A recent study showed all parameters in the Brooks-Corey equations of soil hydraulic properties are strongly correlated to the pore-size distribution index (λ). These λ values relate and can scale cumulative infiltration and water contents during redistribution across dissimilar textural classes under different rainfall and initial conditions. The objectives of this work were to explore if relationships exist between evaporation (E) and transpiration (T) and λ across different soil types and if these relationships can be used to scale E and T among these soils. The Root Zone Water Quality Model generated evaporation under four potential rates and transpiration under one potential rate with a goosegrass [Eleusine indica (L.) Gaertn.] in 11 soil textural classes under near-saturated initial conditions. Stage I cumulative evaporation or transpiration that occurs when the soil is sufficiently wet to meet the potential rates had a quadratic relationship with λ. However, both Stage II cumulative evaporation and transpiration were cubic functions of λ with time-dependent coefficients. It is shown that these relationships can be used to estimate both Stage I and II cumulative evaporation and transpiration across unknown soils, especially when data for one dominant reference soil type is known. The methods developed for estimating cumulative evaporation were applied and compared with experimental results of three initially saturated soils under constant evaporation with good results. These results for simple homogeneous soils should be useful in quantifying spatial variability of evaporation and transpiration in the field under similar conditions, and could form the basis for further research of more complex conditions.