Abstract How many species have gone extinct in modern times before being described by science? To answer this question, and thereby get a full assessment of humanity's impact on biodiversity, statistical methods that quantify undetected extinctions are required. Such methods have been developed recently, but they are limited by their reliance on parametric assumptions; specifically, they assume the pools of extant and undetected species decay exponentially, whereas real detection rates vary temporally with survey effort and real extinction rates vary with the waxing and waning of threatening processes. We devised a new, nonparametric method for estimating undetected extinctions. As inputs, the method requires only the first and last date at which each species in an ensemble was recorded. As outputs, the method provides estimates of the proportion of species that have gone extinct, detected, or undetected and, in the special case where the number of undetected extant species in the present day is assumed close to zero, of the absolute number of undetected extinct species. The main assumption of the method is that the per‐species extinction rate is independent of whether a species has been detected or not. We applied the method to the resident native bird fauna of Singapore. Of 195 recorded species, 58 (29.7%) have gone extinct in the last 200 years. Our method projected that an additional 9.6 species (95% CI 3.4, 19.8) have gone extinct without first being recorded, implying a true extinction rate of 33.0% (95% CI 31.0%, 36.2%). We provide R code for implementing our method. Because our method does not depend on strong assumptions, we expect it to be broadly useful for quantifying undetected extinctions.