Reconcile one conventional J-bend wheel side from measured ERD, hub-flange geometry, matched holes, and source-owned lacing—without an order approval.
Specialist tool for Cycling1 documented formulaFocused single-task workflowPrivate in your browser
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A quick decision brief for this specific tool
Inputs that matter
One de-identified completed wheelbuilder, owner/mechanic or reviewed-training conventional J-bend wheel-side record; responsible revision/date/reviewer; one exact wheel side; exact rim, hub, spoke, nipple and washer records; ERD, spoke pitch-diameter and center-to-flange measurement methods; matched rim/hub hole count; source-owned lacing; proprietary-geometry, compatibility, tension/dish, assembly/condition, safety/code, tolerance and review/retention boundaries; measured millimeter geometry; whole even total hole count and whole crossing count; completed theoretical-length report; and an optional same-record independent source and length
Output to expect
Rim and flange radii, side spoke-position count, reproduced same-side spoke-hole angle, raw theoretical three-dimensional spoke path, completed reported-minus-reproduced signed difference, and optional independent same-record difference
How it works
Validate every provenance field and positive bounded value; require pitch diameter below ERD; require an equal even whole rim/hub hole count; require a whole nonnegative crossing count below one quarter of total holes for the supported shorter arc; calculate the side hole angle as 4π times crossings divided by total spokes; solve the three-dimensional chord as the square root of R squared plus H squared plus D squared minus 2RH cosine angle; compare completed and optional paired independent reports without rounding or clamping; and normalize only mathematical zero
Confirm that wheel side, rim/hub/spoke/nipple/washer revisions, ERD end-position convention, measurement methods, matched drilling, lacing, completed report and optional independent report all match. Another side, component, convention, pattern or revision needs another run.
Use the result only for one completed conventional J-bend wheel-side geometry and transcription check. It does not choose or round a stock length; silently support straight-pull, paired, asymmetric, offset-hole or proprietary corrections; establish nipple engagement or washer correction; select spoke type/gauge/strength; validate tension, dish, alignment, stress relief, assembly, condition, wheel testing, safety or tolerance; or authorize purchase, build, service or riding.
Choose your path
Built around the job you need to finish
Reconcile one completed conventional J-bend wheel-side spoke-length geometry record without choosing an order length or approving components, wheel building, safety or use.
Wheelbuilder checking one exact wheel side
Replace the legacy half-angle formula and unconditional round-down instruction with traceable same-component geometry.
Freeze one rim/hub/spoke/nipple/washer revision and wheel side, measure ERD, pitch diameter and center-to-flange distance, verify matched holes and source-owned lacing, then enter the completed report independently.
Receives a reproducible raw theoretical path and signed report difference while stock-length and build disposition remain explicit external decisions.
Owner or mechanic auditing a replacement-spoke record
Avoid treating one generic flange offset or a nominal wheel label as proof of both side lengths or component compatibility.
Identify the exact side and components, retain the ERD/thread-end convention and measurement records, and compare only the controlled completed same-side length report.
Can detect geometry or transcription differences without receiving an unsupported purchase, reuse, installation, tension or riding approval.
Prevent another wheel side, component revision, ERD convention, drilling or lacing pattern from being presented as corroboration.
Use the optional report only when wheel side, exact components, measurement methods, holes, crossing count and formula basis match completely.
Gets deterministic paired validation and a separate independent difference without implying proprietary-geometry or complete-wheel acceptance.
Authoritative checks for this tool
Outputs and checklists are planning aids. Review the linked current authorities and the records, terms, instructions, and requirements that apply to your exact situation before a consequential decision.
Identify the exact rim, hub, spoke, nipple, washer state and intended fully threaded spoke-end position. A catalog ERD or another nipple convention is not automatically the same record.
Reproduce one wheel side
Use measured ERD, this flange's spoke pitch diameter, its center-plane distance, one equal even rim/hub hole count and a source-owned whole cross count.
L = √(R² + H² + D² − 2RH cos(4πC/N))
Compare reports without ordering
Keep the raw reproduced length, completed report and optional same-record independent report separate. Available stock, nipple engagement and rounding need a responsible wheelbuilder disposition.
Keep wheel-build acceptance external
Component compatibility, proprietary geometry, spoke type and gauge, tension, dish, alignment, stress relief, assembly, condition, wheel testing and safety are not established by length arithmetic.
Updated: August 2026
Example Scenarios
Reconcile one measured conventional flange and 3-cross record, then run the opposite side separately.
Enter zero crossings only when the exact hub/rim source owns that lacing; the Tool does not approve radial use.
Use the optional report only when the exact wheel side, components, measurements, ERD convention, holes and lacing match.
Common Mistakes to Avoid
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Using tire, bead-seat or outer rim diameter as ERD
✓
Use the effective spoke-end diameter under the named nipple and washer convention.
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Applying one flange distance to both wheel sides
✓
Run each side separately with its own pitch diameter and center-to-flange distance.
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Rounding down automatically
✓
Retain the raw theoretical path and document the component-specific stock-length and thread-engagement disposition separately.
FAQ
No. It reproduces a raw theoretical path. Available increments, nipple and washer geometry, thread engagement, manufacturing variation and the wheelbuilder's tolerance decide stock length.
Left and right flanges commonly have different pitch diameters and center-plane distances. Pooling them can hide different theoretical lengths.
Only when it belongs to the exact rim revision and matches the intended nipple, washer and spoke-end convention. Retain the source and measurement decision.
No. Zero is geometrically supported, but manufacturer permissions, hub/rim strength, brake/drive use and build acceptance remain external.
No. Length geometry does not establish spoke selection, tension, balance, dish, alignment, stress relief, assembly quality, condition or wheel-test compliance.
Not silently. Use it only if the manufacturer supplies an equivalent conventional measurement model for the exact product; otherwise use the specified method.
About Reviewed Wheel-Side Spoke-Length Record
Reproduce the raw theoretical spoke path for one exact conventional J-bend wheel side. Preserve component, measurement and lacing evidence; make stock-length and wheel-build decisions outside the arithmetic.
