A simple method is proposed for measuring cross-sections of fast negative atomic and molecular ions colliding with atoms and molecules. The method, applicable to tandem accelerators, uses the stripping process of the negative ions, occurring at the gas target placed in the accelerator high-voltage terminal. The target (stripper) gas pressure, not directly measurable, is measured with an improved version of a method that we have recently proposed. The total destruction cross-sections of negative atomic or molecular ion projectiles may be obtained, as well as those for each specific destruction channel. As an example of the validity of the method, we measured the destruction cross-sections of Si 2 − in Ar, from 30 keV to 1.3 MeV laboratory energies.