The LM317 adjustable regulator
The LM317 (and its negative counterpart the LM337) holds a constant 1.25 V between its OUT and ADJ pins. Put a resistor R1 across that gap and a fixed current flows through it; a second resistor R2 from ADJ to ground turns that current into an output voltage:
Vout = 1.25 × (1 + R2/R1)
R1 is conventionally 240 Ω. That value draws 1.25 V / 240 Ω ≈ 5.2 mA, which is comfortably above the regulator's minimum load current, so the output stays in regulation even with nothing connected. There is also a small 50 µA current out of the ADJ pin; it adds R2 × 50 µA to the output, which is negligible until R2 reaches several kΩ.
Worked examples
For 5 V with R1 = 240 Ω: R2 = 240 × (5/1.25 − 1) = 240 × 3 = 720 Ω. For a 13.8 V bench supply: R2 = 240 × (13.8/1.25 − 1) = 240 × 10.04 = 2.41 kΩ. The calculator also lists standard E24 pairs and the exact voltage each one produces, so you can pick real parts instead of trimming.
The zener shunt regulator
A zener diode plus one series resistor makes the simplest voltage reference. The resistor drops the difference between supply and zener voltage; it must be small enough that the zener still gets its minimum bias current at full load:
Rs = (Vin − Vz) / (Iload + Iz,min)
Because a larger resistor would starve the diode, the calculator rounds down to the nearest standard value. It then reports the worst-case power in both parts — the zener's worst case is with the load disconnected, when the entire current flows through the diode — and suggests wattage ratings with 2× headroom. Zener shunt regulators suit light loads (up to roughly 50 mA); above that the resistor and diode dissipation grow wasteful and an LM317 or a switching regulator is the better choice.
Related tools: the voltage divider calculator shares the same E-series pair solver, and Ohm's law covers the resistor and power arithmetic behind both circuits.