I currently have 700 x 40 tyres fitted. I don't know what size the rims are as they are not marked. The tyres are the original ones fitted when I bought the bike. How can I tell what size the rims are?
There should be a label on the rim that says "622-19" or something similar. The second number is the width.
Failing that, look at sheldonbrown.com to find the proper definition of rim width and measure it yourself.
Quoted message said:
What's the narrowest tyre I can fit?
The same reference from above has a table to answer that question at: