Species richness is an essential biodiversity variable indicative of ecosystem states and rates of invasion, speciation and extinction both contemporarily and in fossil records. However, limited sampling effort and spatial aggregation of organisms mean that biodiversity surveys rarely observe every species in the survey area. Here we present a non-parametric, asymptotic and bias-minimized richness estimator,Ωby modelling how spatial abundance characteristics affect observation of species richness. Improved asymptotic estimators are critical when both absolute richness and difference detection are important. We conduct simulation tests and appliedΩto a tree census and a seaweed survey.Ωconsistently outperforms other estimators in balancing bias, precision and difference detection accuracy. However, small difference detection is poor with any asymptotic estimator. An R-package,Richness, performs the proposed richness estimations along with other asymptotic estimators and bootstrapped precisions. Our results explain how natural and observer-induced variations affect species observation, how these factors can be used to correct observed richness using the estimatorΩon a variety of data, and why further improvements are critical for biodiversity assessments.This article is part of the theme issue ‘Detecting and attributing the causes of biodiversity change: needs, gaps and solutions’.