I did this last night and didn't check it. Getting a little more organized, I wrote it out again and discovered I forgot the bike weight. And apparenetly there is another mistake, either last night of today because the bike weight should have made the final slope less steep but it increased 2%. Again, this is not thoroughly checked, but here are the steps. You math and physics whizzes can correct my mistakes while I go for a ride.

Fb – Tangential force developed at rear wheel
Fp – Force on pedal
Wr – Rider weight, Wb – Bike weight, W total weight
H – hill rise, l – hill run, alpha – hill angle
In – Gear in inches, d – wheel diameter, Cr – Crank length

Basic physics: W sin(alpha) = Fb

Basic gearing: Fb = Fp (d/In) x (Cr/d/2) = 2Fp x Cr/In

Combining: Sin(alpha) = Fb/W and alpha = arcsin(Fb/W)
But: W = Wb + Wr and Fp(max, no pulling) = Wr
And: alpha = arcsin(2Fp x Cr/In)/(Wb + Wr) = arcsin(2Wr x Cr/In)/(Wb + Wr)

So, say Wr = 180, Wb = 20, W = 200, therefor Wr/(W) = 0.9
Cr = 7” (178 mm), d = 27”, In = 72” (the gear)
Then: alpha = arcsin(2 x 0.9 x 7/72) = arcsin(0.175) = 10.1 degrees
But: rise over run x 100 (ie “percentage) = 100 x tan(alpha) = 18%