We have applied a one-dimensional fractal analysis to Magellan altimetry data for two 20° × 20° equatorial regions on Venus. For the Ovda Regio highlands the power spectra of the altimetry data correlate well with power law (fractal) statistics over the full range of wavelengths considered 36 km ≤ λ ≤ 703 km; the mean fractal dimension is DOvda = 1.64. For the Tinatin Planitia lowlands the power spectra consistently show a rollover at long wavelengths, λ > 200 km; the long-wavelength topography in this region either never developed or has subsequently relaxed. The mean of the best fit fractal dimension for Tinatin is DTinatin = 1.41. The measure of roughness (RA) correlates well with variations in relief, especially at short wavelengths λ ∼ 50 km. Our quantitative analysis of Venus topography can be applied on a global scale. The one-dimensional method can be extended to two-dimensional space, yielding two-dimensional maps of regional D and RA, allowing a more complete use of regional two-dimensional altimetry data.