Methods and apparatus to determine parameters of a pumping unit for use with wells are disclosed. An example apparatus includes a housing and a processor positioned in the housing. The processor is to determine a first load on a polished rod of a pumping unit, to estimate a first torque of a motor of the pumping unit, and determine a first torque factor for the pumping unit. The processor is to, based on the first load, the first torque, and the first torque factor, determine a phase angle of a counterbalance of the pumping unit or a moment of the counterbalance.