Extinction from habitat loss is the signature conservation problem of the twenty-first century. Despite its importance, estimating extinction rates is still highly uncertain because no proven direct methods or reliable data exist for verifying extinctions. The most widely used indirect method is to estimate extinction rates by reversing the species-area accumulation curve, extrapolating backwards to smaller areas to calculate expected species loss. Estimates of extinction rates based on this method are almost always much higher than those actually observed. This discrepancy gave rise to the concept of an `extinction debt', referring to species `committed to extinction' owing to habitat loss and reduced population size but not yet extinct during a non-equilibrium period. Here we show that the extinction debt as currently defined is largely a sampling artefact due to an unrecognized difference between the underlying sampling problems when constructing a species-area relationship (SAR) and when extrapolating species extinction from habitat loss. The key mathematical result is that the area required to remove the last individual of a species (extinction) is larger, almost always much larger, than the sample area needed to encounter the first individual of a species, irrespective of species distribution and spatial scale. We illustrate these results with data from a global network of large, mapped forest plots and ranges of passerine bird species in the continental USA; and we show that overestimation can be greater than 160%. Although we conclude that extinctions caused by habitat loss require greater loss of habitat than previously thought, our results must not lead to complacency about extinction due to habitat loss, which is a real and growing threat.