Bonus Tolerance Is Entered
Under ASME Y14.5, a position tolerance modified by Maximum Material Condition (MMC) or Least Material Condition (LMC) allows additional tolerance — called bonus tolerance — when the controlled feature departs from its material condition limit. The amount of bonus equals the difference between the actual mating size of the feature and the MMC (or LMC) size.
This calculator does not measure feature size and cannot derive bonus tolerance automatically. If your drawing specifies an MMC or LMC modifier and you have measured the feature size, calculate the bonus separately and enter it into the Bonus Tolerance Entered field. The calculator will add it directly to the base position tolerance:
Total Allowed Tolerance = Position Tolerance + Bonus Tolerance Entered
Example: a 0.010 in position tolerance with 0.003 in bonus entered gives a total allowed tolerance of 0.013 in. The true position comparison and PASS/FAIL verdict both use the total allowed tolerance figure.
⚠ Important: RFS conditions
If the position tolerance on your drawing carries no material condition modifier, it applies at Regardless of Feature Size (RFS) under ASME Y14.5. In that case, no bonus tolerance is available and the Bonus Tolerance Entered field should remain at 0.000.
Always verify the modifier symbol in the feature control frame on the drawing and confirm which edition of ASME Y14.5 or ISO GPS standard your organisation is working to before deciding whether bonus tolerance applies.
Result Interpretation Notes
The PASS/FAIL verdict and percentage figures this calculator produces are mathematically correct for the inputs entered. Before using results in an acceptance decision, be aware of the following:
The measured feature centre lies within the specified diametric tolerance zone. The tolerance margin value shows how much of the zone is still available. A PASS result here reflects only the positional deviation from the entered coordinates — it does not evaluate feature size, form, orientation, or any other characteristic on the drawing.
The part is still within specification, but the feature is using more than 80% of the available tolerance zone. This is an informational flag — it does not change the acceptance decision. The 80% threshold is not a GD&T standard requirement; it is a practical indicator that the process may be drifting close to the limit.
The measured feature centre falls outside the specified diametric tolerance zone by the amount shown in the Tolerance Margin field. Disposition of a non-conforming part — rework, scrap, or engineering review — must follow your organisation's quality system. This calculator result is not a substitute for formal inspection documentation or drawing authority review.
⚠ Scope and Limitations
This calculator evaluates positional deviation in a 2D X–Y plane only. It does not calculate or account for:
- Z-axis (axial) positional deviation for 3D position control
- Datum shift from a datum feature at MMC or LMC
- Projected tolerance zones
- Feature size conformance or virtual condition checks
- Composite position tolerance (two-tier feature control frames)
- Pattern-level and feature-level positional requirements evaluated separately
- Any GD&T characteristic other than position (perpendicularity, cylindricity, etc.)
Results should be verified against the applicable drawing standard and edition used by your organisation. Formal part acceptance must use calibrated measurement equipment and documented inspection procedures.
References
The formulas, terminology, and geometric interpretation used in this calculator are consistent with the following standards. Consult them directly for complete tolerance tables, modifier rules, datum reference frame requirements, and boundary conditions. Verify which edition and standard your organisation's drawings reference before applying any tolerance decision.