Scholars and experts in transportation, economics, geography and environmental studies have largely assumed the distance flown by commercial planes represents the shortest route (also known as the great-circle or orthodromic route). However, in the real world, planes follow longer itineraries for various reasons. The magnitude of these detours is assessed through a large, one-week sample of actual flight traces obtained from Flightradar, which we compare with great-circle distances (n=393,360). The results suggest that the average lengthening is 7.6 %, although under conservative hypotheses and with high standard deviation. The shortest flights are proportionally more affected. They also contribute more to the global amount of extra kilometres. The geography of detours by departure airport is the consequence of a wide range of factors. As a result, considering the use of great-circle distances to feed spatial interaction models, emission (or fuel burnt) assessments or airline rankings can lead to significantly skewed outcomes. In addition, detours imposed on certain airlines for geopolitical reasons increase costs, emissions and time aboard, and could be anticompetitive.