Contrast sensitivity (CS) quantifies an observer's ability to detect the smallest (threshold) luminance difference between a target and its surrounding. In clinical settings, printed letter contrast charts are commonly used, and the contrast of the letter stimuli is specified by the Weber contrast definition. Those paper-printed charts use negative polarity contrast (NP, dark letters on bright background) and are not available with positive polarity contrast (PP, bright letters on dark background), as needed in a number of applications. We implemented a mobile CS measuring app supporting both NP and PP contrast stimuli that mimic the paper charts for NP. A novel modified Weber definition was developed to specify the contrast of PP letters. The validity of the app is established in comparison with the paper chart. We found that our app generates more accurate and a wider range of contrast stimuli than the paper chart (especially at the critical high CS, low contrast range), and found a clear difference between NP and PP CS measures (CSNP>CSPP) despite the symmetry afforded by the modified Weber contrast definition. Our app provides a convenient way to measure CS in both lighted and dark environments.