True Position Calculator — GD&T Tolerance
Enter the nominal (design) X/Y coordinates, the measured actual coordinates, and the position tolerance diameter. The calculator gives the true position deviation, pass/fail result, and remaining margin — with optional bonus tolerance from maximum material condition (MMC).
FAIL — outside tolerance
- 1
X deviation (Δx)
25.042 − 25 = 0.042 - 2
Y deviation (Δy)
14.967 − 15 = -0.033 - 3
Radial distance
√(0.042² + -0.033²) = 0.05341Euclidean distance from the nominal position to the actual measured position. - 4
True position (diameter)
2 × 0.05341 = 0.1068Multiplied by 2 because GD&T position tolerances are stated as a diameter, not a radius.
How does this calculator work?
True position deviation = 2 × √(Δx² + Δy²). If deviation ≤ tolerance (+ any MMC bonus tolerance), the feature passes. The factor of 2 converts the radial distance to a diametrical value, matching how drawings state position tolerances. Used in CNC machining, CMM inspection, and GD&T callout evaluation.
Formula
How this is calculated
True position is a GD&T (Geometric Dimensioning and Tolerancing) callout that defines how far a feature's actual centre may be from its theoretically exact (nominal) location. The tolerance zone is a circle (or cylinder in 3D) of a specified diameter centred on the nominal point. The measured centre of the feature must fall inside that circle to pass.
The deviation formula is: TP = 2 × √((X_actual − X_nominal)² + (Y_actual − Y_nominal)²). The factor of 2 converts the radial distance from the nominal to a diameter, matching how tolerance is stated on engineering drawings (always as a diameter). If the deviation is less than or equal to the specified tolerance diameter, the part passes.
When the feature is inspected under the maximum material condition (MMC) modifier, a bonus tolerance applies. The bonus equals the difference between the MMC size and the actual produced size of the feature. For example, a hole whose MMC is 10.0 mm but was actually produced at 10.2 mm earns a 0.2 mm bonus, making the total tolerance 0.2 mm wider. This calculator adds the bonus directly to the basic tolerance before comparing with the deviation.
Frequently asked questions
GD&T position tolerances are always expressed as a diameter, not a radius. The basic formula √(Δx² + Δy²) gives the radial distance from nominal to actual. Multiplying by 2 converts that to a diametrical value so it can be directly compared to the tolerance diameter on the drawing. If you prefer to work in radii, the deviation radius = TP / 2.
Bonus tolerance applies when the feature size is modified with the MMC (maximum material condition) symbol ⓜ. At MMC (smallest hole or largest pin) no bonus exists. As the feature departs from MMC, the tolerance zone grows by the same amount — the "bonus." For a hole at 10.0 mm MMC produced at 10.3 mm, the bonus is 0.3 mm, widening the position tolerance zone by 0.3 mm. Without the ⓜ modifier, enter 0.
For a 3D position the formula is TP = 2 × √(Δx² + Δy² + Δz²). In that case the tolerance zone is a sphere. This calculator covers the common 2D case (position of a hole centre on a flat surface). For 3D positions, add the Z deviation manually: if the 3D radial deviation is r₃ = √(Δx² + Δy² + Δz²), TP = 2 × r₃.
Also known as
TG we-Calculate Editorial Team. (2026). True Position Calculator — GD&T Tolerance [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/true-position-calculator
TG we-Calculate Editorial Team. "True Position Calculator — GD&T Tolerance." TG we-Calculate. 2026. https://we-calculate.com/calculator/true-position-calculator.
TG we-Calculate Editorial Team, "True Position Calculator — GD&T Tolerance," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/true-position-calculator
@misc{wecalculate_true_position_calculator, title = {True Position Calculator — GD&T Tolerance}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/true-position-calculator}}, year = {2026}, note = {TG we-Calculate} }
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