Adjustable regulator (LM317)

The regulator keeps exactly 1.25 V across R1 no matter what. R2 just multiplies that fixed slice up to the output you want.

Vo = Vref × (1 + R2 / R1) Vref ≈ 1.25 V

Ignores the adjust-pin current (about 50 µA), which raises the output slightly with large R2. Input must stay 3 V above the output; dropout, heat and the 1.5 A limit are set by the datasheet, not by this formula.