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The primary fertility index for a population, the total fertility rate (TFR), cannot be calculated for many areas and periods because it requires disaggregation of births by mother's age. Here we discuss a flexible framework for estimating TFR using inputs as minimal as a population pyramid. We develop five variants, each with increasing complexity and data requirements. We test accuracy across a diverse set of data sources that comprise more than 2,400 fertility schedules with known TFR values, including the Human Fertility Database, Demographic and Health Surveys, U.S. counties, and nonhuman species. We show that even the simplest and least accurate variant has a median error of only 0.09 births per woman over 2,400 fertility schedules, suggesting accurate TFR estimation over a wide range of demographic conditions. We anticipate that this framework will extend fertility analysis to new subpopulations, periods, geographies, and even species. To demonstrate the framework's utility in new applications, we produce subnational estimates of African fertility levels, reconstruct historical European TFRs for periods up to 150 years before the collection of detailed birth records, and estimate TFR for the United States conditional on race and household income.