Measured points, tolerance annulus, and magnified residual spokesLive current inputs
Math & Statistics
Circle Verification Calculator
Verify whether four measured points agree with a stated circle center and radius, classify each radial residual, and separate systematic radius bias from point-to-point scatter.
Tolerance verdict-
Points within tolerance-
Mean signed residual-
RMS radial error-
Maximum absolute residual-
Bias interpretation-
Points inside claimed circle-
Points outside claimed circle-
RADIAL CONFORMANCE MAP
Measured points, tolerance annulus, and magnified residual spokes
The claimed circle sits inside a tolerance band. Every measured point is color-coded and linked to its ideal radial projection so direction and magnitude remain visible.
POINT-BY-POINT AUDIT
Distance, signed residual, and pass status for every observation
Positive residuals lie outside the claimed radius; negative residuals lie inside.
| Point | Coordinates | Center distance | Signed residual | |Residual| / tolerance | Status |
|---|
VERIFICATION SETUP
Enter observations from around the circumference, not one local arc
- Enter the stated center and radius.
- Set a defensible radial tolerance.
- Enter four measured points in the same coordinate system.
- Use signed residuals to distinguish inside from outside.
- Review spatial pattern as well as the overall verdict.
BIAS VERSUS SCATTER
A circle can miss consistently or vary around the target
A large signed mean with residuals pointing mostly one way suggests a radius or center bias. Mixed positive and negative residuals with small mean but large RMS suggest scatter or shape error.
Four points cannot diagnose all roundness defects. Their angular coverage matters; clustered points can hide errors elsewhere on the circumference.
RADIAL RESIDUAL TEST
Measure every point against the stated circle before summarizing error
Each point's center distance is compared with the claimed radius. Signed mean detects consistent radius bias, while RMS and maximum absolute residual describe scatter and worst case.
Detailed calculation process and general formulas
dᵢ=√[(xᵢ-h)²+(yᵢ-k)²]eᵢ=dᵢ-rē=(Σeᵢ)/4RMS=√(Σeᵢ²/4)passᵢ ⇔ |eᵢ|≤TSymbols, meanings, and units
- h,k
- claimed circle centercoordinate units
- r
- claimed radiuslength
- T
- allowed radial tolerancelength
- dᵢ
- center distance to point ilength
- eᵢ
- signed radial residuallength
- RMS
- root mean square radial errorlength
CONFORMANCE DIAGNOSIS
The same pass count can hide different failure patterns
Use three summaries and the spatial map together.
Systematic shift
-Mean signed residual reveals whether measurements sit mostly outside or inside.
Typical departure
-RMS gives a magnitude-sensitive overall error.
Worst observation
-Maximum absolute residual catches a local outlier.
Decision takeaway: A pass/fail badge is incomplete without the residual signs, magnitudes, and angular locations.
MEASUREMENT TRACEABILITY
Record these with a real verification
- Instrument resolution
- Coordinate datum
- Probe or target offset
- Temperature condition
- Point angular positions
- Tolerance authority
Applied decisions
Two different circle-verification patterns
Machined bore check
Four probe points are compared with a nominal center and radius.
What the result clarifies: Consistent positive residuals suggest an underspecified nominal radius or center error.
Mapped circular feature
Surveyed perimeter points are tested against a design circle.
What the result clarifies: The residual map shows where the as-built edge departs from the claim.
Worked default scenario
Current-input substitution and reconciliation
Method references
References for this calculator's specific method
Scope and limitations
This is a radial conformance audit against an entered circle, not a roundness standard, best-fit circle, minimum-zone circle, or metrology acceptance procedure. The tolerance must come from the governing drawing or specification.
Circle Verification Calculator | Point Residuals, RMS Error, and Tolerance Audit FAQ
What does a positive residual mean?
The measured point is farther from the claimed center than the claimed radius.
Can the mean residual be near zero while the circle fails?
Yes. Positive and negative errors can cancel even when RMS or maximum error is large.
Why show a tolerance annulus?
It spatially represents the accepted radial band r±T.
Does four-point verification prove roundness?
No. Sparse observations cannot establish full-form roundness.