Countries depending on small-scale agriculture, such as Bangladesh, are susceptible to climate change and variability. Changes in the frequency and intensity of drought are a crucial aspect of this issue and the focus of this research. The goal of this work is to use SPI (standardized precipitation index) and SPEI (standardized precipitation evapotranspiration index) 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, decreasing dry trend was found in Eastern hill regions, whereas an increasing drought trends were found in the in the rest of the regions in all time scaless (range is from − 0.08 decade−1 to − 0.15 decade−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) SPEI is anticipated to be better at capturing dry/wet cycles in more complex regions than SPI. (3) According to the MLR, longitude and maximum temperature can both influence precipitation. (4) 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. Findings can be used to improve drought evaluation, hazard management, and application policymaking in Bangladesh. This has implications for agricultural catastrophe prevention and mitigation.