How this calculation works
A spoke spans both a lateral offset and an angular displacement between hub flange and rim. Changing cross pattern changes that angular displacement, so the length cannot be found from rim radius minus flange radius alone.
Angle = 2π × crosses/(total spokes/2); length = sqrt(R² + r² + offset² − 2Rr cos(angle)) − hole diameter/2A worked example
For a 600 mm ERD, 60 mm flange diameter, 35 mm offset, 32 total spokes and three crosses, the angular displacement is 67.5 degrees. The unadjusted geometric distance is about 291.953 mm. Subtracting half a 2.6 mm flange hole gives about 290.653 mm. This result is deliberately not rounded to a commercial spoke length; stock selection depends on the actual components and engagement requirements.
Good to know
Conventional one-side J-bend geometry only; no straight-pull dimensions, spoke tension, nipple engagement, strength or build approval. Small measurement errors can alter stock selection. Verify ERD and hub measurements using the component maker’s method before ordering or assembling a wheel.
Reference: Park Tool — measuring rim and hub for spoke length (opens in a new tab) ↗
What this model answers
A spoke spans both a lateral offset and an angular displacement between hub flange and rim. Changing cross pattern changes that angular displacement, so the length cannot be found from rim radius minus flange radius alone.
This page calculates one side of a conventional equally spaced J-bend wheel. The left and right flange offsets can differ, particularly on dished wheels. Run each side with its own flange dimensions rather than assuming the first result applies to the whole wheel.
The Bicycle climbing power and grade calculator models the mechanical effort of riding a completed bicycle. It does not validate spoke length, wheel tension or component compatibility.
Measure the right inputs
Effective rim diameter must locate the intended spoke-end seating position with the actual nipple arrangement. It is not automatically the nominal wheel size, tyre bead-seat diameter or outside rim diameter.
Flange diameter is measured through the centers of its spoke holes. Lateral offset is from the wheel center plane to the selected flange. The flange-hole diameter contributes a simple radius subtraction in this conventional geometric approximation.
Read the result in context
The formula first calculates the distance to the center of the flange hole, then applies the entered hole-radius correction. Real spoke bends, nipple thread engagement and drilling offsets can require manufacturer-specific treatment.
Total spoke count must be divisible by four within the supported range. The cross-count bound prevents unsupported lacing-angle combinations, but passing it is not a recommendation to use that pattern on the actual hub and rim.
Work through the numbers
For a 600 mm ERD, 60 mm flange diameter, 35 mm offset, 32 total spokes and three crosses, the angular displacement is 67.5 degrees. The unadjusted geometric distance is about 291.953 mm.
Subtracting half a 2.6 mm flange hole gives about 290.653 mm. This result is deliberately not rounded to a commercial spoke length; stock selection depends on the actual components and engagement requirements.
Where the model stops
Conventional one-side J-bend geometry only; no straight-pull dimensions, spoke tension, nipple engagement, strength or build approval.
Small measurement errors can alter stock selection. Verify ERD and hub measurements using the component maker’s method before ordering or assembling a wheel.
A few questions, answered
Which rim diameter should I enter?
Use effective rim diameter at the intended spoke-end seat, measured for the nipple arrangement being used.
Does this choose a stock spoke size?
No. It returns the geometric estimate; it does not apply a universal rounding or engagement rule.