How To Calculate Concentricity Of Two Circle

Enter the center coordinates and radii of two circles to calculate center offset, radial concentricity error, diametric error, and tolerance status.

Expert Guide: How to Calculate Concentricity of Two Circle Features

Concentricity is one of the most important geometry checks in machining, rotating equipment design, shaft and bearing assemblies, and precision inspection. If two circular features are supposed to share the same center point, any center shift between them can create vibration, uneven wear, noise, poor sealing, or assembly failure. The good news is that the core calculation is straightforward: find the distance between the two centers.

In practical terms, engineers often evaluate two values. The first is radial offset, which is the direct center-to-center distance. The second is diametric error, which is typically two times the radial offset. Many prints, software packages, and quality teams use one or the other depending on inspection conventions, GD&T interpretation, and company standards. This guide gives you both values so you can compare results clearly and avoid tolerance misunderstandings.

1) Core definition and geometry

For two circles, define center points as C1(x1, y1) and C2(x2, y2). The center offset is:

d = sqrt((x2 – x1)^2 + (y2 – y1)^2)

This value d is the radial concentricity error in the same unit system as your inputs. If your drawing or process reports concentricity as a diameter-like value, use:

Diametric error = 2d

You may also track a normalized value to compare parts of different sizes:

Percent center offset = (d / reference radius) x 100

Reference radius can be circle 1, circle 2, or the average of both, depending on your internal standard.

2) Step-by-step procedure used in inspection

1. Measure each circle center using a reliable method (CMM, vision system, bore gauge with fixture, or spindle-based probing).
2. Record x and y coordinates in one consistent coordinate frame.
3. Compute delta x and delta y.
4. Calculate center offset using the distance formula.
5. Compute diametric error by doubling radial offset if required by the print or quality plan.
6. Compare against tolerance and report pass or fail.

3) Worked example

Suppose:

• Circle 1 center = (0.000, 0.000) mm
• Circle 2 center = (0.080, 0.060) mm
• Circle 1 radius = 25 mm
• Circle 2 radius = 15 mm

Then:

• delta x = 0.080 mm
• delta y = 0.060 mm
• d = sqrt(0.080^2 + 0.060^2) = 0.100 mm
• Diametric error = 0.200 mm
• If average reference radius is 20 mm, percent offset = 0.100 / 20 x 100 = 0.5%

If your tolerance is 0.25 mm diametric, this part passes. If the limit is 0.18 mm diametric, it fails.

4) Concentricity vs similar geometric checks

Teams often mix up concentricity, circularity, position, and runout. These checks are related but not identical:

• Concentricity: how closely two center points align.
• Circularity: how round one feature is by itself.
• Position: how far a feature center is from its true location relative to datums.
• Runout: variation observed while rotating relative to a datum axis.

In rotating assemblies, runout often captures functional behavior directly, but center alignment calculations remain essential for root-cause analysis and process correction.

5) Comparison table: center offset impact at common tolerance bands

Radial Offset d (mm)	Diametric Error 2d (mm)	Status at 0.05 mm Tol	Status at 0.10 mm Tol	Status at 0.20 mm Tol
0.010	0.020	Pass	Pass	Pass
0.020	0.040	Pass	Pass	Pass
0.035	0.070	Fail	Pass	Pass
0.060	0.120	Fail	Fail	Pass
0.110	0.220	Fail	Fail	Fail

6) Comparison table: capability levels and expected nonconformance rates

The following rates are standard normal-distribution benchmarks frequently used in process quality planning. They help estimate how often a concentricity characteristic might fall out of tolerance when centered and stable.

Sigma Level	Approx. Defects per Million (ppm)	Approx. Yield	Interpretation for Concentricity Control
3 sigma	66,807 ppm	93.32%	High scrap risk for precision rotating parts.
4 sigma	6,210 ppm	99.38%	Usable for moderate tolerance applications.
5 sigma	233 ppm	99.9767%	Strong production capability for tight fit parts.
6 sigma (long-term convention)	3.4 ppm	99.99966%	Very high reliability target for critical assemblies.

7) Measurement system selection and uncertainty awareness

A good formula cannot compensate for poor measurement strategy. To calculate concentricity accurately, your measurement uncertainty should be comfortably smaller than tolerance. A common practical guideline is to keep effective gage discrimination around one tenth of the tolerance band when feasible.

• If tolerance is 0.020 mm diametric, target measurement resolution near 0.002 mm or better.
• If tolerance is 0.200 mm diametric, a simpler setup can still be appropriate.
• For small bores and thin walls, fixturing repeatability can dominate the total error budget.

Always document how the centers are fitted, what filtering is used, and whether you are reporting radial or diametric values. This removes ambiguity across suppliers, customers, and auditors.

8) Common mistakes that cause bad concentricity decisions

1. Mixing radial and diametric reporting: this can double or halve reported error by mistake.
2. Using different datums for each feature: invalidates center comparison.
3. Ignoring unit mismatch: inch and millimeter confusion is still a major source of error.
4. Assuming perfect circles: lobe shape or form error can bias fitted centers.
5. Overlooking thermal effects: precision checks can drift with temperature change.

9) Practical process tips for machining teams

• Use one setup when possible to reduce stack-up between features.
• Stabilize clamping force and fixture contact points.
• Track tool wear and spindle condition for trends in center drift.
• Record concentricity by cavity, spindle, and machine to isolate root causes quickly.
• Pair geometry data with vibration or balance data for rotating products.

10) Standards and metrology references

If you need authoritative measurement foundations, SI unit consistency, and dimensional metrology guidance, start with these high-quality references:

• NIST Dimensional Metrology Resources (.gov)
• NIST SI Units and Measurement Guidance (.gov)
• MIT OpenCourseWare: Manufacturing Process Control (.edu)

Final takeaway: calculating concentricity of two circles is fundamentally a center-distance problem. Define centers consistently, compute radial offset, convert to diametric error when needed, and compare against the exact tolerance definition on the drawing. Consistent units, clear reporting, and reliable metrology practice make the result trustworthy and actionable.