The body’s postural control system is responsible for responding to perturbations of balance and keeping the body upright. During quiet standing, the center of pressure oscillates about the center of mass, counteracting imbalances. These oscillations can be analyzed to determine the degree of stability, which could be helpful in quantifying the effects of brain injuries. In this research, the center of pressure was recorded for stances with feet together and feet tandem, with eyes opened and eyes closed, in neurotypical participants. These signals were analyzed using indices of approximate entropy and velocity to determine how sensitive the measures were in tracking changes to stability levels. One-way ANOVA test results showed increased approximate entropy in anterior/posterior and medial/lateral directions (p = 1.21 × 10−11, 3 × 10−14) and increased velocity in both directions (p = 2.87 × 10−6, 4.87 × 10−7) during conditions with decreased stability. Dunnett’s post hoc testing indicated that approximate entropy was significantly greater in all the less stable feet tandem trials in comparison to the most stable eyes open, feet together condition with p < 0.001 in nearly every participant and that velocity was significantly greater in the least stable eyes closed, feet tandem trials in comparison to the most stable condition with p < 0.01 in nearly every participant.