We present a fast algorithm using the Y- transformation for calculating the conductance of large two-dimensional random resistor lattices. The procedure can also be used to calculate other quantities for which Y- transformations can be defined. As an example of the methods usefulness, we present extensive data on square random resistor lattices as large as 1000 bonds on a side. Using this data, we estimate that the conductivity exponent t=1.303-0.014+0.004 in two dimensions. © 1988 The American Physical Society.