AtlasCalcsUtility Calculation Suite
2026-07-30 8 min

Concentricity Calculator

Calculate concentricity error, center offset, and tolerance compliance per ISO 1101 and ASME Y14.5 GD&T standards.

Calculator

Unit System
Datum Center X (mm)
Datum Center Y (mm)
Measured Center X (mm)
Measured Center Y (mm)
Nominal Diameter (mm)
Tolerance Value (mm)

Results

Critical

Concentricity Error

0.1166mm

Total concentricity error (twice the center offset) per ASME Y14.5 definition

Center Offset

0.0583mm

Radial distance between datum center and measured center

Deviation Ratio

1.1662

Ratio of concentricity error to tolerance. Pass if ≤ 1.0

Datum Center

(0.00, 0.00)

Coordinates of the datum (reference) center point

Measured Center

(0.05, 0.03)

Coordinates of the measured center point

Status

Fail

Accept/Reject based on concentricity deviation ratio

Visualizations

Results Overview

0.1mmConcentricity Error
0.1mmCenter Offset
1.2mmDeviation Ratio
0.1mmMeasured Center

Formula

Concentricity is the condition where the median points of all diametrically opposed elements of a feature are congruent with the datum axis. The concentricity error is twice the offset distance.

Offset = √((Mx - Dx)² + (My - Dy)²)

Alternative Form

Concentricity Error = 2 × Offset

Variables

SymbolNameUnitDescription
Dx, DyDatum Center CoordinatesmmCoordinates of the datum axis center
Mx, MyMeasured Center CoordinatesmmCoordinates of the measured feature center
eOffsetmmRadial distance between datum and measured centers
tTolerancemmSpecified concentricity tolerance (diameter)

Explanation

Concentricity controls the central axis of a feature relative to a datum axis. It is a complex tolerance requiring median point evaluation. The measured feature must have all median points within a cylindrical tolerance zone centered on the datum axis.

Derivation

The radial offset between two points is the Euclidean distance. Concentricity error is defined as the diameter of the smallest circle centered at the datum axis that contains the measured center point, hence 2× the offset.

Step-by-Step Calculation

Follow each step to understand how the result is calculated from your inputs.

Step 1

Establish the datum axis from the reference feature and measure the actual center coordinates of the feature being inspected.

Datum Center:(0, 0)
Measured Center:(0.05, 0.03)
Result: Center coordinates established
Step 2

Calculate the radial offset between the datum and measured centers.

e = √((Mx - Dx)² + (My - Dy)²)
ΔX:0.0583 mm
ΔY:0.0583 mm
Intermediate: e = √((0.05 - 0)² + (0.03 - 0)²)
Result: Center Offset: 0.0583 mm
Step 3

Compute the concentricity error as twice the offset and compare to tolerance.

Concentricity Error = 2 × e
Offset:0.0583 mm
Tolerance:--- mm
Intermediate: Error = 2 × 0.0583
Result: Concentricity Error: 0.1166 mm → Fail
Final Answer
0.1166

Worked Examples

See how the calculator works with different scenarios.

Scenario

A 50 mm diameter shaft has a datum axis at (0,0). CMM measures the center of a journal at (0.05, 0.03). Tolerance: 0.1 mm concentricity.

Inputs

Datum Center:(0, 0)
Measured Center:(0.05, 0.03)
Tolerance:0.1 mm

Calculation

Offset = √(0.05² + 0.03²) = √(0.0025 + 0.0009) = √0.0034 = 0.0583 mm Concentricity Error = 2 × 0.0583 = 0.1166 mm

Result

Deviation Ratio: 1.166 → Fail (exceeds 0.1 mm tolerance)

Interpretation

The shaft journal has slightly excessive concentricity error. The center offset of 0.058 mm produces a concentricity error of 0.117 mm, exceeding the 0.1 mm tolerance by 16.6%.

Understanding Your Result

Your Result: Concentricity Error: 0.1166 mm

Typical range: Concentricity tolerances: 0.01-0.05 mm for precision ground spindles, 0.05-0.2 mm for machined shafts, 0.2-0.5 mm for general turned parts, 0.5-2.0 mm for cast or welded assemblies.

