Photon-counting CT (PCCT) may yield potential value for many clinical applications due to its relative immunity to electronic noise, increased geometric efficiency relative to current scintillating detectors, and the ability to resolve energy information about the detected photons. However, there are a large number of parameters that require optimization, particularly the energy thresholds configuration. Fast and accurate estimation of signal and noise in PCCT can benefit the optimization of acquisition parameters for specific diagnostic tasks. Based on the acquisition parameters and detector response of our research PCCT system, we derived mathematical models for both signal and noise. The signal model took the tube spectrum, beam filtration, object attenuation, water beam hardening, and detector response into account. The noise model considered the relationship between noise and radiation dose, as well as the propagation of noise as threshold data are subtracted to yield energy bin data. To determine the absolute noise value, a noise look-up table (LUT) was acquired using a limited 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 attenuation. Validation of the estimation algorithms was performed on our whole-body research PCCT system using semianthropomorphic water phantoms and solutions of calcium and iodine. The algorithms achieved accurate estimation of signal and noise for a variety of scanning parameter combinations. The proposed method can be used to optimize energy thresholds configuration for many clinical applications of PCCT.