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newSchoolWorks.com › VoTechWorks › Manufacturing & Marine › CNC Machining › Blueprint Reading and GD&T for CNC Machining › Lesson 9
MFG-CNC14-02 · Lesson 9 · 16 clock hours · demo

Location Tolerances: True Position, Concentricity, and Symmetry

Objective. Students calculate true-position tolerance zones, apply MMC and RFS modifiers, and determine whether a measured hole or feature location conforms to a position callout using the formula and on a CMM or manual layout.

⚠ Pending professional review

This lesson, its worked examples and its practice questions has not yet been verified by a licensed engineer or certified journey-level tradesperson or by a certification or approval body. It is a study draft and may contain errors. Do not use it as instructions for work on a job site or on live equipment. Always follow your instructor, your supervising professional, and current official references and regulations.

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What Location Tolerances Control

Location tolerances tell you exactly where a feature — a hole, a boss, a slot — must be relative to a set of datums. Three GD&T controls fall under this category: true position, concentricity, and symmetry. True position is by far the most common in CNC machining and the one most likely to appear on shop drawings and NIMS credentialing assessments.

True Position

A true position callout defines a tolerance zone centered on the theoretically exact location of a feature. That exact location is set by basic dimensions (boxed dimensions on the drawing) from the specified datum reference frame.

For a round hole, the tolerance zone is a cylinder whose diameter equals the value in the feature control frame. The center axis of the actual hole must fall inside that cylinder. For a point feature in a plane, the zone collapses to a circle.

The feature control frame reads left to right: the position symbol (a target/crosshair circle), the total tolerance diameter, and any material condition modifier, then the datum references in order of precedence — primary, secondary, tertiary.

MMC and RFS Modifiers

MMC (Maximum Material Condition) — the modifier circle-M — means the stated tolerance applies when the feature is at its largest allowable material size (smallest hole, largest pin). As the feature departs from MMC toward LMC, the position tolerance is allowed to increase by the same amount as the size departure. This bonus tolerance only exists at MMC; it rewards the inspector for a feature that has "extra" material removed.

RFS (Regardless of Feature Size) — implied when no modifier is shown in current ASME Y14.5 practice — means the stated tolerance applies at every actual feature size. There is no bonus. The tolerance zone stays fixed.

Example: a hole is ⌀0.500 +0.002/−0.000 (MMC = 0.500 in.) with a position tolerance of ⌀0.010 at MMC. If the hole is actually measured at ⌀0.501, the bonus is 0.001 in., and the allowable position tolerance opens to ⌀0.011.

Calculating True Position from Coordinate Measurements

When you measure a hole's actual center with a caliper, height gauge, or CMM, you get an X and Y coordinate. Compare those to the basic (theoretically exact) X and Y from the drawing. The deviations are Δx and Δy.

The diametral position error (the diameter of the smallest circle centered on the true position that contains the measured center) is:

Position error = 2 × √(Δx² + Δy²)

The factor of 2 converts the radial error to a diametral tolerance zone so it can be directly compared to the diametral tolerance in the feature control frame.

If the calculated position error ≤ the allowable tolerance (stated tolerance + any bonus), the hole passes. If it exceeds the allowable tolerance, the hole fails — it is out of location.

Concentricity and Symmetry

Concentricity controls the median points of a diametrically opposed surface relative to a datum axis. All median points must lie within a cylindrical tolerance zone coaxial with the datum. Because establishing median points requires many cross-sectional measurements, concentricity is difficult and expensive to verify — it is rarely used in modern practice. Runout or position controls are preferred for most coaxial features.

Symmetry controls the median points of a feature relative to a datum plane, requiring them to fall within two parallel planes equally disposed about the datum. Like concentricity, it is measurement-intensive and is used infrequently. Many designers substitute position or profile controls.

Setting Up for Manual Layout Measurement

To measure hole positions manually:

1. Place the part on a surface plate (flat reference surface). Use an angle plate or V-blocks as needed to establish datum A (usually the bottom face) perpendicular and stable.

2. Zero your height gauge on the surface plate to establish the Z reference, then measure from the datum edge using a digital caliper or step measurement to establish X and Y coordinates of each hole center.

3. Record measurements carefully — repeat each reading twice and average to reduce error.

4. Calculate Δx and Δy by subtracting the basic dimension from your measured coordinate, then apply the formula.

Safety on the surface plate: burrs on the part or chips under the part will gouge the lapped surface and throw off all measurements. Deburr the part before placing it. Never slide steel parts; lift and set them. Keep the plate clean and covered when not in use.

