True Position Calculator
### ASME Y14.5 & ISO 1101 GD&T Positional Tolerancing **Geometric Dimensioning and Tolerancing (GD&T)** defines true position as the theoretically exact location of a feature of size established by.
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📐 Formula
💡 Practical Example
A CNC-milled hole drilled at X=50.015 and Y=24.980 off a nominal 50.000/25.000 target has a radial deviation of 0.025, producing a diametrical True Position of Ø0.0500.
📖 About True Position Calculator
ASME Y14.5 & ISO 1101 GD&T Positional Tolerancing
Geometric Dimensioning and Tolerancing (GD&T) defines true position as the theoretically exact location of a feature of size established by basic dimensions.
Primary True Position Equations
- Linear Deviations: Δ X = X_act - X_basic, Δ Y = Y_act - Y_basic
- Diametrical True Position (2D):
True Position () = 2 × √((Δ X)^2 + (Δ Y)^2)
- 3D Positional Tolerancing:
True Position () = 2 × √((Δ X)^2 + (Δ Y)^2 + (Δ Z)^2)
- Bonus Tolerance at Maximum Material Condition (MMC):
- Internal Hole: Bonus = Measured Diameter - MMC Diameter (Smallest Hole)
- External Pin / Boss: Bonus = MMC Diameter (Largest Pin) - Measured Diameter
- Total Allowable Tolerance: Total Allowed = Specified Tolerance + Bonus
How to Use This Calculator
Enter your Basic X Coordinate (Nominal) (e.g. 50.000), Basic Y Coordinate (Nominal) (e.g. 25.000), Measured Actual X Coordinate (e.g. 50.015), Measured Actual Y Coordinate (e.g. 24.980), Specified GD&T Tolerance (Diameter) (e.g. 0.050), Material Condition Modifier — choose from Regardless of Feature Size (RFS — Standard), Maximum Material Condition (MMC Hole — Ⓜ), Maximum Material Condition (MMC Pin/Shaft — Ⓜ), Actual Feature Diameter (Optional for MMC) (e.g. 10.020), and MMC Limit Diameter (Smallest Hole / Largest Pin) (e.g. 10.000). Results update instantly as you type — adjust any value to compare scenarios.
The Formula
Diametrical True Position TP = 2 * sqrt(dx^2 + dy^2)
Worked Example
A CNC-milled hole drilled at X=50.015 and Y=24.980 off a nominal 50.000/25.000 target has a radial deviation of 0.025, producing a diametrical True Position of Ø0.
0500.
Understanding Your Result
Evaluate your result in the context of your specific use case and relevant industry standards or reference values. A single calculated result is a starting point — test two to three scenarios to understand how sensitive the outcome is to your key input assumptions. For high-stakes decisions, verify your result against a secondary source or subject-matter expert before acting.
💡 Mathematical Rigor & Applied Context
- This calculator applies exact mathematical definitions following conventions established by NIST and international standards bodies.
- Rounding errors accumulate across multi-step calculations. For precision-critical work, maintain extra significant figures through all intermediate steps.
- Many mathematical concepts have multiple valid formulations — if a result seems unexpected, verify which convention or definition applies to your context.
- Dimensional analysis (unit tracking) is the fastest way to catch formula errors. Every term in an equation must have consistent, compatible units.
- Numerical methods used in digital calculators introduce floating-point precision limits (~15 significant digits for IEEE 754 double precision).
- For statistical and probabilistic calculations, always specify whether you are working with population parameters or sample statistics — formulas differ.
- Visualizing a problem geometrically or testing with known boundary values (zero, infinity, negative) reveals hidden errors faster than algebraic checking.
- When in doubt, validate your result against a simplified hand calculation or a published worked example from a textbook or standards document.
Results are for informational and educational purposes only. Always verify critical decisions with a qualified professional.