A method is presented to measure the spherical aberration constant of a transmission electron microscope with high precision. The method is based on the measurement of a series of beam-tilt-induced image displacements. The displacements are calculated via cross-correlation and subsequently fitted to a third-order polynomial in the beam tilt. Calibration of the magnification and of the beam-tilt coils is a crucial step. The spherical aberration constant of two microscopes is measured with a precision better than 1%, apart from calibration errors. A computer is used to direct the experiments via remote control of the microscope and perform fast image processing to calculate the cross-correlations.