ABSTRACT: Over the several past years, economists have wondered if poor countries grow faster than rich ones in order to catch up the rich countries, that is if there is a convergence in GDP per capital values. Later, this convergence test included tests on other macroeconomic variables; and moreover beta vs sigma convergence tests emerged. The objective of this research is to determine whether there is any sigma-convergence among 31 European Countries, such as sigma convergence on per capita GDP, sigma convergence on inflation rate, and sigma convergence in interest rate. We carry the test for: (i) 31 European countries, (ii) West European countries only, and (iii) the 12 original Eurozone countries that adopted the euro before or at the start of circulation of euro banknotes. This research project analyzes panel data to examine sigma convergence using statistical tools including OLS and Coefficient Variance between 1998 and 2020. The findings indicate that there is no sigma convergence in the interest rate variable but that there is statistically significant and a negative coefficient estimate that supports the sigma convergence for the GDP per capita variable and CPI-based inflation rate among the 31 European Countries. Similarly, there is statistically significant sigma convergence for the inflation rate variable in Western European countries but no sigma convergence for the interest rate variable in Western European and Eurozone countries. Keywords: Sigma Convergence, Sigma Convergence per GDP, Inflation Rate, Interest Rate, European Countries