The morphology of red blood cells is affected significantly during maturation of malaria parasites, Plasmodium falciparum and Plasmodium vivax. A novel shape equation is presented that defines shape of parasitized red blood cells by P. falciparum (Pf-red blood cells) and P. vivax (Pv-red blood cells) at four stages of infection. The Giemsa-stained thin blood films are prepared using blood samples collected from healthy donors, patients having P. falciparum and P. vivax malaria. The diameter and thickness of healthy red blood cells plus Pf-red blood cells and Pv-red blood cells at each stage of infection are measured from their optical images using Olysia and Scanning Probe Image Processor softwares, respectively. Using diameters and thicknesses of parasitized red blood cells, a shape equation is fitted and relative two-dimensional shapes are plotted using MATHEMATICA. The shape of Pf-red blood cell drastically changes at ring stage as its thickness increases by 82%, while Pv-red blood cell remains biconcave (30% increase in thickness). By trophozoite and subsequent schizont stage, the Pf-red blood cell entirely loses its biconcave shape and becomes near spherical (diameter and thickness of ~8 µm). The Pv-red blood cell remains biconcave throughout the parasite development even though its volume increases. These results could have practical use for faster diagnosis, prediction, and treatment of human malaria and sickle-cell diseases.