A search for excited electrons produced in pp collisions at Formula omitted = 13 Formula omitted via a contact interaction Formula omitted is presented. The search uses 36.1 fb Formula omitted of data collected in 2015 and 2016 by the ATLAS experiment at the Large Hadron Collider. Decays of the excited electron into an electron and a pair of quarks ( Formula omitted) are targeted in final states with two electrons and two hadronic jets, and decays via a gauge interaction into a neutrino and a Formula omitted boson ( Formula omitted) are probed in final states with an electron, missing transverse momentum, and a large-radius jet consistent with a hadronically decaying Formula omitted boson. No significant excess is observed over the expected backgrounds. Upper limits are calculated for the Formula omitted and Formula omitted production cross sections as a function of the excited electron mass Formula omitted at 95% confidence level. The limits are translated into lower bounds on the compositeness scale parameter Formula omitted of the model as a function of Formula omitted. For Formula omitted Formula omitted, the lower bound for Formula omitted is 11 Formula omitted. In the special case of Formula omitted, the values of Formula omitted Formula omitted are excluded. The presented limits on Formula omitted are more stringent than those obtained in previous searches.