How to use the calculator
- Enter the rim ERD. It’s in the manufacturer’s specs. If you have the rim, measure it (see how below).
- Choose the spoke count: the number of holes in the rim, which must match the hub.
- Enter the hub measurements for each side: the flange diameter (PCD) and the distance from hub center to flange. On a non-disc front wheel both flanges are the same: turn on “Both flanges equal”.
- Choose the cross pattern for each side. Three-cross is the classic for 32 and 36 spokes; two-cross for 24 and 28; radial only where the hub maker allows it (usually non-disc front wheels).
- If the rim is asymmetric, enter its offset: how far the spoke holes are shifted from the center.
- Read the length for each side and what to buy.
The left side is the disc side on front wheels and the non-drive side on rear wheels.
How we calculate spoke length
Picture the spoke as the diagonal of a box: it runs from the flange hole to the nipple in the rim. The law of cosines gives the distance in the plane of the wheel, and adding the sideways distance to the flange gives the total length:
L = √( d² + r₁² + r₂² − 2 · r₁ · r₂ · cos α ) − s ÷ 2
α = 4π · crosses ÷ number of spokes
- d: distance from hub center to flange.
- r₁: flange radius (PCD ÷ 2).
- r₂: effective rim radius (ERD ÷ 2).
- α: the angle the spoke sweeps at the flange. With 28 spokes and 3-cross, it’s 77°.
- s: diameter of the spoke hole in the flange. We subtract half of it because the spoke head bears on the edge of the hole, not its center.
Asymmetric rims (offset)
On an asymmetric rim the spoke holes aren’t centered: they’re shifted toward the farther flange to even out tension. We subtract the offset from that flange’s distance and add it to the other. For example, flanges at 35 and 18 mm with a 3 mm offset are calculated as 32 and 21 mm.
Bracing angle and tension
The bracing angle is how much the spoke leans toward its flange. The larger it is, the stiffer the wheel laterally. Because both sides have to balance, the tension on each side is inversely proportional to the sine of its angle:
T left ÷ T right = sin θ right ÷ sin θ left
In the example the calculator opens with (a 28-spoke rear wheel with flanges at 35 and 18 mm), the left side ends up at 52% of the right side’s tension. With a 3 mm offset rim it rises to 66%: that’s why offset rims exist.
How many spokes and how many crosses
More spokes make a wheel stronger and easier to repair, but heavier. On stock wheels, the most common setups are:
| Use | Front | Rear | Crosses |
|---|---|---|---|
| Lightweight road | 20-24 | 24-28 | Radial or 2 front, 2 rear |
| Road and gravel | 24-28 | 28 | 2 or 3 |
| Mountain | 28-32 | 28-32 | 3 |
| Loaded touring or tandem | 32-36 | 36 | 3 |
With disc brakes, the spokes on the disc side can’t be radial: they have to transmit braking torque, so they’re crossed. The same goes for the drive side of a rear wheel.
How to measure ERD and the hub
ERD. Take two spokes of known length, thread a nipple onto each and insert them into two exactly opposite holes in the rim. Pull them toward the center, measure the distance between the two spoke ends inside the rim and add twice the length of nipple the spoke reaches into. Repeat on two other holes and average the results. This is the method Damon Rinard describes.
Flange diameter (PCD). It’s the center-to-center distance between two opposite holes on the same flange. To measure it with calipers, go from the inner edge of one hole to the outer edge of the opposite one: that gives the same result as center to center.
Center to flange. Measure the distance between the outer faces of the locknuts (the hub width, for example 100, 142 or 148 mm; the widths for each standard are in the axle sizes chart) and divide by two: that’s the center. Then measure from the outer face of each locknut to the middle of its flange’s thickness and subtract that from half the width. Many hub makers publish these measurements in their tech specs.
How much each measurement matters
With the example wheel (ERD 600, 45 mm flange, 28 spokes, 3-cross):
| If you’re off on… | By | The spoke changes |
|---|---|---|
| ERD | 1 mm | 0.5 mm |
| Center-to-flange distance | 1 mm | 0.1 mm |
| Flange diameter | 1 mm | 0.1 mm |
That’s why ERD matters most. As for crosses: with 32 spokes, going from 2-cross to 3-cross makes each spoke about 7 mm longer.
Common mistakes
- Trusting the catalog ERD without checking. It changes between model years and versions of the same rim, and some manufacturers measure it differently. Measure it.
- Using the formula on a straight-pull hub. The spoke head doesn’t sit in a flange hole and the geometry is different. Use the hub maker’s calculator.
- Forgetting the offset on an asymmetric rim. With a 3 mm offset the spoke length changes little, but the tension balance does.
- Mixing up sides. On the rear, the cassette side is the right side: flange closer to the center, slightly shorter spokes and higher tension.
- Too many crosses. If the spoke sweeps more than 90° at the flange, it passes over the head of its neighbor. The calculator only lets you pick cross patterns that are possible for your spoke count.
Building the wheel for gravel or mountain? Check which tires your rim takes in the tire size converter.
Frequently asked questions
What is rim ERD?
The Effective Rim Diameter: the diameter at which the spoke ends sit inside the nipples. The manufacturer lists it in the rim specs, but it's worth measuring: a 2 mm error changes spoke length by 1 mm.
Why are spokes different lengths on each side?
Because on a rear wheel (and a disc front wheel) the flanges aren't the same distance from the center. On the rear, the cassette side has its flange closer to the center, so its spokes are a bit shorter and run at much higher tension.
Should I round spoke length up or down?
To the nearest millimeter, and if it falls right in the middle, round down: the spoke stretches a little under tension and the threads shouldn't poke through the nipple. Spokes are sold in 1 or 2 mm steps.
Does this work for straight-pull hubs?
No. On straight-pull hubs the spoke head exits tangent to the flange and the geometry is different. Use the hub maker's data and calculator, or a calculator with a straight-pull mode.