<p>The paper focuses on developing a goodness-of-fit test statistic for testing the exponentiality based on relative extropy. Relative extropy is a tool for quantifying the dissimilarity between two probability density functions. The estimates of relative extropy can be determined using kernel density and empirical estimation. However, the challenge lies in determining the bandwidth or the gap of order statistics when using kernel density estimators. Therefore, our focus is on empirical estimation. Two estimators of relative extropy divergence are employed in constructing the test statistics based on empirical estimation. Firstly, we opted to utilize the equilibrium distribution, motivated by the fact that the exponential distribution is the only one for which the equilibrium distribution coincides with the original distribution. Secondly, we considered the estimator based on Vasicek’s difference operator. And, to evaluate the performance of the proposed test statistics, we conducted Monte Carlo simulations explicitly tailored to the exponential distribution. Additionally, we compared the proposed statistics with previously defined test statistics based on divergence measures. Finally, we illustrated the application of the proposed statistics with real-life examples.</p>