CMM Verification

A coordinate measuring machine (CMM) uses a touch-trigger probe to capture feature coordinates with high accuracy and repeatability. The CMM software computes position errors automatically using the same formula, applies the datum reference frame, and generates a report showing each feature's deviation and pass/fail status.

When reconciling CMM output with hand calculations: small differences (within about 0.001 in.) are normal given surface plate setup limitations. Larger disagreements usually point to an error in your datum setup — the part was not seated squarely on the reference plane, or you measured from the wrong edge.

CMM safety: the probe tip is fragile and expensive. Never jog the ram at high speed near the part. Follow the instructor's directions for loading and fixturing. Wear safety glasses; a dropped probe or part can cause injury.

Key terms10

True PositionA GD&T location control defining a cylindrical (or circular) tolerance zone centered on the theoretically exact location of a feature, established by basic dimensions and a datum reference frame.
Basic DimensionA theoretically exact dimension shown in a box on the drawing; it locates the true position of a feature and has no tolerance itself — tolerance is given only in the feature control frame.
Feature Control FrameThe rectangular symbol block on a drawing that contains the GD&T characteristic symbol, tolerance value, material condition modifier, and datum references in order.
MMC (Maximum Material Condition)The condition in which a feature contains the most material: the smallest allowable hole diameter or largest allowable pin diameter. A circle-M modifier allows bonus position tolerance as the feature departs from MMC.
Bonus ToleranceAdditional position tolerance earned at MMC; equals the difference between the feature's actual mating size and its MMC size. Only available when the circle-M modifier is specified.
RFS (Regardless of Feature Size)The condition in which the stated geometric tolerance applies at any actual feature size, with no bonus. The current default in ASME Y14.5 when no modifier is shown.
Diametral Position ErrorThe diameter of the smallest circle centered at true position that encloses the measured feature center; calculated as 2 × √(Δx² + Δy²) and compared directly to the diametral tolerance.
Datum Reference FrameA set of up to three mutually perpendicular datum planes (primary, secondary, tertiary) established from datum features on the part to provide a repeatable measurement origin.
ConcentricityA GD&T control requiring that all median points of a cylindrical feature lie within a cylindrical tolerance zone coaxial with a datum axis; rarely used because of measurement difficulty.
CMM (Coordinate Measuring Machine)A precision inspection machine that uses a touch-trigger or scanning probe to capture X, Y, Z coordinates of part features; software then computes GD&T deviations and generates a pass/fail report.

Worked examples4

1. A hole has a basic position of X = 1.000 in., Y = 1.000 in. from datums B and C. The measured center is at X = 1.008 in., Y = 0.995 in. The position tolerance is ⌀0.020 RFS. Does the hole pass?
  1. Find Δx: 1.008 − 1.000 = +0.008 in.
  2. Find Δy: 0.995 − 1.000 = −0.005 in.
  3. Square each deviation: Δx² = 0.000064; Δy² = 0.000025
  4. Sum of squares: 0.000064 + 0.000025 = 0.000089
  5. Square root: √0.000089 ≈ 0.009434 in.
  6. Multiply by 2 (diametral): 2 × 0.009434 ≈ 0.01887 in.
  7. Compare to tolerance: 0.01887 < 0.020 — the hole PASSES.
Answer: Diametral position error ≈ 0.019 in.; allowable tolerance = 0.020 in. RFS. The hole passes.
2. A hole callout is ⌀0.500 +0.003/−0.000 with a position tolerance of ⌀0.010 at MMC. The hole is measured at an actual size of ⌀0.502 in. The measured center deviates Δx = +0.006 in., Δy = −0.004 in. from true position. Does the hole pass?
  1. Determine MMC for the hole: smallest hole = ⌀0.500 in. (most material for a hole at minimum size).
  2. Actual size = 0.502 in. Departure from MMC = 0.502 − 0.500 = 0.002 in.
  3. Bonus tolerance = 0.002 in.
  4. Total allowable position tolerance = 0.010 + 0.002 = 0.012 in. (diametral).
  5. Calculate diametral position error: 2 × √(0.006² + 0.004²) = 2 × √(0.000036 + 0.000016) = 2 × √0.000052 ≈ 2 × 0.007211 ≈ 0.01442 in.
  6. Compare: 0.01442 > 0.012 — the hole FAILS.
Answer: Diametral position error ≈ 0.0144 in.; allowable tolerance (with bonus) = 0.012 in. The hole fails.
3. A drilled plate is measured on a surface plate. Hole No. 3 has basic coordinates X = 2.500 in., Y = 3.000 in. Your height-gauge and caliper readings give an actual center at X = 2.497 in., Y = 3.006 in. The drawing calls for ⌀0.015 position tolerance at MMC; the hole is at MMC. What is the diametral position error, and does the hole pass?
  1. Δx = 2.497 − 2.500 = −0.003 in.
  2. Δy = 3.006 − 3.000 = +0.006 in.
  3. Δx² = 0.000009; Δy² = 0.000036
  4. Sum = 0.000045; √0.000045 ≈ 0.006708 in.
  5. Diametral error = 2 × 0.006708 ≈ 0.01342 in.
  6. Hole is at MMC, so no bonus tolerance; allowable = 0.015 in.
  7. 0.01342 < 0.015 — the hole PASSES.
Answer: Diametral position error ≈ 0.013 in.; allowable tolerance = 0.015 in. The hole passes.
4. A hole deviates Δx = +0.012 in. and Δy = +0.012 in. from its true position. The position tolerance is ⌀0.030 RFS. Calculate the diametral position error and determine conformance.
  1. Δx² = 0.000144; Δy² = 0.000144
  2. Sum = 0.000288; √0.000288 ≈ 0.016971 in.
  3. Diametral error = 2 × 0.016971 ≈ 0.03394 in.
  4. Compare to tolerance: 0.03394 > 0.030 — the hole FAILS.
Answer: Diametral position error ≈ 0.034 in.; allowable tolerance = 0.030 in. RFS. The hole fails.

