We introduce a new methodology to predict the topographic site‐effect amplification. Ground motions obtained from a large database of 3D earthquake simulations show that the curvature of the Earth’s surface, defined as the second spatial derivative of the elevation map, is correlated with the topographic site amplification. The highest correlation between the frequency‐dependent topographic amplification and the topographic curvature is reached when the curvature is smoothed over a characteristic length equal to the S wavelength divided by two (i.e., frequency‐scaled curvature [FSC]). This implies the amplification is caused by topographic features for which horizontal dimensions are similar to half of the S wavelength. The largest ground‐motion variabilities are found at sites located on slopes and on the largest summits, whereas intermediate variabilities occur over narrow ridges and a stable behavior in the bottom valleys. The FSC proxy allows the identification of topographic features with similar characteristic dimensions and probabilistic estimates of amplification values accounting on the variability of ground motions due to source–site interactions. Amplification estimates using the FSC proxy are robust and easily computed from digital elevation maps provided that reasonable values of S‐wave velocities are available in the area of interest.