A spoke calculator does one thing: measure the hypotenuse of a triangle in three dimensions. All the difficulty lies in the four numbers you feed it — and that is where most failed wheels go wrong.

The ERD, and the mistake that costs three millimetres

The ERD is the diameter of the circle on which the spoke ends come to rest, nipples fitted. It is neither the outer diameter of the rim, nor its inner diameter, nor the ETRTO: it is the distance from one spoke-hole seat to the seat opposite, nipple head included.

Why you don't have to go looking for it

The rims we use are Mach1 and Ryde, and their ERDs are published by the manufacturers. The list above reproduces them as they stand, one per model and per diameter. So the only thing you measure is the one thing we cannot know: your hub.

If you are building with another brand, measure it: two opposite spokes threaded into the rim, nipples wound down flush, the distance between the two spoke heads, plus twice the length of one spoke. Or ask the manufacturer for the figure, which is safer.

The four hub dimensions

They are taken with the hub in your hand, using a caliper, and they are not symmetrical: that is precisely why a left spoke and a right spoke almost never have the same length.

Left PCD and right PCD. The diameter of the circle through the centres of the spoke holes on each flange. The simplest way: measure from the outer edge of one hole to the inner edge of the hole diametrically opposite.
WG and WD. The distance from the wheel's centre plane — the exact midpoint between the locknuts, not the middle of the hub shell — to the inner face of each flange, where the spoke elbow bears.
The right side is the cassette side on a rear wheel, the disc side on a disc-braked front wheel. What matters is not which one you call right, but not mixing them up: right PCD and WD must come from the same flange.

The centre plane, not the middle of the hub

WG and WD are counted from the middle of the over-locknut dimension, that is, from the midpoint of the distance between the frame dropouts. On a rear wheel that point is never in the middle of the hub shell: the cassette pushes the right flange inwards. That offset is what produces the familiar dish.

What the calculation does

A spoke joins a point on the flange to a point on the rim. Those two points are separated by three independent gaps: a difference in radius (ERD/2 minus PCD/2), an angular offset from the cross, and a lateral offset (WG or WD). The length is the root of the sum of their squares — Pythagoras in three dimensions, nothing more.

The cross sets the angle: a spoke crossed by three points at a rim hole three spokes further round. The higher the cross, the more tangential the spoke is to the flange, the longer it is, and the better it takes torque — driving or braking. That is why nobody laces radially on the cassette side, the disc side, or a hub motor.

The millimetre too many

The result is given to a tenth, then rounded to the millimetre. If you are hesitating between two lengths, take the shorter one: a spoke a millimetre short still holds the thread, a spoke a millimetre long comes out of the nipple and punctures the tube through the rim bed.

Hands of a Mach1 operator holding four J-bend steel spokes — J-bend spokes — the ones this calculator sizes. — Photo Mach1

What the calculation does not tell you

It gives a geometric length, on an untensioned wheel exactly matching the figures entered. Three things escape it:

Tensioning. At 100 to 120 daN a spoke stretches by a few tenths and the rim pulls in slightly. That stays within the tolerance of rounding to the millimetre, but it explains why a tightly built wheel always feels a shade short.
Component tolerance. A published ERD is a nominal value; from batch to batch it moves half a millimetre. On an unfamiliar hub, measured with a workshop caliper, the uncertainty is of the same order.
Tension balance. The calculation gives you two lengths, not a durable wheel. On a heavily dished wheel the left spokes work at less than half the tension of the right ones, and they are the ones that come loose first.

It is also why we don't ask our customers for these dimensions: when a wheel comes in for rebuilding, the hub reaches the workshop and we measure it ourselves, on our machines, with our spokes. This calculator is here for those who build their own wheels — and to explain what we do.