Photon-counting detector CT has a large number of acquisition parameters that require optimization, particularly the energy threshold configurations. Fast and accurate estimation of both signal and noise in photon-counting CT (PCCT) images can facilitate such optimization. Using the detector response function of a research PCCT system, we derived mathematical models for both signal and noise estimation, taking into account beam spectrum and filtration, object attenuation, water beam hardening, detector response, radiation dose, energy thresholds, and the propagation of noise. To determine the absolute noise value, a noise lookup table (LUT) for all available energy thresholds was acquired using a number of calibration scans. The noise estimation algorithm then used the noise LUT to estimate noise for scans with a variety of combination of energy thresholds, dose levels, and object attenuations. Validation of the estimation algorithms was performed on a whole-body research PCCT system using semianthropomorphic water phantoms and solutions of calcium and iodine. Clinical feasibility of noise estimation was assessed with scans of a cadaver head and a living swine. The algorithms achieved accurate estimation of both signal and noise for a variety of scanning parameter combinations. Maximum discrepancies were below 15%, while most errors were below 5%.