Voltage Divider Calculator

An unloaded series pair of resistors splits a voltage in proportion to resistance: the output equals the input times R2 divided by R1 plus R2. The same current flows through both resistors, each drops that current times its own resistance, and the ratio therefore always falls between zero and one. The formula follows directly from Ohm's law and Kirchhoff's voltage law, and it is exact only while nothing draws current from the output node. Connect a load and it sits in parallel with R2, lowering the effective bottom resistance and the output with it. The usual working rule keeps load impedance at least ten times R2, which holds the error under roughly ten percent; a unity-gain op-amp buffer removes the problem outright and is standard practice ahead of an analog-to-digital converter input. Choosing values trades off two failure modes. Low resistances hold the output stiff against loading but draw continuous quiescent current, which matters in battery-powered designs where a 12 volt monitoring divider of 27 kilohm and 10 kilohm still consumes about 324 microamps around the clock. High resistances save power but raise source impedance, worsen loading error, slow settling into any capacitance at the node, and increase susceptibility to leakage and noise pickup. Dissipation in each resistor is current squared times resistance, and standard through-hole parts are usually rated a quarter watt. Because standard E12 and E24 values rarely produce an exact ratio, achievable output typically lands a percent or two off the intended target.

The divider is the simplest application of the relationship Georg Simon Ohm published in 1827 in Die galvanische Kette, mathematisch bearbeitet, work that was received poorly in Germany at first and recognized only years later. Gustav Kirchhoff's circuit laws of 1845 supplied the second half of the justification, and Leon Charles Thevenin's theorem of 1883 explained precisely why a loaded divider sags: any such network is equivalent to a single source in series with the parallel combination of R1 and R2, and that output resistance is what the load works against. The idea saw instrument use well before it saw electronic use. Johann Christian Poggendorff described the potentiometer method around 1841, comparing an unknown electromotive force against an adjustable fraction of a known one and drawing no current from the source at balance, thereby avoiding the error a direct voltmeter reading introduces. Charles Wheatstone's rheostat and slide wires supplied the adjustable elements for such measurements. Mass-produced fixed resistors arrived with carbon composition parts in the early twentieth century, and the preferred-value system now standardized as IEC 60063, whose E12 and E24 decades are spaced logarithmically to match component tolerance bands, was formalized in the 1950s. That standard is the reason practical dividers are designed around a small set of available ratios rather than arbitrary ones.