Spoke Length Calculator

How Spoke Length Calculator works

Spoke length is fixed by four things: how far the nipple seats sit from the axle, how far the hub's spoke holes sit from the axle, how far that flange sits sideways from the wheel centreline, and how far around the hub the spoke travels before it reaches the rim. Enter the rim ERD, the hub flange pitch circle diameter, the flange offset, the spoke count, and the crossing pattern, and the tool returns the length for that one flange. A dished rear wheel has a different offset on each side, so it needs two runs, one per flange.

The formula

L = √(d² + R² + F² − 2·R·F·cos α) − hole/2

R is the rim radius, ERD ÷ 2. F is the flange radius, the spoke-hole pitch circle diameter ÷ 2. d is the flange offset from the wheel centreline. The spoke angle is α = 720° × crossings ÷ spoke count, so a 3-cross 32-spoke wheel gives 720 × 3 ÷ 32 = 67.5°. The law of cosines gives the spoke's length as projected onto the plane of the wheel, and the offset d turns that into the true three-dimensional length. Finally, half the hub's spoke-hole diameter is subtracted, taken here as 2.6 mm, so 1.3 mm; real hubs run about 2.4 to 3.0 mm, a spread of only 0.3 mm across that whole range.

Working the default: R = 300, F = 22, d = 35, α = 67.5°, so d² + R² + F² = 1,225 + 90,000 + 484 = 91,709, and 2 × 300 × 22 × cos 67.5° = 13,200 × 0.38268 = 5,051. The square root of 86,658 is 294.4, less 1.3, giving 293.1 mm.

Why the crossing pattern changes the answer so much

At radial lacing α is zero, cos α is 1, and the formula collapses to √(d² + (R − F)²): the spoke spans the difference between rim radius and flange radius. Every crossing swings the spoke further around the flange and lengthens it. On the default wheel the progression is 278.9 mm radial, 280.7 mm at 1-cross, 285.7 mm at 2-cross, 293.1 mm at 3-cross, and 301.5 mm at 4-cross. That is 14.2 mm between radial and 3-cross, on a component sold in 1 and 2 mm steps, which is why a radial figure cannot stand in for a crossed build. The effect grows with flange size, so a large-flange track hub separates further still.

Measuring the inputs

ERD is measured nipple seat to nipple seat across the rim, and rim makers publish it, though published figures and measured ones sometimes disagree by a millimetre or two. The flange pitch circle diameter is measured across the circle the spoke holes sit on, centre of hole to centre of hole on the far side, not the outer edge of the flange. Flange offset is the distance from the wheel centreline, the midpoint between the locknuts, out to the flange face. Front hubs are usually close to symmetrical, while a rear hub sits the drive-side flange much nearer the centreline to make room for the cassette, which is why the two sides need different spokes.

Where this method is most accurate

This is the same formula the manufacturers' own calculators use (DT Swiss, Sapim), so the arithmetic is not the limiting factor: the measurements are. An ERD that is 2 mm out moves the answer by about 1 mm, which is a whole spoke size. Straight-pull hubs, hubs with asymmetric or offset flanges, and rims with an offset spoke bed all need geometry this five-input model does not capture. Before ordering, it is worth checking the figure against the hub and rim maker's published data or a dedicated wheelbuilding tool (Musson, Wheelbuilding).

What this tool does not do

It calculates one flange at a time and does not compute both sides of a dished wheel in a single pass. It does not check whether the answer matches a length any manufacturer stocks, or handle straight-pull and proprietary hub interfaces, asymmetric rims, or hub-specific hole chamfering. It does not judge whether a chosen crossing pattern suits the wheel's intended use.

Disclaimer

This tool is provided for educational and informational purposes only. It is not a substitute for professional wheelbuilding consultation or the hub and rim manufacturers' own specifications. Incorrect spoke length can result in wheel failure, loss of control, and injury. Users are responsible for verifying all measurements and confirming spoke lengths for their specific hub, rim, and lacing pattern before purchasing spokes or building wheels.