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Derived from electron flux measurements, the TRBEC reduces the spatial information into a scalar quantity that concisely describes global aspects of the system. This index provides a simple, global, and long\u2010term assessment of the radiation belts that enables systematic analysis. In this work, we examine the TRBEC using the adiabatic invariants of  which has been used in previous articles as this coordinate system removes reversible adiabatic effects. We then introduce a new expression to compute the TRBEC using the non\u2010adiabatic coordinates of , relevant in the contexts of energetic electron precipitation, chorus, and hiss scattering where adiabatic invariant quantities are no longer conserved. From both expressions of the TRBEC we demonstrate that an erroneous factor of  that appeared in previous works using the adiabatic derivation led to an overestimate of the reported electron populations. In addition, we quantify electron loss in the outer radiation belt  via a case study using the Van Allen Probes data over a 20\u2010day period from March 2013 specifying particle populations both in terms of the aforementioned adiabatic and non\u2010adiabatic variables. The total number of electrons in the outer radiation belt reached upwards of  electrons at the peak of the storm, a rest mass of roughly 10\u00a0g.<\/jats:p>","DOI":"10.1029\/2024ja032940","type":"journal-article","created":{"date-parts":[[2024,11,27]],"date-time":"2024-11-27T20:23:42Z","timestamp":1732739022000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Derivations of the Total Radiation Belt Electron Content"],"prefix":"10.1029","volume":"129","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-5821-0879","authenticated-orcid":false,"given":"Jared C.","family":"Pitzel","sequence":"first","affiliation":[{"name":"Department of Physics and Astronomy University of Calgary  Calgary AB Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7242-8872","authenticated-orcid":false,"given":"Christopher M.","family":"Cully","sequence":"additional","affiliation":[{"name":"Department of Physics and Astronomy University of Calgary  Calgary AB Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1177-519X","authenticated-orcid":false,"given":"Jean\u2010Francois","family":"Ripoll","sequence":"additional","affiliation":[{"name":"CEA DAM DIF  Arpajon France"},{"name":"UPS CEA LMCE  Bruy\u00e8res\u2010le\u2010Ch\u00e2tel France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2452-383X","authenticated-orcid":false,"given":"Vivien","family":"Loridan","sequence":"additional","affiliation":[{"name":"CEA DAM DIF  Arpajon France"},{"name":"CEA CESTA  Le Barp France"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4681-8655","authenticated-orcid":false,"given":"Chia\u2010Lin","family":"Huang","sequence":"additional","affiliation":[{"name":"The University of New Hampshire  Durham NH USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2526-2205","authenticated-orcid":false,"given":"Harlan E.","family":"Spence","sequence":"additional","affiliation":[{"name":"The University of New Hampshire  Durham NH USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7985-8098","authenticated-orcid":false,"given":"Geoff D.","family":"Reeves","sequence":"additional","affiliation":[{"name":"Los Alamos National Laboratory  Los Alamos NM USA"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3063-6451","authenticated-orcid":false,"given":"Kyle R.","family":"Murphy","sequence":"additional","affiliation":[{"name":"Self\u2010Independent Researcher  Thunder Bay ON Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"13","published-online":{"date-parts":[[2024,11,27]]},"reference":[{"key":"e_1_2_9_2_1","volume-title":"Mathematical methods of classical mechanics","author":"Arnold V. 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