The CALorimetric Electron Telescope (CALET) is a space experiment installed aboard the International Space Station (ISS). The instrument has been accumulating data since October 2015, searching for nearby cosmic-ray sources and dark matter signatures with accurate measurements of the inclusive spectrum of cosmic electrons and positrons up to the TeV region. The CALET main detector consists of a charge detector, an imaging calorimeter and a total absorption calorimeter: the total depth of the instrument for vertical incidence is about 30 radiation lengths. This design offers excellent performances in terms of the reconstruction of: the particle charge up to and above Iron, the primary track with an angular resolution better than $1^\circ$, the incident energy with a resolution better than 2% for electrons up to 1 TeV and a good proton/electron identification corresponding to a proton rejection factor of about $10^5$. In this contribution the analysis steps for the measurement of the electron flux are discussed and, by exploiting the full statistics accumulated by the CALET experiment, the measurement of the inclusive spectrum of cosmic electrons and positrons (all-electron) is presented.