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The normalized antecedent precipitation index (NAPI) model by Heggen for the prediction of runoff yield is analytically derived from the water balance equation. Heggen’s model has been simplified further to a rational form and its performance verified with the Soil Conservation Service Curve Number (SCS-CN) model. The simplified model has three coefficients specific to a watershed, and requires two inputs: rainfall and the derived parameter, NAPI. The characteristic behaviour of the NAPI has resonance with the curve number (CN) of the SCS model. The proposed NAPI model was applied to three watersheds in the semi-arid region of India to simulate runoff yield. The model showed improved correlation between the observed and predicted runoff data compared to the SCS-CN model. The F test and paired t test also confirmed the reliability of the model with significance levels of 0.01 and 0.001%, respectively. The proposed model could be used successfully for rainfall-runoff modelling in a watershed.