I am working on smaller designs and would like to utilize a more classical design using the "golden rule", but can't seem to locate the formula. I may not be referring to formula by the correct name, but is a percentage of the one of building diamensions to set the others such as eave height and roof picth.

Free State,
you can find a description of "A Geometer's Delight" in TFG's book "Timber Frame Joinery & Design Workbook", page 6. It's a guide how to do an elevation with a straightedge and a compass. Maybe this is what you are looking for...

Free State

The term you looking for is either the golden section or the divine proportion also related is the Fibonacci series which was discovered in a thought experiment concerning the propagation of breeding rabbit pairs. The basic idea of the golden section is that the proportions of the whole regress through the proportions of the parts. Given a line segment AC with a point B between points A and C, and segment AB is a greater length than BC. The golden section is when, AC / AB = AB / BC = 1.618. The golden section has been observed through the magnitudes of the organization of the galaxy to the molecule. An interesting book for the general reader is "A Beginner's Guide to Designing the Universe" by Michael Schneider. Consume with a grain of salt.

Here is a website to look at.

The Divine Proportion

I think I'm after the same formula as Free State. Something which will give me the ratio of width to height for a barn so that the proportions look "right".
I have a copy of the "Golden Section" but don't see how it can be applied.

Hi Nic

In all truthfulness, the golden section is just one element of design vocabulary and its value phi is a first order mathematical curiosity, but phi, whether squared, cubed, rooted, inverted, multiplied or divided, will not alone solve your problem and neither will any other single factor or formula. It will be up to you to find what looks right but barns were built to do right and well, to fill needs and service a farms economy. So I would suggest, fill the need simply and follow old barn patterns and looking good is nearly automatic.

Back to phi:

the math, http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fib.html

classic design, http://www.aboutscotland.com/harmony/harmony.html

fun with a geometer, http://www.nexusjournal.com/GA-contents.html

1:1.618 will do the trick.

Amazingingly, this number is the only one I know of which is its own reciprocal minus one.

Spooky.

check out Fine WoodWorking, Feb.2004, issue168, page48