Bicycle Spoke Length Geometry Calculator

Method and units

With rim radius R = ERD/2, flange radius r = flange diameter/2, lateral offset z and angle θ = 2π × crosses ÷ spokes per flange, length = √(R² + r² + z² − 2Rr cos θ). Round to the nearest millimeter only for presentation; actual spoke selection must follow rim and hub maker guidance.

Worked example

For 600 mm ERD, 45 mm flange diameter, 32 spokes, 3 crosses and 35 mm flange offset, θ = 67.5° and the calculated spoke is about 294.2 mm.

Supported inputs and interpretation

ERD 200–800 mm; flange diameter 10–100 mm; offset 0–100 mm; total spokes 16–48, even; crossings 0–6 and fewer than spokes per flange. Results are rounded for display only; internal calculations retain full JavaScript precision. Entered measurements and assumptions determine the answer.

References and limitations

The equations here use the stated unit conversions and geometric or accounting relationships; no empirical vehicle limits or manufacturer presets are supplied.

Assumes evenly spaced holes and a conventional laced wheel; it does not cover paired/asymmetric holes, nipple engagement, washers, radial restrictions or build tolerances. Confirm inputs and length with the rim/hub manufacturers or a qualified wheel builder. Geometry is not build approval.

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This planner performs the stated arithmetic; it is not a vehicle inspection, engineering approval, manufacturer's recommendation or professional review.