MINOS is a long-baseline neutrino oscillation experiment. A neutrino beam is created at the Fermi National Accelerator Laboratory in Illinois and fired down through the Earth. Measurements of the energy spectra and composition of the neutrino beam are made both at the source using the Near detector and 735 km away at the Soudan Underground Laboratory in Minnesota using the Far detector. By comparing the spectrum and flavour composition of the neutrino beam between the two detectors neutrino oscillations can be observed. Such a comparison depends on the accuracy of the relative calorimetric energy scale.This thesis details a precise measurement of the calorimetric energy scale of the MINOS Far detector and Calibration detector using stopping muons with a new "track window" technique. These measurements are used to perform the relative calibration between the two detectors. This calibration has been accomplished to 1.7% in data and to significantly better than 2% in the Monte Carlo simulation, thus achieving the MINOS relative calibration target of 2%.A number of cross-checks have been performed to ensure the robustness of the calorimetric energy scale measurements. At the Calibration detector the test-beam energy between run periods is found to be consistent with the detector response to better than 2% after the relative calibration is applied. The muon energy loss in the MINOS detectors determined from Bethe-Bloch predictions, data and Monte Carlo are compared and understood.To estimate the systematic error on the measurement of the neutrino oscillation parameters caused by a relative miscalibration a study is performed. A 2% relative miscalibration is shown to cause a 0.6% bias in the values of ∆m 2 and sin 2 (2θ).To my parents.i