How cells control their size and maintain size homeostasis is a fundamental open question. Cell-size homeostasis has been discussed in the context of two major paradigms: "sizer," in which the cell actively monitors its size and triggers the cell cycle once it reaches a critical size, and "timer," in which the cell attempts to grow for a specific amount of time before division. These paradigms, in conjunction with the "growth law"  and the quantitative bacterial cell-cycle model , inspired numerous theoretical models [3-9] and experimental investigations, from growth [10, 11] to cell cycle and size control [12-15]. However, experimental evidence involved difficult-to-verify assumptions or population-averaged data, which allowed different interpretations [1-5, 16-20] or limited conclusions [4-9]. In particular, population-averaged data and correlations are inconclusive as the averaging process masks causal effects at the cellular level. In this work, we extended a microfluidic "mother machine"  and monitored hundreds of thousands of Gram-negative Escherichia coli and Gram-positive Bacillus subtilis cells under a wide range of steady-state growth conditions. Our combined experimental results and quantitative analysis demonstrate that cells add a constant volume each generation, irrespective of their newborn sizes, conclusively supporting the so-called constant Δ model. This model was introduced for E. coli [6, 7] and recently revisited , but experimental evidence was limited to correlations. This "adder" principle quantitatively explains experimental data at both the population and single-cell levels, including the origin and the hierarchy of variability in the size-control mechanisms and how cells maintain size homeostasis.