There is a bewildering range of estimates for the number of arthropods on Earth. Several measures are based on extrapolation from species specialized to tropical rain forest, each using specific assumptions and justifications. These approaches have not provided any sound measure of uncertainty associated with richness estimates. We present two models that account for parameter uncertainty by replacing point estimates with probability distributions. The models predict medians of 3.7 million and 2.5 million tropical arthropod species globally, with 90% confidence intervals of [2.0, 7.4] million and [1.1, 5.4] million, respectively. Estimates of 30 million or greater are predicted to have <0.00001 probability. Sensitivity analyses identified uncertainty in the proportion of canopy arthropod species that are beetles as the most influential parameter, although uncertainties associated with three other parameters were also important. Using the median estimates suggests that in spite of 250 years of taxonomy and around 855,000 species of arthropods already described, approximately 70% await description.