This paper introduces a new method for comparing species richness between communities by standardizing samples based on completeness (sample coverage) rather than size. Traditional rarefaction or extrapolation methods, which standardize samples by size, can lead to biased comparisons because a sample of a given size may fully characterize a low-diversity community but not a high-diversity one. The proposed method uses coverage-based rarefaction and extrapolation, which standardize samples by their completeness. This approach yields less biased comparisons and requires less sampling effort. When integrated with an adaptive stopping rule, samples can be compared directly without rarefaction, avoiding data loss. Coverage-based rarefaction also throws away less data than traditional size-based rarefaction and more accurately reflects the true richness of communities. The method is demonstrated using hypothetical and real examples, showing its advantages in comparing species richness. The paper also presents an analytical formula for estimating species richness at a given coverage and an unbiased algorithm for rarefaction. Coverage-based extrapolation is also introduced, allowing for predictions of species richness beyond the reference sample size. The method is validated using real ecological data, showing its effectiveness in comparing species richness between communities. The results demonstrate that coverage-based rarefaction and extrapolation provide more accurate and meaningful comparisons of species richness than traditional size-based methods.This paper introduces a new method for comparing species richness between communities by standardizing samples based on completeness (sample coverage) rather than size. Traditional rarefaction or extrapolation methods, which standardize samples by size, can lead to biased comparisons because a sample of a given size may fully characterize a low-diversity community but not a high-diversity one. The proposed method uses coverage-based rarefaction and extrapolation, which standardize samples by their completeness. This approach yields less biased comparisons and requires less sampling effort. When integrated with an adaptive stopping rule, samples can be compared directly without rarefaction, avoiding data loss. Coverage-based rarefaction also throws away less data than traditional size-based rarefaction and more accurately reflects the true richness of communities. The method is demonstrated using hypothetical and real examples, showing its advantages in comparing species richness. The paper also presents an analytical formula for estimating species richness at a given coverage and an unbiased algorithm for rarefaction. Coverage-based extrapolation is also introduced, allowing for predictions of species richness beyond the reference sample size. The method is validated using real ecological data, showing its effectiveness in comparing species richness between communities. The results demonstrate that coverage-based rarefaction and extrapolation provide more accurate and meaningful comparisons of species richness than traditional size-based methods.