Spoke Length Calculator (Wheel Building)
Calculate spoke length for building a bicycle wheel from the rim ERD, hub flange diameter, flange offset (centre to flange) and spoke hole diameter, for each side separately, with 1-, 2-, 3- or 4-cross or radial lacing and any spoke count — plus the recommended rounding and dish check.
How it works
L = √(r² + R² + d² − 2 r R cos θ) − hole ÷ 2, with r = flange radius, R = ERD ÷ 2, d = flange offset, θ = 360° × crosses ÷ (spokes ÷ 2)
A spoke runs from a hole on the hub flange to a hole on the rim, and its length is the three-dimensional distance between them: the flange radius and rim radius form a triangle whose included angle depends on how many spokes the lacing crosses, while the flange's offset from the wheel centre adds the third dimension. Subtracting half the spoke-hole diameter accounts for the spoke elbow sitting at the edge of the hole. Because a rear hub's drive-side flange sits close to the centre to make room for the cassette, the two sides have different offsets and hence different lengths and tensions — the "dish" that makes rear wheels harder to build. Getting ERD right is everything: it is measured at the nipple seat, not the rim edge, and errors double into the spoke length.
Worked example
A 32-hole 3-cross wheel on a 602 mm ERD rim with 45 mm flanges, left offset 33 mm and right 18 mm needs spokes of about 293.7 mm on the left and 292.4 mm on the right — order 294 and 292 mm. The left bracing angle is 6.5°, the right only 3.5°, so drive-side tension will be roughly 1.8× the non-drive side.
Frequently asked questions
What is ERD and how do I measure it?
Effective rim diameter: the diameter at which the spoke ends sit — roughly the rim's inner diameter plus twice the nipple head thickness. Measure by fitting two spokes with nipples opposite each other, taping them and measuring across, or trust the rim maker's published value.
Should front and rear spokes differ?
Yes, usually — the rear drive side is shortest because of the cassette offset; disc-brake fronts also differ slightly side to side. Buy each side's length separately and label the bundles.
Related calculators
Standard bicycle-mechanics formulas (spoke-length geometry, ETRTO circumferences, Sheldon Brown / Park Tool conventions). Measure your own components — rim ERD, hub dimensions and tyre size vary by make — and verify on the bike before cutting or ordering.