Extending the current theory, a new formula, concerning the average tilt angle for a thermally undulating fluid membrane in an, on average, equally spaced stack, has been developed. For large interlayer spacings, this new formula resembles the existing one-the tilt angle varies logarithmically with the interlayer spacing. When the interlayer spacing is relatively small, the new formula differs from the existing theory. This new formula is then used to extract the membrane bending curvature modulus kappa for membranes in a lamellar phase made from sodium dodecyl sulfate, water, pentanol, and dodecane. The fit of the water layer thickness to the formula shows that the membrane has a bending curvature modulus of 2.1 +/- 0.5 b(B)T, with T = 300 K. The water layer thicknesses are accurately determined by combining X-ray scattering determined interlayer spacings with sample specific gravities.