<p>As the climate is becoming drier and extreme climatic patterns intensify worldwide, the present water scarcity worsens. Options are urgently needed for harvesting the increasingly variable rainwater to secure water supplies for societies and the environment. Here, new formulae are presented for quantifying water infiltration into soils without compromising the mathematical physics of water flow. These equations are derived from the rapidly developing area of random fractional partial differential equations and verified with data measured in the field, and these equations can be used as models for infiltration with random or deterministic parameters. It is shown that a generic equation of cumulative infiltration can be derived independently with either an initial condition of the surface moisture distribution or mixed boundary conditions by using the versatile homotopy perturbation method. One demonstration of this method is the assessment of infiltration into the same soil by altering land surface covers, and its implications are significant for managing land without high costs associated with engineering works which cause environmental concerns. These new equations of infiltration can be equally used for assessing infiltration rates on both rural and urban soil surfaces.</p>