Completeness of sources in N2CLS as a function of the ratio between source flux density and instrumental noise level (f_true/σ_inst) at 1.2 mm (left panels) and 2 mm (right panels) in GOODS-N (upper panels) and COSMOS (lower panels). The completeness in various survey areas with different instrumental noise levels is presented as bluish color-coded dots, and the average completeness over the whole survey area is shown using oranges dots. The red line shows the best fit of the average completeness using the functional form of Eq. (3).