We derive scaling properties of the intensity-duration-frequency (IDF) curves under the condition that temporal rainfall is a stationary multifractal process. We find that under limiting conditions (very short durations D or very long return periods T), the IDF values are simple scaling with a power law dependence on D and T. The exponents of D and T differ in the two limiting cases of very short D and very long T and can be calculated from the moment scaling function K(q) of the rainfall time series. These theoretical findings differ from those of previous studies. They are validated through direct calculation and analysis of an actual rainfall record.