Enter the previous day’s Antecedent Precipitation Index, decay constant, and daily precipitation amount into the calculator to determine the Antecedent Precipitation Index.

Antecedent Precipitation Index Formula

The following formula is used to calculate the Antecedent Precipitation Index (API).

API = API_prev * k + P


  • API is the Antecedent Precipitation Index
  • API_prev is the previous day’s Antecedent Precipitation Index
  • k is the decay constant (0 ≤ k ≤ 1)
  • P is the daily precipitation amount (mm)

To calculate the Antecedent Precipitation Index, multiply the previous day’s API by the decay constant, then add the daily precipitation amount. The decay constant is a value between 0 and 1 that represents the rate at which the influence of previous precipitation diminishes over time. The daily precipitation amount is the total amount of rainfall recorded in a day.

What is an Antecedent Precipitation Index?

The Antecedent Precipitation Index (API) is a hydrological index used to quantify the amount of moisture in the soil. It is calculated based on the amount of rainfall that has occurred over a certain period of time, typically a few days to a few weeks, prior to a specific event. The API is used to predict the likelihood of flooding or landslides, as higher values indicate more saturated soil that is less able to absorb additional rainfall.

How to Calculate Antecedent Precipitation Index?

The following steps outline how to calculate the Antecedent Precipitation Index (API).

  1. First, determine the previous day’s API (API_prev).
  2. Next, determine the decay constant (k) within the range of 0 to 1.
  3. Next, determine the daily precipitation amount (P) in millimeters (mm).
  4. Next, gather the formula from above = API = API_prev * k + P.
  5. Finally, calculate the Antecedent Precipitation Index (API).
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Previous day’s API (API_prev) = 0.5

Decay constant (k) = 0.8

Daily precipitation amount (P) = 10 mm