We assess the surface roughness of Europa by reevaluating Galileo stereo images. Roughness provides important information about surface textures, which are related to geologic processes operating at a variety of scales. Roughness also sets important performance requirements for various remote sensing instruments on board the upcoming icy satellite missions to the Jovian System. In this study, roughness is derived for different geologic terrains on Europa, which have been distinguished through geomorphological mapping. For each terrain type we derive the scale dependent root-mean-square roughness and corresponding Hurst exponents. We investigate the scale between 30 m and 5 km and show that Europa's surface can mostly be described by a monofractal behavior over these baselines (i.e., surface roughness follows power laws with breakpoints located at a few hundred meters). Hurst exponents are higher below the breakpoints with typical values between 0.4 and 0.8 and lower above, typically between 0.2 and 0.6. This behavior is mostly controlled by ridges which are dominating the topography on Europa. At unity scale (1 m) roughness is extrapolated to be around 0.4-0.7 m with strong exceptions on chaos terrain where values over 1-2 m can be achieved, assuming that no further breakpoints are present below the resolution of the digital terrain models used in this study.