In this study we explored factors that determine the knowledge of L2 words with orthographic neighbours in L1 (cognates and false cognates). We asked 150 Polish learners of English to translate 105 English non-cognate words, cognates, and false-cognates into Polish, and to assess the confidence of each translation. Confidence ratings allows us to employ a novel analytic procedure which disentangles knowing cognates and false cognates from strategic guessing. Mixed-effects logistic regression models revealed that cognates were known better, whereas false cognates were known worse, relative to non-cognate controls. The advantage of knowing cognates, but not false cognates, was modulated by the degree of similarity to their L1 equivalents. The knowledge of cognates and false cognates was not affected by the frequency of their formal equivalent in L1. Based on these findings we conclude how cross-linguistic formal similarity affects L2 word learnability, proposing a mechanism by which cognates and false cognates are acquired.