This paper develops a construction-based dialectometry capable of identifying previously unknown constructions and measuring the degree to which a given construction is subject to regional variation. The central idea is to learn a grammar of constructions (a CxG) using construction grammar induction and then to use these constructions as features for dialectometry. This offers a method for measuring the aggregate similarity between regional CxGs without limiting in advance the set of constructions subject to variation. The learned CxG is evaluated on how well it describes held-out test corpora while dialectometry is evaluated on how well it can model regional varieties of English. Themethod is tested using two distinct datasets: First, the International Corpus of English representing eight outer circle varieties; Second, a web-crawled corpus representing five inner circle varieties. Results show that themethod (1) produces a grammar with stable quality across sub-sets of a single corpus that is (2) capable of distinguishing between regional varieties of Englishwith a high degree of accuracy, thus (3) supporting dialectometricmethods formeasuring the similarity between varieties of English and (4) measuring the degree to which each construction is subject to regional variation. This is important for cognitive sociolinguistics because it operationalizes the idea that competition between constructions is organized at the functional level so that dialectometry needs to represent as much of the available functional space as possible.