While poverty incidence is well-studied, its depth and severity remain underexplored, limiting a comprehensive understanding of the multifaceted nature of poverty. This gap constrains policy interventions, particularly in the agricultural sector, which employs the majority of the population in developing countries. This study bridges the gap using data from the Ghana Living Standards Survey, which comprises 4,670 agricultural households. The three Foster-Greer-Thorbecke (FGT) indices were employed as a methodological approach to measure poverty status, depth, and severity. While the determinants of poverty status were examined using a multinomial logit model, linear regression was employed to investigate factors influencing the depth and severity of poverty. The analysis revealed that primary and secondary education significantly reduces the likelihood of poverty, but does not affect its depth and severity. This challenges existing studies that emphasize education as a cure-all approach to poverty by arguing that education has a preventive but not a remedial role in addressing poverty. Similarly, home and agricultural equipment ownership reduces poverty status without significantly impacting poverty depth and severity. Conversely, mixed-and-mono cropping lowers poverty severity. Farm size and its squared term show no effect on poverty status but demonstrate a non-linear impact on depth and severity—initially reducing intensity before increasing it, reflecting diminishing returns. Market outlets also matter: engagement with pre-harvest contractors, farm gate buyers, and market traders increases the risk of poverty, its severity, and depth, whereas sales through state trading organizations consistently reduce these risks. Household size, bank account ownership, asset ownership, farm labor, and urban location are all significant predictors of poverty. However, very large household sizes reduce poverty, challenging the traditional linear causality between household size and poverty. The findings support education and tenure reforms for poverty prevention, while advocating for enhanced financial access, asset security, and equitable markets to eradicate entrenched poverty.