Total reaction and partial cross section calculations in proton-nucleus (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="italic">Z</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>≤26) and nucleus-nucleus reactions (<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="italic">Z</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">p</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="italic">Z</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">t</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>≤26)

We have developed semiempirical total reaction cross section formulas for proton-nucleus (with ${\mathit{Z}}_{\mathit{t}}$\ensuremath{\le}26) and nucleus-nucleus (with ${\mathit{Z}}_{\mathit{p}}$ and ${\mathit{Z}}_{\mathit{t}}$\ensuremath{\le}26) reactions. These formulas apply for incident energies above \ensuremath{\approxeq}15 MeV and \ensuremath{\approxeq}100 MeV/nucleon, respectively. We have also constructed a procedure for calculating the projectile-fragment production cross sections, by scaling semiempirical proton-nucleus partial cross section systematics. The scaling is done by a scaling parameter, which is based on a Bradt-Peters-type law and also takes advantage of the weak-factorization property of projectile fragments. All products from the Z of the projectile down to Z=2 can be calculated. The agreement between the calculated partial cross sections and the experimental data is better than all earlier published results.