Abstract The lack of precipitation for an extended period is what meteorologists call a drought, and it results in low soil moisture and crop water stress. Drought has become one of the most important global challenges due to inadequate water supplies. Drought monitoring is frequently conducted using the SPI (standardized precipitation index) and the SPEI (standardized precipitation evapotranspiration index). The goal of this work is to use SPI and SPEI to investigate the differences in drought characteristics across different physiognomy types in Bangladesh and to highlight how drought characteristics change over time and spatial scales when considering different geomorphologies. This study used monthly precipitation and temperature data from 29 metrological stations for 39 years (1980–2018) for calculating SPI and SPEI values. To determine the significance of drought characteristic trends over different temporal and spatial scales, the modified Mann–Kendall trend test and multivariable linear regression (MLR) techniques were used. The results are as follows: (1) Overall, an increasing dry trend was found in Eastern hill regions, whereas decreasing trends were found rest of the regions in all time scale (range is from − 0.008 year−1 to − 0.015 year−1 for 3-month time scale). However, except for the one-month time scale, the statistically significant trend was identified mostly in the north-central and northeast regions, indicating that drought patterns migrate from the northwest to the center region. (2) Drought intensity increased gradually from the southern to the northern regions (1.26–1.56), and drought events occurred predominantly in the northwestern regions (27–30 times), indicating that drought meteorological hotspots were primarily concentrated in the Barind Tract and Tista River basin over time. (3) According to the MLR, longitude and maximum temperature can both influence precipitation. Findings can be used to improve drought evaluation, hazard management, and application policymaking in Bangladesh. This has implications for agricultural catastrophe prevention and mitigation.