What This Means

Concentricity controls the central axis of a feature to be coaxial with a datum axis. The tolerance zone is a cylinder whose axis is the datum axis. All median points of the feature must fall within this cylinder.

Why It Matters

Concentricity is critical for rotating parts, precision mating features, and components where mass balance or uniform wall thickness is required. Poor concentricity causes vibration, uneven wear, and assembly difficulties.

Professional Interpretation

Concentricity is one of the most difficult GD&T controls to inspect because it requires establishing median points from multiple cross-sections. For most applications, runout or position tolerances are preferred as they are easier to measure and provide similar functional control.

Recommendations

  • •Prefer runout or position tolerances over concentricity when possible
  • •Use concentricity only when median point alignment is functionally critical
  • •Ensure CMM or inspection equipment has adequate resolution for the tolerance
  • •Measure at multiple cross-sections along the feature length
  • •Consider the effects of form errors (cylindricity) on concentricity results
  • •Document the datum establishment method for measurement repeatability

Educational Content

Introduction

Concentricity is a GD&T tolerance that controls the coaxial alignment of a feature to a datum axis. Unlike runout (which controls surface variation), concentricity controls the median points of the feature cross-sections.

Concept Explanation

The concentricity tolerance defines a cylindrical zone centered on the datum axis. The median points of all diametrically opposed elements of the controlled feature must lie within this cylinder. This requires establishing the center point at multiple cross-sections along the feature.

Applications

▸Precision rotating shafts and spindles
▸Bearing journals and housings
▸Turbine and compressor rotor stages
▸Engine crankshaft main bearing journals
▸Hydraulic and pneumatic cylinder bores
▸Precision gear and pulley bores
▸Medical implant coaxial surfaces

Benefits

  • •Controls coaxial alignment of functional surfaces
  • •Ensures uniform wall thickness in cylindrical parts
  • •Reduces vibration in rotating assemblies
  • •Provides consistent clearance in mating cylindrical features
  • •Improves load distribution in press-fit assemblies

Limitations

  • •Difficult and time-consuming to inspect
  • •Requires multiple cross-sectional measurements
  • •Form errors (lobing, ovality) affect median point determination
  • •ASME Y14.5-2018 has deprecated concentricity; use position or runout instead
  • •Not suitable for Thin-walled parts that may distort under measurement forces

Best Practices

  • •Use concentricity only where median point control is essential
  • •Prefer circular runout for surface variation control
  • •Prefer position tolerance for center axis location
  • •Specify multiple cross-sections for evaluation on the drawing
  • •Use temperature compensation for high-precision measurements
  • •Calibrate CMM probe tip radius accurately for concentricity measurements

Common Misconceptions

Myth: Concentricity is the same as runout.
Truth: Runout controls surface variation as the part rotates. Concentricity controls the median points of cross-sections independent of surface irregularities.
Myth: Concentricity is easy to measure with a dial indicator.
Truth: Dial indicators measure runout (surface variation), not concentricity. Concentricity requires establishing center points from diametrically opposed measurements.
Myth: Concentricity tolerance applies to the entire surface.
Truth: Concentricity controls the median points of cross-sectional elements, not the surface directly. The surface is constrained indirectly through the median point requirement.

Practical Tips

  • •Use a CMM with rotary table for efficient concentricity measurement at multiple cross-sections
  • •When possible, replace concentricity with position tolerance at MMC for easier inspection
  • •Ensure the datum feature is sufficiently accurate (cylindrical and straight) for meaningful concentricity results
  • •Consider the effect of feature weight and fixturing on measured center locations
  • •Use multiple measurement cross-sections and take the worst-case concentricity result
  • •Document the number and location of measurement cross-sections for repeatability
  • •For thin-walled parts, consider free-state concentricity specifications

Common Mistakes

Specifying concentricity when runout would suffice
Runout is easier to measure and provides similar control for most applications. Use runout unless median point control is specifically required.
Measuring concentricity with a single cross-section
Concentricity must be evaluated at multiple cross-sections along the feature length to ensure the entire axis is within the tolerance zone.
Confusing concentricity with coaxiality terminology
In ISO standards, coaxiality is a similar concept to concentricity. In ASME, concentricity specifically refers to median point control.
Ignoring datum form error in concentricity evaluation
The datum axis must be well-defined. Datum form errors (cylindricity, straightness) propagate into concentricity measurement uncertainty.

