Position Error – Deviation from True Position in Surveying and GD&T

Introduction

Position error, or deviation from true position, is a fundamental metric in fields like manufacturing, engineering, and surveying. It quantifies the difference between a feature’s actual location and its intended, theoretical (true) position. In high-precision industries—such as aerospace, automotive, electronics, and civil infrastructure—tight control of position error ensures that parts fit together, assemblies function as designed, and structures are built to specification.

True position and position error are central to the language of Geometric Dimensioning and Tolerancing (GD&T), as established by standards such as ASME Y14.5 and ISO 1101. They also underpin surveying practices, where accurate point positioning determines project success. Accurate calculation and control of position error enable manufacturers and engineers to optimize processes, minimize waste, and guarantee quality.

This guide explores the concepts of true position, position tolerance, and position error, drawing connections between their use in manufacturing and surveying. You’ll learn how to calculate position error, identify its sources, apply best practices, and ensure your projects meet the strictest standards for quality and reliability.

Definition

True Position

True position is the mathematically exact location where a feature (like a hole, pin, or survey marker) should be, as defined by basic (untoleranced) dimensions and referenced datums on a technical drawing or survey plan. It represents the ideal target in the coordinate system established by the design.

• In GD&T: True position is the theoretical intersection point, axis, or plane where a feature should exist, undisturbed by manufacturing or measurement imperfections.
• In Surveying: True position means the planned coordinates of a marker, boundary, or construction element within a geodetic or local coordinate system.

Analogy: Imagine a dartboard. The bullseye is the true position; wherever the dart lands is the actual position. The distance between the dart and the bullseye is the position error.

Position, True Position, and Position Error

• Position (⊕ symbol in GD&T): Defines the 3D cylindrical or spherical tolerance zone around the true position; feature’s axis or center must fall within this zone.
• Position Error: The actual measured offset from the true position.

Why is this important?
Because even small deviations can cause assembly misfits, leaks, or failures—especially in tightly-toleranced products or critical infrastructure.

Technical Explanation & Application

Position Tolerance in GD&T

Position tolerance is a geometric control that sets the allowable deviation for a feature’s axis, center, or plane relative to its true position. It’s specified in a feature control frame and always references datums to anchor the tolerance zone.

How It Works

• Tolerance Zone: Imagine a perfect cylinder (for holes/pins) or a sphere (for points). The feature’s measured center or axis must fall within this zone, which is centered at the true position.
• Datums: Serve as the coordinate axes for all measurements, ensuring consistent, repeatable inspection.
• Material Condition Modifiers: RFS (default), MMC, and LMC adjust allowable tolerance based on size or functional criteria.

Advantages Over Plus/Minus Tolerancing

• Circular/Cylindrical Zone: More accurately reflects real-world assembly, increasing acceptance area (by up to 57% over square zones for the same tolerance).
• Orientation Control: Referencing datums inherently controls both location and orientation.
• Interchangeability: Ensures parts from different batches or suppliers will fit and function together.

Application Examples

• Holes: Cylinder axis must be within the tolerance cylinder.
• Pins: Center axis must not stray outside the tolerance cylinder.
• Slots: Position and orientation of slot axis are controlled.
• Surveying Points: Measured coordinates must lie within a specified radius or sphere from the design coordinates.

Common Sources of Position Error

Position error can arise during design, manufacturing, measurement, or from environmental effects. Key sources include:

Manufacturing & Measurement

• Part Flexibility: Thin or flexible parts may shift during or after machining.
• Residual Stress: Stresses from forming, machining, or welding can warp parts when released.
• Thermal Expansion: Even a small temperature change can cause significant dimensional changes, especially over large distances.
• Machine Travel Error: CNCs and CMMs have inherent accuracy limits, often specified as a function of travel length.
• Drill Walk: Drill bits can drift off the intended path during machining.
• Measurement Uncertainty: All measurement devices have accuracy limits, and improper setup adds error.