The math in this lesson2

Learners compute diametral position error as 2√(Δx² + Δy²) from measured hole coordinates.
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Brush up in the math halls at newSchoolWorks.com:
In class: Instructor derives the true-position formula (diametral position error = 2 × √(Δx² + Δy²)) and works three examples; students solve six additional problems using coordinate measurements and the formula to determine pass/fail. · Students measure a drilled plate with a digital caliper and height gauge using a datum reference setup on a surface plate, record actual hole center coordinates, calculate true position, and compare to the drawing callout at MMC. · Instructor demonstrates use of a CMM (coordinate measuring machine) to verify hole positions on the same plate; students observe the CMM report and reconcile it with their hand-calculated results.
Materials: Drilled steel demonstration plate (multiple holes at known positions), digital calipers, height gauge, surface plate, angle plate, CMM (shop CMM or instructor demonstration), true-position calculation worksheet, scientific calculator
Check: Calculation worksheet: 5 of 6 true-position problems solved correctly (83%); plate measurement: calculated position error within ±0.002 in. of instructor-measured reference value and correct conformance decision required.

Practice check8

Answer each question, then check it. Nothing is recorded; this is your own practice.

NIMS Machining L1-2 — Blueprint Reading and Inspection
1. The formula for diametral true-position error from measured coordinate deviations Δx and Δy is:
NIMS Machining L1-2 — Blueprint Reading and Inspection
2. A hole has a position tolerance of ⌀0.014 at MMC. The hole MMC is ⌀0.625 in. and the actual measured size is ⌀0.628 in. What is the total allowable position tolerance?
NIMS Machining L1-2 — Blueprint Reading and Inspection
3. On a drawing, a dimension enclosed in a rectangle (boxed dimension) is called a:
NIMS Machining L1-2 — Blueprint Reading and Inspection
4. A hole's measured center is at X = 3.004 in., Y = 1.997 in. The true position is X = 3.000 in., Y = 2.000 in. What is the diametral position error? (Round to three decimal places.)
NIMS Machining L1-2 — Blueprint Reading and Inspection
5. The circle-M modifier in a position feature control frame means the tolerance applies at:
NIMS Machining L1-2 — Blueprint Reading and Inspection
6. When reconciling hand-calculated position results with a CMM report, a difference of 0.015 in. between the two most likely indicates:
NIMS Machining L1-2 — Blueprint Reading and Inspection
7. Concentricity and symmetry controls are used infrequently in modern drawings primarily because:
NIMS Machining L1-2 — Safety and Shop Practices
8. Before placing a steel workpiece on a surface plate for height-gauge measurement, the most important preparation step is to:
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