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Precision & Quality Control

True Position Calculator

Verify that anchor bolts, drilled holes, and embed plates are within GD&T position tolerance. Enter the nominal (designed) coordinates from your drawing and the actual (measured) coordinates from your survey or CMM report. The calculator returns the True Position diameter and a clear Pass / Fail result for each feature — in metric (mm) or imperial (inches).

True Position Calculator

GD&T position tolerance — check actual vs nominal coordinates

Axes:
FeatureNominal (mm)Actual (mm)Tol ⌀ (mm)
XYXY

Enter nominal & actual coordinates, then click Calculate

Tolerance Zone Diagram

The true position tolerance zone is a cylinder (shown here as a circle in plan view) centred on the nominal coordinate. The actual feature must lie within this zone.

Nominal (True Position) Actual Position ΔX ΔY TP/2 ⌀ Tolerance Zone FORMULA (2D) TP = 2√(ΔX²+ΔY²) PASS if TP ≤ ⌀ Tolerance X → ↑ Y

Step-by-Step Formulas

1. True Position Formula (2D)

TP = 2 × √(ΔX² + ΔY²)

ΔX and ΔY are the deviations between the actual measured coordinate and the nominal (designed) coordinate. The factor of 2 converts the radial error into a diameter, because the position tolerance zone is always specified as a diameter (⌀) in GD&T — matching the cylindrical zone a bolt or hole must fall within.

2. True Position Formula (3D)

TP = 2 × √(ΔX² + ΔY² + ΔZ²)

For features where the axial deviation also matters — such as the height of an embed plate stud or a through-bolt in a deep foundation — the Z-axis deviation is included. This is less common on structural drawings but standard in precision machining (ASME Y14.5).

3. Tolerance Zone

PASS if TP ≤ ⌀ Tolerance | FAIL if TP > ⌀ Tolerance

The tolerance zone is a cylinder of the specified diameter centred on the true (nominal) position. The actual feature axis or centre point must lie entirely within this cylinder. Common structural tolerances: anchor bolts ±3 mm (1/8 in) for standard connections; ±1.5 mm (1/16 in) for precision moment connections per AISC Code of Standard Practice Section 7.

4. Bonus Tolerance (MMC)

Bonus Tolerance = Actual Size − MMC Size

When a feature of size (hole or pin) is produced away from its Maximum Material Condition (MMC — smallest hole or largest pin), the position tolerance may be increased by the bonus amount. For example, a 20 mm hole drilled at 20.5 mm earns 0.5 mm extra position tolerance. This is the most common modifier in machined part GD&T but less frequently applied in structural construction.

Worked Example — Anchor Bolt Inspection

Column base plate: 4 anchor bolts at corners of a 200 × 200 mm pattern. Tolerance ⌀3.0 mm.

BLT-1: Nom (0, 0) → Act (1.20, 0.80)
ΔX = 1.20, ΔY = 0.80
TP = 2 × √(1.20² + 0.80²) = 2 × √(1.44 + 0.64) = 2 × √2.08 = 2.884 mm
2.884 ≤ 3.0 → ✓ PASS (96.1% of tolerance used)
BLT-2: Nom (200, 0) → Act (201.80, 0.60)
ΔX = 1.80, ΔY = 0.60
TP = 2 × √(1.80² + 0.60²) = 2 × √(3.24 + 0.36) = 2 × √3.60 = 3.795 mm
3.795 > 3.0 → ✗ FAIL — must re-grout or notify engineer

Deviation to True Position

True position is twice the radial deviation. This shows the largest X/Y offset that still passes a given zone:

Tolerance zone (Ø) Max radial deviation Max equal X & Y offset Zone vs square
0.005 0.0025 0.0018 +57% area
0.010 0.0050 0.0035 +57% area
0.015 0.0075 0.0053 +57% area
0.030 0.0150 0.0106 +57% area

GD&T Position Tolerance

True position describes a circular tolerance zone, which is why the deviation gets doubled:

  • A Round Zone, Not a Square One: Position tolerance defines a cylindrical zone around the nominal point. This permits 57% more area than an equivalent square coordinate tolerance while still controlling the fit.
  • Bonus Tolerance at MMC: When a feature departs from maximum material condition, the difference becomes additional position tolerance. A hole drilled larger than minimum legitimately earns extra positional freedom.
  • Datums Must Be Established First: Position is meaningless without the datum reference frame. Measuring from the wrong origin produces numbers that look fine but describe nothing useful.

Benefits of Using This Calculator

Instant Pass or Fail Enter nominal and actual coordinates and see immediately whether the feature is inside the zone.
Diametral Result Reports true position as the diameter of the tolerance zone, matching ASME Y14.5 convention.
Deviation Breakdown Shows the X and Y components alongside the radial deviation for troubleshooting.
Works in Any Units Consistent in inches or millimetres, as long as inputs share the same unit.

