What is ERD and how is it measured?

ERD (Effective Rim Diameter) is the diameter measured from spoke-nipple seat to spoke-nipple seat on the opposite side of the rim. It represents the effective circle where spoke nipples sit. Manufacturers often publish ERD specifications; alternatively, it can be measured by laying two spokes across the rim diameter at the nipple seats and measuring between their inside edges, then adding twice the spoke diameter.

Why does this calculator give different results than professional spoke calculators?

This tool assumes radial (0-cross) lacing with zero hub flange offset and symmetrical geometry. Professional calculators account for spoke crossing pattern (1-cross, 2-cross, 3-cross), left and right flange offset from the wheel centerline (dish), and spoke hole diameter. For a typical 3-cross 32-hole rear wheel, the crossing pattern alone can add 3–5 mm to the required spoke length compared to a radial calculation.

What is the 1.5 mm subtraction for spoke elbow?

The 1.5 mm adjustment accounts for the depth of the spoke elbow—the 90-degree bend at the hub end of a J-bend spoke. When the elbow seats in the hub flange hole, approximately 1.5 mm of spoke length is consumed by the bend geometry. Straight-pull spokes and some proprietary hub designs use different values.

Can I use this calculator for 3-cross lacing?

No. The formula assumes radial lacing where spokes run directly from hub to rim without crossing. A 3-cross pattern, where each spoke crosses three others on the same flange, changes the spoke angle and increases required length. The crossing angle α must be incorporated using the full formula L = √(d² + r² + R² − 2rR·cos(α)) − ø/2 for accurate results.

How do I measure hub flange radius?

Hub flange radius is measured from the hub axle centerline to the center of a spoke hole on the flange. Using calipers, measure the diameter across the spoke hole circle (pitch circle diameter or PCD), then divide by two. This measurement is distinct from the outer flange diameter; only the spoke hole circle matters for spoke length calculation.

Cycling

Spoke Length Calculator

Calculate radial spoke length from rim ERD, flange radius, and spoke hole count.

Last updated: 22 April 2026

What this tool does

This calculator estimates radial spoke length for bicycle wheel building using a simplified geometric formula based on rim ERD (Effective Rim Diameter), hub flange radius, and spoke hole count. It applies the radial approximation L = √((ERD/2)² + flange_radius²) − 1.5 mm, where 1.5 mm accounts for spoke elbow depth, and outputs the required spoke length in millimeters for zero-cross radial lacing. The calculation assumes symmetrical hub geometry with no flange offset and is most accurate for radial-laced wheels; crossed-spoke patterns require additional angular correction factors.

Inputs

Result

—

Formula Used

L_{r a d ia l} = (ERD /2)^{2} + r_{f l an g e}^{2} - 1.5 mm

R

Rim ERD in mm

n

Number of spoke holes

r

Flange radius in mm

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How Spoke Length Calculator works

This tool calculates radial spoke length for bicycle wheels using the rim's effective rim diameter (ERD), the hub flange radius, and the spoke hole count. The calculator assumes a radial (0-cross) lacing pattern, where spokes run directly from hub to rim without crossing other spokes. The formula subtracts 1.5 mm to account for the spoke elbow—the 90-degree bend at the hub end of a J-bend spoke. The output provides a starting reference for radial-laced wheels, a pattern occasionally used for track racing or lightweight front wheels.

The formula

The calculator implements a simplified radial spoke length approximation: L = √((ERD/2)² + r²) − 1.5 mm, where ERD is the effective rim diameter in millimeters, r is the hub flange radius in millimeters, and 1.5 mm is the elbow allowance. This equation treats the spoke as the hypotenuse of a right triangle formed by half the ERD (rim radius) and the flange radius. Most wheelbuilding references use the expanded formula L = √(d² + r² + R² − 2rR·cos(α)) − ø/2, where d is hub flange offset from the wheel centerline, R is ERD/2, α is the spoke angle determined by the crossing pattern (1-cross, 2-cross, 3-cross, etc.), and ø is the spoke hole diameter. This full formula accounts for wheel dish, crossing pattern, and spoke seat geometry—factors critical for accurate spoke length in nearly all practical wheel builds.

