Troubleshooters.Com and 

Steve Litt's Guide to Transportational Bicycling and
the Wheel Building Page Present:

The Math Behind

Copyright (C) 2010 by Steve Litt

If you like this wheelbuilding document, you'll love my books. See the entire list at


The information in this document is information is presented "as is",  without warranty of any kind, either expressed or implied, including, but not limited to, the implied warranties of merchantability and fitness for a particular purpose. The entire risk as to the quality and performance of the information is with you. Should this information prove defective, you assume the cost of all necessary servicing, repair, correction, medical care or any other remediation.

If this is not acceptable to you, you may not read this material.

Dishing calculation diagram  
You can see in the right hand diagram that, if Ch is the hub center and Cf is the fork center:

Ch = L + H/2
Cf = F/2

And looking at the diagram, it's also obvious that:

D = Cf - Ch

So, substituting for Ch and Cf:

D = F/2 - L - H/2

The diagram also clearly shows that:

F = L + H + R

So you can substitute the above expression for F into the expression for D:

D = (L+H+R)/2 - L - H/2

To repeat, so far we've shown that:

D = (L+H+R)/2 - L - H/2

Now use the distributive law on (L+H+R)/2:

D = L/2 + H/2 + R/2 - L - H/2

Cancelling the + and - H/2 terms, and subtracting the L:

D = L/2 + R/2 - L

Now combining the L terms:

D = R/2 - L/2

Simplifying further:

D = (R - L)/2

Or in English, "The dish distance is half the difference between the drive side inner nut to flange distance and the non-drive nut to flange distance."

Please Give Me Some Feedback

I'd like feedback on this document. My email address is here:

The priority is factual errors such as wrong spoking instructions. Next is feedback on how to make the document more helpful. But any kind of feedback is more than welcome.

If you like this wheelbuilding document, you'll love my books. See the entire list at