Error Stackup Example (8-foot aluminum plate):

Calculation

2D True Position Formula

For a feature with nominal coordinates (X_nom, Y_nom) and measured coordinates (X_act, Y_act):

True Position = 2 × √[(X_act – X_nom)² + (Y_act – Y_nom)²]

• The result is the diameter of the tolerance zone (circle) the feature’s center must be within.

3D True Position Formula

For points/features with Z-coordinates:

True Position = 2 × √[(X_act – X_nom)² + (Y_act – Y_nom)² + (Z_act – Z_nom)²]

• This gives the diameter of a spherical tolerance zone.

Slots and Elongated Features

• Position error is calculated at several key points (center, ends); the worst-case is reported for conformance.

Visualizing Tolerance Zones

Step-by-Step Example

Suppose:
Design location: (2.000", 1.000"), position tolerance Ø0.008" (RFS)
Actual location: (2.004", 1.003")

Calculation:

• X deviation = 2.004 – 2.000 = 0.004"
• Y deviation = 1.003 – 1.000 = 0.003"
• Position error = 2 × √[(0.004)² + (0.003)²] = 2 × √[0.000025] = 2 × 0.005 = 0.010"

Interpretation:
0.010" > 0.008" → Feature is out of tolerance.

Material Condition Modifiers: RFS, MMC, LMC & Bonus Tolerance

Regardless of Feature Size (RFS)

• Default GD&T modifier; specified tolerance applies regardless of actual size.

Maximum Material Condition (MMC)

• Applies when tightest fit is the concern (smallest hole, biggest pin).
• Bonus tolerance: If actual feature is less “material” than MMC, extra deviation is allowed.
  • For holes: Bonus = Actual size – MMC size
  • For pins: Bonus = MMC size – Actual size
  • Total position tolerance = Specified tolerance + bonus

Example:
MMC for hole = 0.625", actual size = 0.627", position tolerance = 0.008"
Bonus = 0.627 – 0.625 = 0.002"
Total allowed = 0.008" + 0.002" = 0.010"

Least Material Condition (LMC)

• Used when minimum material thickness is critical (e.g., thin-walled parts).
• Bonus tolerance applies if actual feature is more “material” than LMC.

Inspection and Reporting

Inspection Methods

• CMM (Coordinate Measuring Machine): Automated, highly accurate, ideal for complex or tight-tolerance features.
• Laser Trackers/Portable Arms: Preferred for large assemblies or on-site measurement.
• Manual Tools: Calipers, micrometers, or optical comparators for simple or less critical features.

Key: Always align measurements to the correct datums and control environment for accuracy.

Reporting

• Pass/Fail: Is the position error within the specified tolerance?
• Measured Value: Actual position error (as diameter, e.g., Ø0.006").
• Total Allowed Tolerance: Including bonus from MMC/LMC if used.
• Datum Reference: Basis for all measurements.

Reports may include 3D deviation plots or color maps for visual analysis—especially important in regulated industries or critical assemblies.

Best Practices and Practical Tips

• Control Temperature: Keep manufacturing and inspection environments stable; account for thermal expansion, especially for large parts.
• Calibrate Equipment: Regularly calibrate machines, measurement tools, and fixtures.
• Minimize Stackup: Reduce the number of operations or setups that can add cumulative error.
• Use Datums Effectively: Clearly define and communicate datums on all drawings.
• Leverage Material Condition Modifiers: Use MMC/LMC to increase tolerance without sacrificing function.
• Document Everything: Maintain traceable inspection records, especially for regulated industries.

Summary

Position error is the backbone of interchangeability and quality in both manufacturing and surveying. By understanding true position, applying correct tolerance zones, and using robust measurement techniques, you ensure reliable product performance, regulatory compliance, and satisfied customers. Mastery of position error enables process optimization, cost savings, and seamless communication between design, manufacturing, and quality teams.

For further guidance on implementing position controls or advanced GD&T training, contact our experts or schedule a live demo.