Spoke Calculator

This spoke length calculator can be used to figure out which lacing pattern to use, and how long the spokes will need to be. It supports many unusual features, such as mixed lacing, offset frames and rims, and high-low hubs. To help decide which lacing pattern to use, it computes spoke pull angles. It also computes spoke tensions for dished wheels and uses this to compute spoke stretch for a little extra accuracy.

Instructions

All measurements are in mm. Use a decent vernier caliper for accuracy. If you're building both front and rear wheels, measure both rims and hubs. As front wheels are always symmetric, you'll enter the same data for both drive and non-drive sides.

Enter the wheel data:

Enter the number of spokes. This is typically 32 or 36, with 32 being more common today. I recommend verifying that your rim and hub are compatible. Jobst Brandt^*, among others, recommends using more thin spokes rather than fewer thick spokes for durability.
Enter the lacing pattern. A good rule of thumb is to divide the number of spokes by 9, rounding down. This gives 3-cross for 32h wheels and 4-cross for 36h wheels. Most wheels are built 3-cross today. You can experiment to see what pattern gives you the most tangential spoke pull angle. Using too many crosses can cause spoke head interference problems at the hub for very large or small hub flanges. It can also cause the spokes to enter the rim at too great a angle for very small rims. For example, it's probably best to avoid 4-cross on a 36 spoke BMX wheel. Normally, both sides will use the same lacing. Use 0 for radial lacing (not recommended).
Enter the offset. This should be zero except for frames with their dropouts off-center. Use a positive number if the dropouts are shifted towards the drive side (to reduce wheel dish).

Measure your rim:

If your rim is listed in the rim menu, you can choose it to load the data for that rim. If not, proceed with your measurements...
Measure several diameters and average them. Use spoke nipples and old spokes, as described in Roger Musson's^** User Guide for his spoke length calculator. However, for this calculator, measure from the top of the nipple since spoke stretch is calculated precisely. Note that this is the most important measurement, so do this carefully!
Measure the hole offsets relative to the center of the rim, measured perpendicular to the rim. Normally, the drive and non-drive offsets will be equal and positive. For offset rims such as the Ritchey Rock OCX, the drive hole offset may be negative, indicating that it's to the left of the center of the rim. For example, offsets of -5.0 mm (drive) and 7.0 mm (non-drive) would indicate that the holes are staggered by 2.0 mm and are offset towards the non-drive side by 6.0 mm. This would produce approximately the same spoke tension on the drive and non-drive sides for a typical rear wheel.

Measure your hub:

If your hub is listed in the hub menu, you can choose it to load the data for that hub. If not, proceed with your measurements...
Measure the axle length between the flat spots which seat against the dropouts. The axle will extend several millimeters beyond this on either end.
Measure the flange insets by placing the hub over a hole so that the axle sticks down into the hole. Then measure vertically from the outer edge of the flange down to the surface. For rear hubs, repeat for the other side.
Measure the flange diameter by averaging measurements from the inner and outer edges of the holes. Then divide by 2 to get the radius. For high-low hubs, measure both ends.
Measure the hole diameter by finding a nail or similar object which just barely fits. This is also a fairly sensitive measurement.

Enter the spoke data:

If your spokes are listed in the spoke menus, you can choose them to load the data for those spokes. If not, proceed with your measurements...
For straight gauge spokes, enter the spoke diameter under both "diameter" and "butt diameter". Use 2.0 for 14g or 1.8 for 15g. Enter a butt length of 0.
For butted spokes, enter the larger diameter under "diameter" and the narrower diameter under "butt diameter". Use 1.8 for 15g or 1.6 for 16g. For other gauges, measure the spoke diameter. Measure the length of the narrow section and enter it under "butt length". Use your finger tips to see where the spoke changes diameter if you can't see it.

Press the Calculate button:

If "Invalid data" shows up in the status bar, the field with invalid data gets focus. Either there is a typo, or the value is out of range.
Experiment with different lacing patterns to see which gives the most tangential (closest to 90 degrees) spoke pull angles, as described above.
When you are satisfied with everything, take the lengths shown and round down to the nearest available length. Many stores only stock even lengths, but odd lengths are available. For very short spokes, you may have to have a store cut spokes for you, but my advice is to order pre-cut spokes if you can find them.

Calculator

Wish List

Make initial values be blank instead of zero.

Sort menus either alphabetically or in the order they appear in the main files.

Possibly combine all the data into a single file for download efficiency.

Use Jdoc format for comments and put resulting html online.

Calculate angle spoke enters rim at. Roger Musson suggested keeping this angle no more than 9 degrees from perpendicular.

Feedback

If you find this useful or have any comments, please send me an email. If you send me your measurements, I'll add them to the menus so the next wheel builder won't have to repeat the process. If you find any of the component data inaccurate, please let me know. I suspect there is quite a bit of variation.

Assumptions

The maximum spoke tension (ie. that used on the drive side of a dished wheel) is 180 N.

The desired spoke tension (ie. that used on undished wheels) is 3/4 of the maximum: 135 N.

Spokes are made of steel: modulus of elasticity = 21000 N/mm² (from The Bicycle Wheel^*). Titanium spokes aren't recommended.

The calculator does not compensate for rim shrinkage due to spoke tension. This can reduce the rim diameter by as much as 2 mm, depending on the rim.

References

* The Bicycle Wheel, by Jobst Brandt. Formulae for approximating spoke stretch were taken from this book.

** Roger Musson's spoke length calculator. Ideas for measuring rims were taken from this web page.

This caculator was implemented on Mac OS X using Apple's Project Builder. Here's the source code.

This calculator uses Java^TM utilities courtesy of Core Java, by Gary Cornell and Cay S. Horstmann.

Sheldon Brown's article on wheelbuilding includes lots of good detailed information while still being readable. It is highly recommended. It includes links to several other spoke length calculators, several of which include large databases of pre-measured components.

Version 10. August 3, 2003. Email Danny Epstein