This Web site covers the formula for calculating spoke length based on the measurements of the hub and rim. At the bottom of this page are the links to the related pages of this site. Included is a WHEEL BUILDING page that has a link to the best wheel building site I found on the Internet that could help out an inexperienced builder, and a LINKS page that has links to other Web sites that are cycling related and can provide anyone with information about bicycles and cycling. Throughout this site, text in red is usually links to other pages of the site, like the two just above, and sometimes links to other Web sites.
In order to be able to use the spoke length formula, you will need to be able to take measurements in millimeters (mm), preferably with a Metric tape measure, and you will need a calculator that can do square roots. If you only have an English tape measure, the numbers can be converted to Metric. A scientific calculator that can handle the cosine (COS) function would also be handy, but if you do not have one with the COS function I have included a page that has the COS figures for the most common hubs, this is the COSINE page. A page explaining the measurements that are needed, and how to convert from English to Metric is part of this site, it is very important that the measurements are done properly for the formula to be accurate, this is the MEASURE page. It is recommended that you look over this page before playing around with the formula to see what the measurements entail and what things to check for before starting. This page also tells how to compensate for rear rims that have offset and how to check for rims that have a large amount of spoke hole stagger from the center line that can affect the spoke length values.
There are compensations that need to be made to the calculated spoke length to figure out the proper spokes to get for your wheel. This is due to the fact that spokes stretch under tension. Different lacing patterns and the placement of the spoke (rear drive, non drive, or front) affects the build tension of the spokes, thus their length. These compensations are detailed in the SPOKE LENGTH TOLERANCE chapter of the LACING page. You must follow this information even if you know all of the needed values below, otherwise the spokes can end up being too long.
This site was designed around the bicycle wheels used on racing and mountain bikes, but the information applies to any laced wheel. Single speed and BMX bicycle wheels, tricycle wheels, wheelchair wheels, and motorcycle wheels all can use this formula to determine spoke length, mathematically there is no difference. It can also be used to determine spoke length for wheels for bike trailers, motorcycle sidecars and baby joggers. Any wheel built with spokes can have the spoke length calculated with this formula.
This site was initially constructed to help someone who is building a wheel using vintage or unusual components that aren't listed in spoke length tables. It can also help someone that wishes to calculate the length needed for building non typical wheels, for instance bicycle wheels laced with the Crow's Foot pattern that isn't listed in most spoke length calculators, or wheels for a wheelchair that have the rims off center. Or it can help someone who just wants to calculate spoke length so they don't have to ask down at a bike shop and rely on someone else every time they want to build a new wheel.
This site also has an extensive LACING page that covers many aspects about different lacing patterns. This page is divided into ten chapters that discuss everything from general lacing information to specific rear wheel information including lacing patterns that make for stronger rear wheels. This page also has a CUSTOM LACING PATTERNS chapter that has information about semi-custom patterns (unusual, but done by others), and information on how to design your own fully custom pattern. Included in this chapter are downloadable BMP images of 24, 28, 32, 36, and 48 spoke wheel blanks that can be used to design a lacing pattern and figure out the effective length of the spokes (to aid in calculating the proper spoke lengths). The information on this page will be valuable to anyone interested in learning about spoked wheels.
The formula works off of trigonometry law of right triangles, the length of the longest side squared equals the sum of the squares of the two shorter sides. It also uses the cosine factor of right triangles, which is dependent on the number of spokes in the wheel and the lacing pattern. I have included a page that explains all of this in more detail, the TRIG page. In addition to explaining how trigonometry applies to the formula, this page explains the basic physics of a spoked wheel and how the major weight bearing and road stresses and shocks affect a spoked wheel.
For spokes laced radially from the hub, the formula is simple because all you need to know is the radius at the rim, the radius at the hub and the hub flange's offset from the hubs center. For cross laced patterns, the formula is more complex because in addition to the above, you also need to figure in the distances of both the horizontal and vertical displacement of the spoke at the hub, which is related to where the spoke would go if it was laced radially and the Cosine value of the spoke hole on the hub. Here are the two formulas:

RADIAL SPOKE FORMULA radial spoke formula


CROSS LACED SPOKE FORMULA crossing spoke formula

SL = Spoke Length
RRSP = Rim Radius plus Spoke Penetration
HSR = Hub Spoke Radius
SAA = Spoke Anchor Angle
HFO = Hub Flange Offset

The SL is the calculated value of the spoke length you are looking for.
The RRSP is the radius of the inside of the rim plus the penetration of the spoke into the rim, which is half of the ERD (Effective Rim Diameter) value some rim manufacturer's give plus 2mm for the spokes penetration into the nipple (1/2 ERD + 2).
The HSR is the radius of the spoke holes on the hub. The radius needed is not of the centers of the holes but of their outer most edge.
The SAA is the angle of the spoke hole in the hub that the spoke will connect to, in relation to the spoke hole in the hub that is directly in line with the spoke hole in the rim where the spoke connects. It is dependent upon the lacing pattern. Radial wheels don't have any crosses so the anchor spoke hole of the hub is directly in line with this hole in the rim and the SAA is 0.
The HFO is the distance from the hubs flanges to the hubs center. On most front, or other non dished wheels, this is simply the distance between the flanges divided by two. For wheels with dish like most rear wheels, or for a wheel you would like to build off center, this is different for each side of the hub.

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wheel measure cosine
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