Assumptions

This calculator makes the following assumptions to provide estimates:

Circular Cross-Section: The calculation assumes circular cross-sections at the measurement location. Non-circular shapes require different coaxiality evaluation methods.
Single Cross-Section: This calculator evaluates concentricity at a single cross-section. Full concentricity evaluation requires multiple cross-sections along the feature length.
Center Point Definition: The measured center is assumed to be the true median point of the cross-section, established from diametrically opposed elements.
Rigid Body: The feature is assumed to be rigid. Flexible parts may have different concentricity under free-state vs. restrained conditions.

Limitations

Be aware of these limitations when using this calculator:

Single Cross-Section Only: This calculator evaluates concentricity at one cross-section. Full verification requires multiple sections per ASME Y14.5.
No Form Error Consideration: Form errors (cylindricity, roundness) of the datum and controlled features are not considered but affect actual concentricity results.
2D Approximation: The calculation uses 2D center point coordinates. Real parts require 3D evaluation of the entire axis.
No MMC/LMC Modifiers: This calculator evaluates at RFS (Regardless of Feature Size). MMC or LMC modifiers affect the tolerance zone size and acceptance criteria.

Frequently Asked Questions

Answers to common questions about this calculator.

What is concentricity in GD&T?
Concentricity is a geometric tolerance that controls the coaxial alignment of a feature to a datum axis by requiring all median points of the feature cross-sections to fall within a cylindrical tolerance zone.
How is concentricity measured?
Concentricity is typically measured using a CMM by taking multiple diametrically opposed points at several cross-sections, computing median points, and checking their deviation from the datum axis.
What is the difference between concentricity and runout?
Runout measures surface variation as the part rotates (FIM). Concentricity measures median point location relative to the datum axis. Runout includes both eccentricity and form errors; concentricity isolates center location.
Is concentricity still used in ASME Y14.5-2018?
Concentricity was deprecated in ASME Y14.5-2018. ASME recommends using position tolerance (for center location) or runout (for surface variation) instead. However, concentricity remains in many existing drawings and ISO standards.
What is the concentricity tolerance zone shape?
The concentricity tolerance zone is a cylinder centered on the datum axis. The diameter of the cylinder equals the specified tolerance value.
How do I calculate concentricity error?
Find the radial offset between the datum center and the measured center: e = √(Δx² + Δy²). Concentricity error = 2 × e (the diameter of the smallest cylinder containing the measured axis).
What is a median point?
A median point is the midpoint of all diametrically opposed elements of a feature at a given cross-section. It is found by averaging pairs of opposite surface points.
What is the difference between concentricity and coaxiality?
In ISO standards, coaxiality is a broader term for axis alignment. In ASME, concentricity specifically refers to median point control. Position tolerance at RFS is the ISO equivalent for coaxial control.
How many cross-sections are needed for concentricity?
ASME Y14.5 requires evaluation at multiple cross-sections along the feature length to ensure the entire median axis is within the tolerance zone. A minimum of two sections is recommended; four or more is typical.
What is the RFS modifier in concentricity?
Regardless of Feature Size (RFS) means the concentricity tolerance applies regardless of the actual feature size. This is the default for concentricity tolerances.
Can concentricity be applied at MMC?
Historically, concentricity was always applied at RFS. ASME Y14.5-2009 allowed MMC modifiers, but the 2018 deprecation removed this possibility. ISO standards use position for MMC coaxial control.
How does datum cylindricity affect concentricity?
Datum surface irregularities create uncertainty in the established datum axis. A cylindricity tolerance on the datum feature helps ensure consistent concentricity measurements.
What is the typical concentricity tolerance?
Typical tolerances: 0.01-0.025 mm for precision spindles, 0.05-0.1 mm for machined shafts, 0.1-0.5 mm for general components.
How does concentricity affect rotating machinery?
Poor concentricity causes unbalance, vibration, bearing wear, and noise. The concentricity error directly contributes to rotating imbalance forces.
What is the relationship between concentricity and wall thickness?
Concentricity error causes non-uniform wall thickness in hollow parts. The wall thickness variation equals approximately 2× the concentricity error for thin-walled cylinders.
Can concentricity be measured with a V-block and indicator?
No, V-block methods measure runout, not concentricity. Concentricity requires establishing the actual center point from opposed measurements.
What is the concentricity symbol?
The concentricity symbol is two concentric circles (◎) placed in the feature control frame. In ISO, two concentric circles with a central dot.
How do I inspect concentricity on a production basis?
Production concentricity inspection typically uses dedicated gages with opposed probes or CMM with statistical sampling. Air gaging with opposed jets can also be used.
What is the difference between concentricity and position tolerance?
Position tolerance controls the center point location at RFS or MMC. Concentricity requires establishing median points from opposed measurements and cannot use MMC bonus.
How does concentricity apply to threaded features?
Concentricity on threads is measured at the pitch diameter center. Special thread measuring techniques or wire measurements are needed.
What is the effect of lobing on concentricity?
Lobing (out-of-roundness with odd number of lobes) can cause the median point to deviate even if the overall feature appears centered, making CMM measurement strategy critical.
How does concentricity relate to total runout?
Total runout includes concentricity error plus form errors along the entire surface. Concentricity is a component of total runout.
Can concentricity be applied to a plane surface?
No, concentricity applies to cylindrical or spherical features. For planar surfaces, use parallelism or perpendicularity.
What is the cost of concentricity inspection?
Concentricity inspection with CMM is significantly more expensive than runout due to multiple cross-section requirements and longer measurement time.
How does temperature affect concentricity measurement?
Temperature gradients across the part can distort the center location. Uniform temperature to 20°C ± 1°C is recommended for precision concentricity measurements.
What statistical methods apply to concentricity?
Concentricity is evaluated as a radial metric. Process capability studies use the Rayleigh distribution for concentricity data.
How do I document concentricity results?
Report the maximum concentricity error found across all measured cross-sections, the locations of the worst section, and the datum axis establishment method.
What is the effect of surface finish on concentricity?
Rough surfaces increase measurement uncertainty in center point determination. Surface roughness should be significantly better than the concentricity tolerance.
Can concentricity be improved by machining?
Yes, concentricity can be improved by machining features in the same setup, using steady rests, or with precision grinding between centers.
How do I choose between concentricity and position?
Use position tolerance for most applications. Use concentricity only when median point control (not just center) is functionally required per legacy standards.
What is the relationship between concentricity and balance?
Concentricity directly affects mass balance of rotating parts. Eccentric mass distribution causes imbalance forces proportional to offset distance.
How does concentricity affect press-fit assemblies?
Poor concentricity causes uneven interference in press fits, leading to localized stress concentrations and potential assembly failure.

