- The Kerr effect in silicon ring resonators (RRs) is widely used for switching and regeneration of optical communications signals. In addition, it has been shown to considerably limit the performance of refractive index sensors based on high quality-factor RRs. While the Kerr effect's impact on output signals of silicon RRs is well known, its influence on the properties of the output noise is yet to be explored. In this work, we analytically and numerically analyze the noise properties of Kerr effect in silicon RRs. We show that the input power, RR's bandwidth, and input optical signal to noise ratio (OSNR) have significant influence on the power and distribution of the output noise. We use the developed noise model to evaluate the RR's noise figure and output noise distribution for optical communications and sensing applications. These noise properties can be used for the design and performance evaluation of optical communications systems and sensors using silicon photonic RRs.