Spoke Length Calculator

Brandt Equation 1, from The Bicycle Wheel by Jobst Brandt.

Formula: L = sqrt(A² + B² + C²) − S/2

A = (d/2) × sin(T) spoke offset at flange

B = D/2 − (d/2) × cos(T) radial component

C = W center-to-flange distance

T = 360 × X / (N/2) spoke angle in degrees

Inputs

D — ERD (mm) S — spoke hole diameter (mm) N — total spoke count X — cross pattern (0–4) d_L — left flange PCD (mm) d_R — right flange PCD (mm) W_L — left center-to-flange (mm) W_R — right center-to-flange (mm)

Notes

Always round down to the nearest whole mm — spokes stretch and rims shrink under tension.
ERD is measured to where spoke ends sit flush with the top of the nipple, not the rim bed.
Flange PCD (d) is measured center-to-center across opposite holes, not the outer flange diameter.
W is the distance from the hub center to the inner face of each flange (the face closest to the center of the hub), measured independently per side.
For dished rear wheels the left and right values will differ — calculate each side separately.
Spoke length is measured from the inside of the J-bend elbow to the threaded end.
Spokes must be within 1mm of correct length for safe engagement and thread clearance.
For radial lacing (X=0), T=0° and the formula simplifies to sqrt((D/2 − d/2)² + W²) − S/2.