Fidelity estimates the closeness or degree of overlap between a pair of unknown quantum systems. In quantum information processing study, a primary task is to estimate the fidelity of a pure states pair in a 2-dimensional Hilbert space or between a mixed state, \(\rho \) , and pure state existing in N dimensional Hilbert space while transmitting them through noisy environments. This paper suggests two theorems to estimate fidelity while proving and justifying them numerically. The first theorem computes fidelity between pure states and the second estimates fidelity between mixed and pure states. The mathematical basis of the theorems confirms accuracy in estimation while dealing with single- and multiqubit system environments.