Measurements of mechanical properties by nanoindentation with triangular pyramidal indenters like the Berkovich rely heavily upon the relationship between the contact stiffness, S, the contact area, A, and the reduced elastic modulus, Er. This relationship is often written in the form S = 2βEr(A/π)1/2, where β is a constant that depends on the geometry of the indenter. Although the most common values for β used in experimental measurements are 1.000 and 1.034, various theoretical analyses have yielded values as small as 1.00 or as large as 1.2, depending on the assumptions made to model the deformation. Here, we explore the most appropriate value of β by performing careful experiments in fused quartz with thin gold coatings applied to the surface to reveal the actual contact area when observed in the scanning electron microscope. Experiments were performed not only with the Berkovich indenter, but with five other three-sided pyramidal indenters with centerline-to-face angles ranging from 35.3° (cube corner) to 85°. Results are discussed as they apply to obtaining accurate measurements of mechanical properties by nanoindentation.