RULES for activity calculations and radiometric dating estimations

Calculation of activities and radiometric dating through radioactive series may lead to long or non-explicit mathematical expressions. Thus, dedicated software is required. RULES (RaPCUBES, URADS and LEADS Encompassed Software) is a new computer application dedicated to calculating activities and populations for radionuclides that belong to the four radioactive series (238U, 235U, 232Th and 237Np) and performing dating estimations using methods based on disequilibria between isotopes within the 238U family. RULES contains three different tools. RaPCUBES: Radioactivity and Population Calculator Using Bateman Equations’ Solutions. URADS: Uranium Routines Application for Dating Samples through R or 234U/238U and T or 230Th/234U methods. LEADS: Lead Employed Approaches for Dating Sediments through 210Pb simplest physical models, i.e., CA (Constant Activity), CS (Constant Sedimentation), CF (Constant Flux) and CFCS (Constant Flux Constant Sedimentation). RULES has been programmed in the environment of MATLAB’s AppDesigner (v. 2021b), with a database built in Microsoft Excel. It is available as completely free software via e-mail request, as only the 9.11 version of MATLAB’s Runtime is required. This does not need MATLAB’s license to operate and makes the installation process straightforward through a unique link. Also, as a desktop application, RULES is able to work offline. RULES’s main purpose is to provide simple-to-use software that encompasses three different tools of interest with intuitive user interfaces, so no programming knowledge is required to use the application. Also, novel revised propagation of uncertainties is implemented at all levels of the calculation processes. Furthermore, it has been demonstrated that RULES performs satisfactorily when used in actual high-quality research works. Found discrepancies in results between RULES and some widespread similar software do not exceed 4 % and the implemented propagation of uncertainties seems more conservative than the other tools’ ones. Finally, thanks to its simplicity and results visualization possibilities, RULES stands out as a useful educational instrument to study radioactive series, secular and transient equilibrium and some radiometric dating strategies.