As a catastrophic phenomenon, drought has destructive impacts on water resources, the environment, and the ecosystem. Consequently, drought plays a vital role in risk assessment, water resources management, and drought mitigation plans. The main aim of this research is to obtain critical intensity-duration-frequency (IDF) drought curves and to provide a comprehensive understanding of the drought characteristics by considering the meteorological Standardized Precipitation Index (SPI), Standardized Precipitation Evapotranspiration Index (SPEI), and hydrological Standardized Streamflow Index (SSI). Critical IDF curves for the drought index and return period selection are identified. Also, new terms are defined as the specific drought duration, the maximum drought duration, and the critical intensity based on drought IDF curves. The results show that the SPI3 based on run theory for 500 years return period has higher drought intensity compared with other drought indices. In some IDF curves, the 2-year return period of a 12-month duration timescale is not provided. Regarding the maximum drought duration, the SPEI12 gave a longer duration. With the new concepts in this research, the presented IDF drought methodology has a novel additional practice to identify the critical intensity and maximum drought duration. Using this methodology for any drought index will contribute to converting data with mathematical calculations into IDF curves for design and risk assessment purposes.