This paper describes the step-by-step process of characterizing tephra-fall deposits based on isopach, isomass and isopleth maps as well as thickness transects at different distances from their source. It covers the most frequently used empirical methods of integration (i.e., exponential, power–law and Weibull) and provides a description of the key physical parameters that can be retrieved from tephra-fall deposits. To streamline this process, a Matlab function called TephraFits is proposed, which is highly customizable and also guides the interpretation of the results. The function calculates parameters such as the deposit volume/mass, the VEI/magnitude, and the rates of thickness–decay away from the source and assists in eruption classification using deposit–based schemes. The function also contains a stochastic mode that can be used to propagate the uncertainty from field data to the quantification of eruption source parameters. The use of this function is demonstrated using the the 1180 ±80 years B.P. andesitic subplinian/Plinian tephra deposit Layer 5 of Cotopaxi volcano, Ecuador. In addition, we constrain the often delicate choice of the distal integration limit of the power–law method from synthetic deposits produced with the advection–diffusion model Tephra2.