A potential function using spherical harmonics up to degree and order 90 was derived from a selection of Mars Global Surveyor vector data. These included all three components of those taken below 200 km altitude during the two aerobraking phases (AB1 and AB2), the Science Phase Orbits (SPO), and the higher-altitude (367--435 km) data taken on the nightside during the Mapping Phase Orbits (MPO). The merger of these sets of data provided total global coverage. The technique used was a least squares minimization developed for Earth field analysis whereby the relative weighting of each data source was determined by the width of a Gaussian fit to the residual distribution about the potential function. Also, data selection by area and area weight functions were used to improve normalization. The residual misfit distributions for the vertical component for different data sources are (nT) AB1, 6.5; AB2 (in shadow), 6.7; AB2 (sunlit), 10.3; SPO, 6.4; and MPO, 5.9. The horizontal component misfits are about the same for MPO and AB2 in shadow, but for data taken in sunlight the scatter of horizontal component residuals increases by 50% for AB1, a factor of two for SPO, and 30% for AB2. The energy density spectrum evaluated at 3535 km radius (the mean altitude of the AB and SPO data) decreased from a high of 0.2 J/km3 near n = 20 to an order of magnitude less at n = 90. Most of the power in the spectrum lies between n = 15 and n = 40. The dipole moment was only 8 ¿ 1016 A ¿ m2, which is likely close to the noise of the coefficients. This spectrum is 40 times greater than that of Earth at the scale sizes represented by values of n from 20 to 40. Comparisons with other published maps and models for Mars show general agreement with the field representations at MPO altitudes, but disagreements up to several hundred nT in components calculated for areodetic altitudes below 200 km.