Approximate number perception is noisy, but it is unclear what kind of underlying process the noise reflects. Here we provide evidence that approximate number estimation should be thought of as a sampling procedure. We show that the the average of two approximate number estimates of the same stimulus tends to outperform either estimate alone; additionally, the average difference between the two estimates of a given number linearly increases as a function of number, consistent with Weber’s law. Finally, we provide evidence that people report confidence ranges consistent with Weber’s law. This suggests that they represent a distribution of possible responses even on a single trial.