Formulas

Definitions:

Cad - Cadence (in RPM)

Ct - Nr. of teeth in the front chainring

Rt - Nr. of teeth in the rear sprocket

D - Tire's diameter (in mm)

S - Slope (5% = 0.05, 10% = 0.1, etc.) 

m - Total mass of the set: cyclist+bicycle+cargo [Kg]

Gear ratio in Gear inches:

G = (D/25.4) x Ct/Rt

Bicycle's linear speed:

V [Km/h] = Cad [rpm] x G x 0.0048

V[mph] = Cad [rpm] x G x 0.0029826

Power to overcome gravity:

Pg [Watts] = m [Kg] x Cad [rpm] x G x Sqrt (S^2/(1+S^2)) x 0.013

Note: These and other formulas are present in the downloadable Excel sheet on the left.