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# How to Calculate Spoke Length

Updated March 23, 2017

Spoke length calculations are primarily for racing and mountain bike enthusiasts who design and package their bikes for peak performance. However, the same calculations or formulas can be applied to tricycle wheels, wheelchair wheels and motorcycle wheels. Spoke length is a relationship between rim radius, hub spoke radius and spoke anchor angle as to ensure perfect physical harmony between

the spoke, rim and the hub of the wheel. Proper length ensures roll stability and durability across rough terrain at high speeds. To calculate spoke length, you can use a formula for a radial spoke configuration or a cross-laced spoke configuration, whichever is applicable.

Measure and determine the following variables in units of millimetres: rim radius plus spoke penetration, or "RRSP," hub spoke radius, or "HSR" and spoke anchor angle, or "SAA." Use a micrometer to make these measurements in units of millimetres, or "mm."

Calculate the spoke length, or "SL," for a radial spoke configuration using the formula: SL = SQRT ((RRSP-HSR)^2 + HFO^2 where the word SQRT stands for square root and ^2 denotes to the power of 2.

Calculate SL for a cross-laced spoke configuration using the formula: SL = SQRT [ (RRSP - (HSR * cos(SAA)))^2 + HFO^2 - (HSR * cos(SAA))^2 ] where cos (SSA) means the cosine of SAA.

• Calculator
• Micrometer