A soil's capillarity, associated with the parameter sorptivity, is a dominant control on infiltration, particularly at the onset of rainfall or irrigation. Many mathematical models used to estimate sorptivity are only valid for dry soils. This paper examines how sorptivity and its capillary component (as wetting front potential) change with initial degree of saturation. We capture these effects with a simple modification to the classic Green-Ampt model of sorptivity. The modified model has practical applications, including (1) accurately describing the relative sorptivity of a soil at various water contents and (2) allowing for quantification of a soil's saturated hydraulic conductivity from sorptivity measurements, given estimates of the soil's characteristic curve and initial water content. The latter application is particularly useful in soils of low permeability, where the time required to estimate hydraulic conductivity through steady-state methods can be impractical.