The approximate equations of Hassler and Brunner and of van Domselaar are often used to deduce the capillary pressure curve of a porous medium from centrifuge data. The use of these equations restricts the centrifuge method to short samples. Also, these equations require differentiation of data. We report here methods to determine the capillary pressure curve by the midpoint and least-squares solution of the fundamental equation, relating the average saturation S1 of liquid in the porous medium to the capillary pressure Pc1 at the end of the sample nearest the axis of rotation. The methods do not require differentiation of data and are not restricted to short samples. We introduce and evaluate an approximation based on an exact result derived by Rajan. This new approximation requires the same inputs as do the Hassler-Brunner and the van Domselaar approximations, but it is accurate over a wider range of sample sizes. In addition, an approximate solution which can be used to estimate capillary pressure curves for long cores is developed.