Re-evaluation of the temperature-dependent uncertainty parameter f(T) of elementary reactions is proposed by considering all available direct measurements and theoretical calculations. A procedure is presented for making f(T) consistent with the form of the recommended Arrhenius expression. The corresponding uncertainty domain of the transformed Arrhenius parameters (ln A, n, E/R) is convex and centrally symmetric around the mean parameter set. The f(T) function can be stored efficiently using the covariance matrix of the transformed Arrhenius parameters. The calculation of the uncertainty of a backward rate coefficient from the uncertainty of the forward rate coefficient and thermodynamic data is discussed. For many rate coefficients, a large number of experimental and theoretical determinations are available, and a normal distribution can be assumed for the uncertainty of ln k. If little information is available for the rate coefficient, equal probability of the transformed Arrhenius parameters within their domain of uncertainty (i.e. uniform distribution) can be assumed. Algorithms are provided for sampling the transformed Arrhenius parameters with either normal or uniform distributions. A suite of computer codes is presented that allows the straightforward application of these methods. For 22 important elementary reactions of the H2 and syngas (wet CO) combustion systems, the Arrhenius parameters and 3rd body collision efficiencies were collected from experimental, theoretical and review publications. For each elementary reaction, kmin and kmax limits were determined at several temperatures within a defined range of temperature. These rate coefficient limits were used to obtain a consistent uncertainty function f(T) and to calculate the covariance matrix of the transformed Arrhenius parameters.