Can you give a little more info on the frame you're using. You call it a vintage road bike, but how old is it, and what make?
Road bikes are generally made for either 27" wheels (older frames) or 700c wheels. Yours is likely one or the other. The size actually refers to the tire that will fit, not the actual diameter of the wheel. You can get tires for either, although 700c are far more common. 27" and 700c wheels (not tires!) are sometimes interchangable, depending on whether the brakes can adjust to hit the rims properly.
Is there any printing on the wheels you have? If so, what does it say.
This website will help you measure the wheel properly.
http://www.sheldonbrown.com/rim-sizing.html. This is also helpful:
http://www.sheldonbrown.com/tire-sizing.html
If you happen to have a 29'er MTB frame and wheels, those wheels have the same diameter as a 700c wheel, and both are a little smaller in diameter than a 27".