The nominal peak tube voltage potential (kVp) and measured half-value layer (HVL) are sufficient to generate energy spectra and fluence profiles for characterizing an x-ray source in Computed Tomography (CT). We validate this method for the purpose of calculating patient and machine-specific radiation dose rapidly and accurately using a novel in-house hybrid (i.e., deterministic and stochastic) kV dose computation algorithm (kVDoseCalc). Spatial variation of the x-ray source spectrum was found by measuring HVL across the internal bow tie filter axis and using the nominal kVp settings and third-party software Spektr to generate the spectra. The beam fluence was calculated by dividing the integral product of the spectra and the in-air NIST mass-energy attenuation coefficients by in-air dose measurements along the filter axis. To ensure dose convergence while minimizing calculation time, we examined the sensitivity of kVDoseCalc to the number of photons seeded. We modeled the source of a Philips Brilliance Big Bore CT scanner for 90, 120, and 140 kVp settings. Doses measured using a Farmer-type Capintec ion chamber (0.65 cc) placed in a cylindrical polymethyl methacrylate (PMMA) phantom were compared to those computed with kVDoseCalc. The average percent difference between calculation and measurement pooled over all 12 positions in the phantom was determined to be 1.68%, 1.60% and 1.25% for 90, 120, and 140 kVp, respectively. The maximum percent difference between calculation and measurement was less than 3.64% pooled over all energies and measurement positions. Thirty-one out of a total of 36 simulation conditions were within the experimental uncertainties associated with measurement reproducibility and chamber volume effects. Our source characterization technique, which derives incident fluence and spectra from measurements of HVL across the bow tie profile, is sufficient for accurate patient and machine-specific CT dose calculations.