This paper presents a derivation of the equilibrium free energy difference between two states of a system using nonequilibrium measurements. The result is established within the master equation formalism, showing that the free energy difference ΔF can be obtained from an ensemble of finite-time measurements of the work performed during a parameter switch. The key result is that the average of exp(-βW) over an ensemble of such measurements equals exp(-βΔF), where β is the inverse temperature and W is the work performed. This result holds regardless of the switching time, and is derived by treating the system's evolution as a Markov process with detailed balance. The derivation is shown to be valid for various stochastic processes, including Hamiltonian evolution, Langevin dynamics, and Monte Carlo simulations. The result has implications for the numerical computation of free energy differences, as it provides a method to extract ΔF from finite-time measurements. The paper also discusses the relationship between this result and thermodynamic integration and adiabatic switching methods.This paper presents a derivation of the equilibrium free energy difference between two states of a system using nonequilibrium measurements. The result is established within the master equation formalism, showing that the free energy difference ΔF can be obtained from an ensemble of finite-time measurements of the work performed during a parameter switch. The key result is that the average of exp(-βW) over an ensemble of such measurements equals exp(-βΔF), where β is the inverse temperature and W is the work performed. This result holds regardless of the switching time, and is derived by treating the system's evolution as a Markov process with detailed balance. The derivation is shown to be valid for various stochastic processes, including Hamiltonian evolution, Langevin dynamics, and Monte Carlo simulations. The result has implications for the numerical computation of free energy differences, as it provides a method to extract ΔF from finite-time measurements. The paper also discusses the relationship between this result and thermodynamic integration and adiabatic switching methods.