Where this method is most accurate

The simplified radial formula is accurate for perfectly symmetrical, radially laced wheels with zero flange offset and minimal spoke-hole countersink. Track front wheels, some disc-brake front hubs with centered flanges, and demonstration wheels fit these constraints. The approximation breaks down for crossed lacing patterns (the vast majority of road, mountain, and touring wheels), asymmetric rim profiles, dished rear wheels, and hubs with significant flange offset. A 3-cross 32-spoke rear wheel may require 2–5 mm longer spokes than the radial calculation suggests, depending on flange diameter and offset.

What this tool does not do

This calculator does not account for spoke crossing pattern, hub flange offset (dish), asymmetric rim profiles, or spoke-hole diameter variations. It does not provide spoke lengths for 1-cross, 2-cross, or 3-cross lacing—the patterns used in most rideable wheels. The tool does not verify whether the calculated length matches any commercially available spoke size (spokes are sold in 1 mm or 2 mm increments). For practical wheelbuilding, professional spoke calculators such as DT Swiss Spoke Calculator, Sapim Pi Tool, or Spokomat require five to seven measurements including left and right flange diameters, flange offset, and crossing pattern. This tool serves as an introduction to spoke geometry, not a substitute for comprehensive wheelbuilding software.

Disclaimer

This tool is provided for educational and informational purposes only. It is not a substitute for professional wheelbuilding consultation or detailed spoke-length calculation tools that account for all geometric parameters. Incorrect spoke length can result in wheel failure, loss of control, and injury. Users are responsible for verifying all measurements and selecting appropriate spoke lengths for their specific hub, rim, and lacing pattern before purchasing spokes or building wheels.

Questions

What is ERD and how is it measured?: ERD (Effective Rim Diameter) is the diameter measured from spoke-nipple seat to spoke-nipple seat on the opposite side of the rim. It represents the effective circle where spoke nipples sit. Manufacturers often publish ERD specifications; alternatively, it can be measured by laying two spokes across the rim diameter at the nipple seats and measuring between their inside edges, then adding twice the spoke diameter.
Why does this calculator give different results than professional spoke calculators?: This tool assumes radial (0-cross) lacing with zero hub flange offset and symmetrical geometry. Professional calculators account for spoke crossing pattern (1-cross, 2-cross, 3-cross), left and right flange offset from the wheel centerline (dish), and spoke hole diameter. For a typical 3-cross 32-hole rear wheel, the crossing pattern alone can add 3–5 mm to the required spoke length compared to a radial calculation.
What is the 1.5 mm subtraction for spoke elbow?: The 1.5 mm adjustment accounts for the depth of the spoke elbow—the 90-degree bend at the hub end of a J-bend spoke. When the elbow seats in the hub flange hole, approximately 1.5 mm of spoke length is consumed by the bend geometry. Straight-pull spokes and some proprietary hub designs use different values.
Can I use this calculator for 3-cross lacing?: No. The formula assumes radial lacing where spokes run directly from hub to rim without crossing. A 3-cross pattern, where each spoke crosses three others on the same flange, changes the spoke angle and increases required length. The crossing angle α must be incorporated using the full formula L = √(d² + r² + R² − 2rR·cos(α)) − ø/2 for accurate results.
How do I measure hub flange radius?: Hub flange radius is measured from the hub axle centerline to the center of a spoke hole on the flange. Using calipers, measure the diameter across the spoke hole circle (pitch circle diameter or PCD), then divide by two. This measurement is distinct from the outer flange diameter; only the spoke hole circle matters for spoke length calculation.

Sources & Methodology

Radial spoke length approximation: L = √((ERD/2)² + flange_radius²) − 1.5 mm. The 1.5 mm subtracts spoke elbow depth. This assumes 0-cross radial lacing, zero hub offset, and symmetrical geometry. The canonical crossed-spoke formula L = √(d² + r² + R² − 2rR·cos(α)) − ø/2 accounts for flange offset d, crossing angle α, and hole diameter ø. Derived from wheelbuilding geometry standards documented in professional spoke calculators (DT Swiss, Sapim).

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