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Software Programs are based on finite element analysis which is much more accurate than manual calculation because of the ability of performing non linear analysis which is very important in certain cases. However, mistakes can be easily done as in the case of modelling error so I would say knowing orders of magnitude is extremely important for Engineers so they know when things go wrong.
STAADD Pro, SAP2000 and Prokon are general structural softwares and ETABS is specifically for buildings.
Its better to cross check the results with manual calculations using formulas.