The forces exerted on the flagellum of the swimming alga Chlamydomonas reinhardtii by surrounding fluid are estimated from video data. "Wild-type" cells, as well as cells lacking inner dynein arms (ida3) and cells lacking outer dynein arms (oda2) were imaged (350 fps; 125 nm). Digital image registration and sorting algorithms provide high-resolution descriptions of the kinematics of the cell body and flagellum. The swimming cell is then modeled as an ellipsoid in Stokes flow, propelled by viscous forces that depend linearly on the velocity of the flagellum. The coefficients (C N and CT) that related normal and tangent forces on the flagellum to corresponding velocity components are estimated from equilibrium requirements. Their values are consistent among all three genotypes and similar to theoretical predictions.