Example Calculations

Three scenarios worked through step by step:

Example 1 — Passing Feature

Nominal (2.000, 3.000), actual (2.003, 2.998), tolerance Ø0.010.

ΔX = 2.003 − 2.000 = 0.003

ΔY = 2.998 − 3.000 = −0.002

Deviation = √(0.003² + 0.002²) = 0.003606

True position = 2 × 0.003606 = 0.007211

Result: 0.0072 ≤ 0.010 — PASS

Example 2 — Failing Feature

Nominal (0.000, 0.000), actual (0.006, 0.005), tolerance Ø0.010.

ΔX = 0.006; ΔY = 0.005

Deviation = √(0.006² + 0.005²) = 0.007810

True position = 2 × 0.007810 = 0.015621

Result: 0.0156 > 0.010 — FAIL

The feature sits outside the cylindrical zone

Example 3 — Bonus Tolerance

Hole Ø0.250 MMC, actual Ø0.256, stated tolerance Ø0.010.

Bonus = 0.256 − 0.250 = 0.006

Total allowable = 0.010 + 0.006 = 0.016

Measured true position = 0.0156

Result: 0.0156 ≤ 0.016 — PASS with bonus

The same feature failed without the MMC modifier

Inspection Tip

Inspection Tip

Always confirm which datum reference frame the print calls out before measuring anything. A hole pattern inspected from the part edge instead of the specified datum holes can read perfectly in-tolerance and still not assemble — the numbers are only meaningful relative to the origin the drawing defines.

Frequently Asked Questions

What is True Position in GD&T?
True Position is a GD&T (Geometric Dimensioning and Tolerancing) control that defines the exact theoretical location of a feature relative to datum references. The actual feature centre must fall within a cylindrical tolerance zone (defined by diameter ⌀) centred on that true position.
How is True Position calculated?
For 2D: TP = 2 × √(ΔX² + ΔY²), where ΔX and ΔY are the differences between actual and nominal coordinates. The factor of 2 converts from radius to diameter. For 3D: TP = 2 × √(ΔX² + ΔY² + ΔZ²).
What are typical anchor bolt tolerances in construction?
Per AISC Code of Standard Practice (Section 7.5): standard anchor bolt groups must be within ±3 mm (1/8 in) of their true position for column base plate connections. Critical moment frames or exposed column connections often specify ±1.5 mm (1/16 in). Always confirm with the project structural engineer.
What units should I use?
Use millimetres (mm) for metric projects — all coordinates and tolerances in the same unit. Use inches (in) for imperial projects. The formula works for any consistent unit system. Do not mix units in the same calculation.
Can I check multiple bolts or holes at once?
Yes. The calculator accepts a table of features. Add as many rows as needed — each gets its own ΔX, ΔY, True Position result, tolerance comparison, and Pass/Fail status. This matches a typical anchor bolt survey report or CMM inspection table.
How do you calculate true position?
Find the deviation from nominal in X and Y, combine them as √(ΔX² + ΔY²), then double the result. The doubling converts a radial deviation into the diameter of the cylindrical tolerance zone that ASME Y14.5 specifies.
Why is true position doubled?
Because the tolerance zone is expressed as a diameter, not a radius. Your measured deviation is the distance from the true position, which is a radius, so it must be doubled to compare against a diametral callout.
What is bonus tolerance?
Extra position tolerance earned when a feature of size departs from maximum material condition. A hole made larger than its MMC size can be positioned slightly further off nominal and still assemble, and the MMC modifier permits that.
What is the difference between position and true position?
In current usage they mean the same thing — "true position" is the older term for the theoretically exact location, and "position" is the tolerance controlling it. ASME Y14.5 uses "position" for the geometric characteristic.
Why use position instead of coordinate tolerancing?
A round zone is a better model of how parts assemble and permits about 57% more area than the inscribed square that coordinate tolerances create. It accepts more genuinely good parts without loosening the functional requirement.

Assumptions & Reference Values

This tool returns estimates using standard financial formulas and the default parameters shown in the calculator inputs. Always consult a qualified financial advisor before making investment decisions.

Calculator Defaults:

  • Positional deviation = √((actual X − nominal X)² + (actual Y − nominal Y)²)
  • True position diameter = 2 × positional deviation
  • Pass requires true position ≤ the specified tolerance zone diameter
  • Follows the ASME Y14.5 diametral tolerance zone convention
  • Bonus tolerance from MMC is added to the zone when the callout permits it
  • Assumes the datum reference frame is correctly established before measuring
  • Measurement uncertainty of the gauge is not subtracted from the result

Disclaimer

All calculations are for informational purposes only. Past performance does not guarantee future results. Consult a licensed financial advisor for personalized advice.