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Bicycle Calculator
Unites • SI

Spokes

Guide & Objectives

Calculate the exact spoke length for building your bicycle wheels. This tool applies standard trigonometric formulas to guarantee precise and secure lacing, regardless of the cross pattern.

1

Objective

1 - Determine the exact spoke length for left and right sides. 2 - Account for the hub offset (dishing). 3 - Ensure proper wheel tension and balancing.

2

How to use

1 - Enter the rim's effective diameter (ERD) and spoke count. 2 - Measure and input the left and right hub dimensions. 3 - Select the number of crosses.

3

Value

1 - Avoid buying spokes that are too short or too long. 2 - Get a standard rounded value for purchasing. 3 - Generate a detailed wheel building report with your measurements.

Understanding spoke length calculation

Spoke length is not a universal value and must be calculated for each wheel individually. It depends on the hub geometry, the rim diameter and profile, and the chosen crossing pattern. An error of a few millimetres makes lacing impossible or prevents reaching the recommended spoke tension.

Calculation parameters

Three elements come into play:

1 - The hub
- Left flange diameter
- Right flange diameter
- Flange spacing
- Number of holes.
It is important to note that on a rear hub, dimensions differ between the drive side (right) and the non-drive side. The right flange (drive side) sits closer to the hub centre than the left flange. This asymmetry directly affects spoke length on each side.

2 - The rim
- Effective diameter = ERD — Effective Rim Diameter
That is, the inner diameter at the spoke nipple seat. A value is provided by the manufacturer, but it can also be measured directly.

3 - The crossing pattern
- Cross count
That is, the number of times a spoke crosses others before reaching the rim. 3-cross (3×) is the all-round standard. Radial (0×) is light and aesthetic but concentrates stress on the flanges — not recommended for disc brakes.

Radial vs 3-cross

TypeExample useAdvantagesDisadvantages
Radial (= 0 cross)Light front wheelMinimal weight, clean lookHigh flange stress
2-crossRoad racingLight, laterally stiffLess comfort than 3×
3-crossAll-roundBest cushioning, standardSlightly heavier
4-crossHeavy loads / tandemMaximum strengthLonger spokes, more weight

Enter your hub and rim dimensions in the calculator below to get exact spoke lengths for both left and right sides.

1. Rim & General

mm
mm

2. Left Hub

mm
mm

3. Right Hub

mm
mm

Spoke Length (Left)

-- mm

Exact value: -- mm

Spoke Length (Right)

-- mm

Exact value: -- mm

Spoke Length (Left)
-- mm
Spoke Length (Right)
-- mm
Warning and Disclaimer

Building bicycle wheels is a critical mechanical operation directly impacting rider safety. The calculations generated by this tool are provided for informational purposes only, based on theoretical models.

They depend entirely on the absolute precision of the physical measurements provided by the user. The creator of this site accepts no responsibility for incorrect calculations, incompatible dimensions, equipment breakage, accidents, injuries, or damages resulting from the use of this data.

A wheel should be built, trued, and tensioned by competent personnel using a calibrated tension meter.

Learn More

1. ERD (Effective Rim Diameter)

Nipple seat diameter inside the double-wall rim.

Distance D ERD
  1. Cut 2 spokes to 200 mm. Thread a nipple until the bottom of the slot.
  2. Insert them. Measure the distance D between the two ends.
  3. Formula: ERD = 200 + 200 + D

2. W (Center-to-Flange Offset)

Top view. Horizontal distance between the hub's mathematical center (frame midline) and each flange.

TABLE CENTER (OLD / 2) O.L.D. WL WR H
  • Identify the OLD (e.g., 142mm). The wheel center is at OLD / 2.
  • Place the hub flat. Measure height (H) from the table to the middle of the flange.
  • Formula: W = (OLD / 2) - H

3. d (Pitch Circle Diameter PCD)

Diameter of the imaginary circle passing through the center of all holes on the same flange.

d
  • Measure the direct distance between the center of one hole and the center of the diametrically opposed hole.
  • Tip: Measure from the outside edge of one hole to the outside edge of the diametrically opposite hole. Then subtract the diameter of one hole.

4. S (Flange Hole Diameter)

Hole measurement. Necessary because the spoke elbow rests on the hole edge, not in its center.

Ø S
  • Use the upper jaws (inside measuring jaws) of your caliper.
  • Standard values for J-Bend spokes: usually 2.4 mm, 2.5 mm, or 2.6 mm.

The Fundamental Equation of Spoke Length

Calculating the length of a spoke relies on a representation of the wheel’s geometry in space. The spoke forms the hypotenuse of a triangle whose other sides are defined by the geometry of the hub and the rim.

L=R2+d2+W2−2⋅R⋅d⋅cos⁡(α)−S2L = \sqrt{R^2 + d^2 + W^2 - 2 \cdot R \cdot d \cdot \cos(\alpha)} - \frac{S}{2}

Variable Nomenclature:

  • LL: Exact spoke length (mm)

  • RR: Effective rim radius (Corresponds to ERD/2ERD / 2) (mm)

  • dd: Hub bore radius (Corresponds to half the PCD / Flange Diameter) (mm)

  • WW: Center-to-Flange Distance (Flange Offset) for the side being studied (mm)

  • α\alpha: Crossing angle in radians. Defined by the number of crossings (XX) and the total number of spokes (NN): α=720⋅XN⋅π180\alpha = \frac{720 \cdot X}{N} \cdot \frac{\pi}{180} (rad)

  • SS: Hub bore diameter. Subtracting S2\frac{S}{2} corrects the distance to stop at the edge of the hole (where the spoke bend rests) and not at its center (mm)

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