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:
Radial Center Offset — 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.
True Position Diameter — 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.
| Step | Formula | Notes |
|---|---|---|
| 1 — X-axis deviation | ΔX = X_measured − X_basic | Signed value. Positive = right of nominal; negative = left. |
| 2 — Y-axis deviation | ΔY = Y_measured − Y_basic | Signed value. Positive = above nominal; negative = below. |
| 3 — Radial center offset | Radial Offset = √( ΔX² + ΔY² ) | Euclidean distance from basic centre to measured centre. Always positive. |
| 4 — True position diameter | True Position = 2 × √( ΔX² + ΔY² ) | Multiplied by 2 because GD&T position tolerances are specified as a diameter zone, not a radius. |
| 5 — Total allowed tolerance | Total Allowed = Position Tolerance + Bonus Tolerance Entered | Bonus must be calculated and entered manually — this calculator does not derive it automatically. |
| 6 — Tolerance consumed | Tolerance Used (%) = ( True Position ÷ Total Allowed ) × 100 | Values above 100% indicate a FAIL condition. |
| 7 — Tolerance margin | Tolerance Margin = Total Allowed − True Position | Positive = space remaining; negative = amount exceeded. |
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.
01 — True Position (Diameter) — Primary Output
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.
True Position = 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 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.
02 — Radial Center Offset, ΔX & ΔY
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.
| Output | Formula |
|---|---|
| Radial Offset | √( ΔX² + ΔY² ) = True Position ÷ 2 |
| X Deviation (ΔX) | X_measured − X_basic (signed) |
| Y Deviation (ΔY) | Y_measured − Y_basic (signed) |
The ΔX and ΔY values retain their signs so you can see the direction of the deviation — whether the measured feature has drifted left, right, up, or down from nominal. The radial offset is always positive and is exactly half of the true position diameter.
03 — Tolerance Analysis — PASS / FAIL & Usage
The tolerance analysis card compares the calculated true position diameter against the total allowed tolerance and expresses the result as a percentage consumed.
| Output | Formula |
|---|---|
| Total Allowed Tolerance | Position Tolerance + Bonus Tolerance Entered |
| PASS condition | True Position Diameter ≤ Total Allowed Tolerance |
| Tolerance Used | ( True Position ÷ Total Allowed Tolerance ) × 100 |
The calculator uses three alert states: PASS when true position is within tolerance; PASS — Marginal when true position has consumed more than 80% of the available zone but has not yet exceeded it; and FAIL when true position exceeds total allowed tolerance. The 80% marginal threshold is informational only — the acceptance boundary is strictly at 100% of the total allowed tolerance.
04 — Tolerance Margin
The tolerance margin is the diametric distance between the actual true position and the total allowed tolerance limit.
| Condition | Formula |
|---|---|
| Margin (PASS) | Total Allowed Tolerance − True Position (positive = space remaining) |
| Exceeded (FAIL) | 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.
05 — Converted Values
This card displays the true position diameter, ΔX, and ΔY in the unit system opposite to the one selected. The conversion uses the exact international definition of 1 inch = 25.4 mm.
| Direction | Formula |
|---|---|
| Inches → Millimetres | value (mm) = value (in) × 25.4 |
| Millimetres → Inches | 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.
| Input | Value |
|---|---|
| Position Tolerance (Diameter) | 0.0100 in |
| Bonus Tolerance Entered | 0.0000 in |
| X Basic (Nominal) | 1.0000 in |
| X Measured (Actual) | 1.0020 in |
| Y Basic (Nominal) | 2.0000 in |
| Y Measured (Actual) | 1.9970 in |
| Step | Calculation | Result |
|---|---|---|
| ΔX | 1.0020 − 1.0000 | +0.0020 in |
| ΔY | 1.9970 − 2.0000 | −0.0030 in |
| Radial Offset | √(0.0020² + 0.0030²) | 0.0036 in |
| True Position | 2 × 0.0036 | 0.0072 in |
| Total Allowed | 0.0100 + 0.0000 | 0.0100 in |
| Tolerance Used | (0.0072 ÷ 0.0100) × 100 | 72.1% |
| Tolerance Margin | 0.0100 − 0.0072 | 0.0028 in remaining |
| Verdict | — | PASS |
| True Position (mm) | 0.0072 × 25.4 | 0.183 mm |
| ΔX (mm) | 0.0020 × 25.4 | +0.051 mm |
| ΔY (mm) | 0.0030 × 25.4 | −0.076 mm |
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:
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.
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 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
PASS — True position is within tolerance. The tolerance margin value shows how much of the zone is still available. A PASS result reflects only the positional deviation from the entered coordinates — it does not evaluate feature size, form, orientation, or any other characteristic on the drawing.
PASS — Marginal — The part is still within specification but has consumed 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.
FAIL — 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
- ASME Y14.5 — Dimensioning and Tolerancing. The primary US standard governing GD&T, including the definition of true position, diametric tolerance zones, material condition modifiers (MMC/LMC/RFS), bonus tolerance rules, and datum reference frame requirements. The 2018 edition is current; the 2009 and 1994 editions remain in use on legacy drawings. asme.org — ASME Y14.5
- ISO 1101 — Geometrical Product Specifications (GPS) — Geometrical Tolerancing. The ISO equivalent governing geometrical tolerancing, including position. ISO uses different modifier symbols and terminology from ASME Y14.5 — notably, the default material condition modifier under ISO is RFS unless explicitly stated. iso.org — ISO 1101
- ISO 5458 — GPS — Geometrical Tolerancing — Pattern and Combined Geometrical Specification. Covers the ISO treatment of position tolerances applied to patterns of features, including the distinction between pattern-level and feature-level requirements. iso.org — ISO 5458
- ISO 2692 — GPS — Geometrical Tolerancing — Maximum Material Requirement (MMR), Least Material Requirement (LMR) and Reciprocity Requirement (RPR). Defines how material condition requirements work under the ISO GPS framework, including the rules for deriving additional tolerance when a feature departs from its material condition. iso.org — ISO 2692
- NIST SP 811 — Guide for the Use of the International System of Units (SI). Codifies the exact international definition of 1 inch = 25.4 mm used for all unit conversions in this calculator. nist.gov — NIST SP 811
- ASME Y14.5.1 — Mathematical Definition of Dimensioning and Tolerancing Principles. The mathematical companion to ASME Y14.5 that formalises the geometric definitions — including the exact mathematical basis for tolerance zones, true position, and material condition boundaries. asme.org — ASME Y14.5.1