How the length is calculated
Each spoke forms a triangle with the hub flange and the rim: the flange radius, the rim radius and the flange offset. The angle at the hub is 720 degrees multiplied by the cross count and divided by the total spoke count, which is 67.5 degrees for a 32 spoke three-cross wheel.
Length = square root of (flange radius squared + rim radius squared + offset squared - 2 x flange radius x rim radius x cos of the angle), less half the spoke hole diameter. The subtraction accounts for the hole the spoke seats in.
Worked example
A 600 mm effective rim diameter, a 45 mm flange, offsets of 35 mm left and 20 mm right, 32 spokes and three crosses give 292.9 mm on the left and 291.5 mm on the right. The spoke angle is 67.5 degrees.
The 1.4 mm difference comes from the flange offsets. A rear hub with a cassette has a much shorter right offset, so the right spokes are shorter.
Getting the measurements right
Effective rim diameter is not the same as the bead seat diameter. It is measured to where the spoke nipple sits, and rim makers publish it because it varies between otherwise similar rims.
Flange offsets are measured from the hub centre line to the centre of the flange, not to its outer face. A 1 mm error moves the answer by well under a millimetre, but a wrong effective rim diameter moves it by half as much as the error.
Limits of this calculator
It assumes a symmetric rim, radial spoke holes and no spoke stretch. It does not account for offset spoke holes, hub flange thickness, nipple type or the difference between nominal and actual rim diameter.
Round to the nearest stocked length, and check the result against the rim maker's own chart where one is published.
For overall wheel and tyre diameter, use the UK wheel size calculator.
Inputs for the spoke calculator
Effective rim diameter
The rim maker's ERD, measured to where the spoke ends sit rather than the bead seat.
Hub flange diameter
Pitch circle diameter across the spoke holes, centre to centre.
Left flange offset
Distance from the hub centre line to the left flange.
Right flange offset
Distance from the centre line to the right flange. Rear hubs differ left to right.
Spoke count
Total spokes in the wheel, such as 32 or 36.
Cross pattern
How many other spokes each spoke crosses, usually three.
Spoke hole diameter
Diameter of the flange hole, usually about 2.6 mm.
CALCULATOR QUESTIONS
Spoke calculator UK questions
Why are the left and right lengths different?
The flange offsets differ, especially on a rear hub with a cassette, so each side forms a different triangle.
What is effective rim diameter?
The diameter to the spoke seating surface, which is smaller than the bead seat diameter and published by the rim maker.
Do I round up or down?
Round to the nearest stocked length. Too long is worse than slightly short, but a length more than 2 mm out will not tension correctly.
Does spoke stretch matter?
A little. The calculation is nominal; most builders accept the small difference rather than adjusting for it.