In August 2015, the CALorimetric Electron Telescope (CALET), designed for long exposure observations of high energy cosmic rays, docked with the International Space Station (ISS) and shortly thereafter began tocollect data. CALET will measure the cosmic ray electron spectrum over the energy range of 1 GeV to 20 TeV with a very high resolution of 2% above 100 GeV, based on a dedicated instrument incorporating an exceptionally thick 30 radiation-length calorimeter with both total absorption and imaging (TASC and IMC) units. Each TASC readout channel must be carefully calibrated over the extremely wide dynamic range of CALET that spans six orders of magnitude in order to obtain a degree of calibration accuracy matching the resolution of energy measurements. These calibrations consist of calculating the conversion factors between ADC units and energy deposits, ensuring linearity over each gain range, and providing a seamless transition between neighboring gain ranges. This paper describes these calibration methods in detail, along with the resulting data and associated accuracies. The results presented in this paper show that a sufficient accuracy was achieved for the calibrations of each channel in order to obtain a suitable resolution over the entire dynamic range of the electron spectrum measurement.