Abstract Purpose In this paper, we present new tools to ease the analysis of the effect of variability and uncertainty on life cycle assessment (LCA) results. Methods The tools consist of a standard protocol and an open-source library: lca_algebraic. This library, written in Python and based on the framework Brightway2 (Mutel in J Open Source Softw 2(12):236, 2017) provides functions to support sensitivity analysis by bringing symbolic calculus to LCA. The use of symbolic calculus eases the definition of parametric inventories and enables a very fast evaluation of impacts by factorizing the background activities. Thanks to this processing speed, a large number of Monte Carlo simulations can be generated to evaluate the variation of the impacts and apply advanced statistic tools such as Sobol indices to quantify the contribution of each parameter to the final variance (Sobol in Math Comput Simul 55(1–3):271–280, 2001). An additional algorithm uses the key parameters, identified from their high Sobol indices, to generate simplified arithmetic models for fast estimates of LCA results. Results and discussion The protocol and library were validated through their application to the assessment of impacts of mono crystalline photovoltaic (PV) systems. A comprehensive sensitivity analysis was performed based on the protocol and the complementary functions provided by lca_algebraic. The proposed tools helped building a detailed parametric reference LCA model of the PV system to identify the range of variation of multi-criterion LCA results and the key foreground-related parameters explaining these variations. Based on these key parameters, we generated simplified arithmetic models for quick and simple multi-criteria environmental assessments to be used by non-expert LCA users. The resulting models are both compact and aligned with the reference parametric LCA model of crystalline silicon PV systems. Conclusion This work brings powerful and practical tools to the LCA community to better understand, identify, and quantify the sources of variation of environmental impacts and produce simplified models to spread the use of LCA among non-experts. The library mainly explores the uncertainties of the foreground activities. Further work could also integrate the uncertainty of background activities, described, for example, by pedigree matrices.