Surface gravity is a basic stellar property, but it is difficult to measure accurately, with typical uncertainties of 25 to 50 per cent if measured spectroscopically and 90 to 150 per cent if measured photometrically. Asteroseismology measures gravity with an uncertainty of about 2 per cent but is restricted to relatively small samples of bright stars, most of which are giants. The availability of high-precision measurements of brightness variations for more than 150,000 stars provides an opportunity to investigate whether the variations can be used to determine surface gravities. The Fourier power of granulation on a star's surface correlates physically with surface gravity: if brightness variations on timescales of hours arise from granulation, then such variations should correlate with surface gravity. Here we report an analysis of archival data that reveals an observational correlation between surface gravity and root mean squared brightness variations on timescales of less than eight hours for stars with temperatures of 4,500 to 6,750 kelvin, log surface gravities of 2.5 to 4.5 (cgs units) and overall brightness variations of less than three parts per thousand. A straightforward observation of optical brightness variations therefore allows a determination of the surface gravity with a precision of better than 25 per cent for inactive Sun-like stars at main-sequence to giant stages of evolution.