Electrical conductivity of soil or rock varies as a function of water content, but there is no agreement regarding the functional form of this dependence. Geologists have long used an empirical equation called Archie's Law, σ = σ₀ φ^m, where σ is electrical conductivity, σ₀ is a proportionality coefficient, φ is porosity, and the exponent m is generally near 2.0. Soil physicists more commonly use an empirical equation suggested by Rhoades, σ = σ₀ θ(aθ + b) (where θ is volumetric water content), which has conductivity varying with the sum of a linear and a quadratic water content term. We derive a new relationship, similar to both Archie's Law and Rhoades' equation, using continuum percolation. The new equation, σ = σ₀ (θ - θ_c) ^μ, has a sound theoretical basis and has been confirmed by both experiment and simulation in other fields. The practical implications of this study are, first, σ is not a linear or linear + quadratic function, as commonly assumed. Second, the similarity between this equation and that for liquid-phase diffusion in soils further confirms the analogy between electrical conductivity and diffusion, suggesting possible application to measurement techniques. And third, the exponent μ has a known theoretical value, so the equation uses only two fitting parameters (σ₀ and θ_c) in contrast to Rhoades' three (σ₀, a, and b). We present the derivation of the new equation, and compare theoretical and measured values of σ over the full range of saturation. The newly derived expression is superior to other modeling predictions.