Bicycle Spoke Length Calculator (Wheel Building)
Length of the spokes for a wheel you are building, from the rim's effective diameter, the hub flange, the spoke count and the lacing pattern.
Results
The dashed line marks the value you entered.
What this tool does
A spoke runs from a hole in the hub flange to a hole in the rim, so its length is plain geometry: the distance between two points, one on the flange circle and offset sideways from the wheel centre, the other on the rim circle, turned round by an angle that depends on how many spokes it crosses. Measure the ERD of the rim yourself, as the figure on the rim is a guide, and measure each flange of the hub: left and right differ on a disc or dished wheel, so calculate each side. Round to the nearest millimetre.
Formula
L = √(R² + r² + w² − 2 R r cos α) − d ÷ 2 · R = ERD ÷ 2, r = flange circle radius, w = flange offset, α = 720° × crosses ÷ spokes
Variables
| Symbol | Meaning | Unit |
|---|---|---|
erd | Effective rim diameter (ERD) | mm |
pcd | Hub flange diameter (spoke hole circle) | mm |
fo | Distance from the wheel centre to this flange | mm |
hd | Diameter of the spoke hole in the flange | mm |
ns | Total number of spokes | — |
cr | Crossing pattern (0 = radial, 2, 3, 4...) | — |
L | Spoke length | mm |
LR | Nearest whole millimetre | mm |
AN | Angle between the spoke and the radius | ° |
Worked example
- Effective rim diameter (ERD)600 mm
- Hub flange diameter (spoke hole circle)58 mm
- Distance from the wheel centre to this flange35 mm
- Diameter of the spoke hole in the flange2.6 mm
- Total number of spokes32
- Crossing pattern (0 = radial, 2, 3, 4...)3
- Spoke length290.9 mm
- Nearest whole millimetre291 mm
- Angle between the spoke and the radius67.5 °
Limitations
- Coverage and consumption figures vary between products. Take the values from the manufacturer's datasheet for the product you are actually using.
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.