We reexpress the fermionic probability amplitude as a trace over spinor indices, which reformulation surprisingly does not exist in literature. This reformulation puts the probability amplitude and the probability (squared amplitude) of a given process on equal footing at the algebraic computation level and this is our principal motivation to write the paper. We test the power of the trace formula in three applications: Calculation of the charge-current of fermions by using symbolic programs which current so far was only computable by hand, analytic computation of the quark dipole magnetic moment, rendered less cumbersome, and finally Fiertz rearrangement identities now made more transparent.