The primary role of a red blood cell (RBC) is delivering oxygen throughout our body. Abnormalities of this basic function lead to anemia and are caused by numerous diseases such as malaria and sickle cell anemia. As prompt and inexpensive tests for blood screening are in demand, we have developed a faster and reliable way to measure morphological parameters associated with the structure of red blood cells and the size distribution of the cells in a whole blood smear. Modeling the RBC shape under Born approximation, we are able to determine parameters of clinical relevance, such as the diameter, thickness and dimple size. From a measured quantitative phase image of a blood smear, we can determine the average and standard deviation of the red blood cell volume simultaneously, i.e., without analyzing each cell individually. This approach may open the door for a new generation of label-free, high-throughput blood testing.