This paper compares algorithms for velocity estimation for feedback control using position encoder measurements. Simulations and experiments for position-velocity control of motors using both fixed-time and fixed-displacement algorithms are compared for various operating conditions. While no single approach is optimal for all situations, least-squares fit algorithms are promising in general. Mathematical models are developed to predict the performances of the algorithms. Specifically, upper bounds on absolute and relative errors for each of the algorithms under different constant velocity and constant acceleration conditions are derived. The algorithms are extensively tested in simulation and also on data obtained from an experimental setup consisting of a motor, two encoders with different resolutions, and a real-time feedback control system. The theory and simulations are confirmed by experimental results.