This contribution presents a general numerical method for computing lower and upper bound of the optimal constant in Friedrichs’ inequality. The standard Rayleigh-Ritz method is used for the lower bound and the method of $𝑎\mathrm{𝑝𝑟𝑖𝑜𝑟𝑖}-𝑎\mathrm{𝑝𝑜𝑠𝑡𝑒𝑟𝑖𝑜𝑟𝑖}\mathrm{𝑖𝑛𝑒𝑞𝑢𝑎𝑙𝑖𝑡𝑖𝑒𝑠}$ is employed for the upper bound. Several numerical experiments show applicability and accuracy of this approach.