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Glossary

Technical terms used in mortgage calculations explained in plain language.

Coaxiality
The condition where two or more features share a common axis. In ISO, the broader term for axis alignment control.
Concentricity
A GD&T tolerance controlling the median points of a feature to be coaxial with a datum axis within a cylindrical tolerance zone.
Datum Axis
The theoretically exact axis established from a datum feature, serving as the reference for geometric tolerances.
Deviation Ratio
The ratio of actual concentricity error to the specified tolerance. Pass/fail determined by whether this ratio ≤ 1.0.
FIM
Full Indicator Movement — the total range of a dial indicator reading as a part is rotated, used for runout measurement.
Median Point
The midpoint of all diametrically opposed elements of a feature at a given cross-section.
RFS
Regardless of Feature Size — a modifier specifying that the geometric tolerance applies regardless of the actual feature size.
Rotary Table
A precision rotating device used with CMMs to measure concentricity and runout at multiple angular positions and cross-sections.
Runout
A GD&T tolerance controlling surface variation as a part rotates about a datum axis. Includes both circular and total runout.
Tolerance Zone
For concentricity, a cylinder centered on the datum axis within which all median points of the controlled feature must lie.

Authoritative References

Trusted sources and standards referenced by this calculator.

Applicable Standards

ISO 1101ASME Y14.5ISO 5458ISO 1938ISO 14405-1ASME B89.1.6M

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Page Information

Last Updated:

2026-07-30

Version:

2.0.0

License:

Free to use for educational and professional purposes.