Processes for the purification of bio-based acrylic acid to crude and glacial acrylic acid are provided. The bio-based acrylic acid is produced from hydroxypropionic acid, hydroxypropionic acid derivatives, or mixtures thereof. The purification includes some or all of the following processes: extraction, drying, distillation, and melt crystallization. The produced glacial or crude acrylic acid contains hydroxypropionic, hydroxypropionic acid derivatives, or mixtures thereof as an impurity.