Activity Materials

  • About this resource
  • Educational Objectives
  • Background Science
  • Mathematics
  • Run the Model

  • Glossary of Terms
  • Credits

    Related Links
  • Contact Webmaster

  • Algorithm: The Mathematics of Surface Water Runoff

    The equation used to calculate runoff is from the U.S. Soil Conservation Service. It is as follows:

    Q = the amount of runoff in inches
    P = rainfall in inches
    S = maximum amount of water that will be absorbed after runoff begins (inches)
    Ia= initial abstraction

    The initial abstraction (Ia) includes all losses before runoff begins, and includes water retained in surface depressions, water taken up by vegetation, evaporation, and infiltration. This value is related to characteristics of the soil and the soil cover. Ia is approximated through the use of:


    This relationship was determined through the study of many small watersheds. Setting Ia equal to a ratio of S also allows for simplification of the above equation if necessary to:

    S is related to the soil and cover characterstics of the soil. This is represented through its relationship to the value of the runoff curve number (CN), which has a value from 0 to 100. The runoff curve number is a description of how much water will run off out of 100 cm3 of water. So a parking lot would have a high value, around 99, whereas a field with lots of grass and healthy soil would have a much lower value (around 35).

    CN is determined through several factors. The most important are the hydrologic soil group (HSG), the ground cover type, treatment, hydrologic condition, the antecedent runoff condition (ARC), and whether impervious areas are connected to drainage systems, or whether they first outlet to pervious area before entering the drainage system.

    The runoff curve numbers here represent average antecedent runoff condition (describes the soil before it is saturated by a storm to the point of runoff).

    Soils are extremely important in determining the runoff curve number, since these values can vary widely. Soils are generally divided into four HSG's (hydrological soil groups: A,B,C, and D) and are classified according to how well the soil absorbs water after a period of prolonged wetting.

    Developed by
    Shodor logoThe Shodor Education Foundation, Inc.
    in cooperation with the
    North Carolina State University
    Cooperative Extension Service
    Neuse River Education Team

    Copyright © 1998