Math & Engineering
True Position Calculator
Calculate true position tolerance and verify if measurements meet specifications in geometric dimensioning and tolerancing (GD&T).
Enter values to calculate true position
Related to True Position Calculator
The True Position Calculator is a precision engineering tool used in Geometric Dimensioning and Tolerancing (GD&T) to determine how accurately a feature's actual position matches its theoretically perfect position. It uses the Pythagorean theorem to calculate the total positional deviation from two coordinate measurements (X and Y deviations).
The Formula
True Position = √(X² + Y²)
Where:
- X is the deviation along the X-axis
- Y is the deviation along the Y-axis
The calculator compares this true position value against the specified tolerance to determine if the measured position falls within acceptable limits. The tolerance remaining is calculated by subtracting the true position from the tolerance value, indicating how much deviation margin remains before exceeding specifications.
The calculator provides three key pieces of information to help you interpret the measurement results:
True Position Value
This is the actual distance from the theoretically perfect position. A smaller value indicates better accuracy. The value is calculated using both X and Y deviations to give a single measurement of position error.
Tolerance Status
A clear indication of whether the measured position falls within the specified tolerance. "Within Tolerance" (green) means the part meets specifications, while "Out of Tolerance" (red) indicates the position error exceeds acceptable limits.
Tolerance Remaining
Shows how much additional deviation could occur before reaching the tolerance limit. A negative value indicates the position has exceeded the tolerance by that amount.
1. What is true position in GD&T?
True position in Geometric Dimensioning and Tolerancing (GD&T) is a measurement of how far a feature's actual location deviates from its theoretically perfect position. It's used to control the location of features like holes, pins, or other geometric elements in manufacturing.
2. How is true position tolerance different from dimensional tolerance?
True position tolerance is a radial or cylindrical tolerance zone around the theoretically perfect position, while dimensional tolerance is a linear ±tolerance on a size or location dimension. True position provides better control of feature location and is often more appropriate for functional requirements.
3. Why use true position instead of coordinate tolerances?
True position provides a single tolerance zone that better represents the functional requirements of most parts. It's more efficient than using separate X and Y tolerances because it accounts for the combined effect of all positional deviations, making it easier to verify compliance.
4. Can true position be negative?
No, true position cannot be negative because it represents a distance calculated using the Pythagorean theorem. While individual X and Y deviations can be negative, the true position value is always positive as it represents the absolute distance from the theoretical position.
5. What is the scientific source for this calculator?
This calculator is based on the mathematical principles defined in the ASME Y14.5-2018 Dimensioning and Tolerancing standard, which is the internationally recognized standard for GD&T. The calculation uses the Pythagorean theorem to determine the true position value, which is a fundamental geometric principle first described in Euclid's Elements (c. 300 BCE) and validated through centuries of mathematical and engineering applications. The implementation follows the guidelines set forth by the American Society of Mechanical Engineers (ASME) for geometric tolerancing calculations.