Voltage divider calculator

V_out = V_in × R2 / (R1 + R2)

The same current flows through both resistors, so each one takes a share of the input voltage in proportion to its resistance. The output is the voltage across R2. The voltage divider lesson derives it and works through where dividers turn up.

That formula assumes nothing draws current from the output. Anything you connect does, and electrically it sits in parallel with R2, so the bottom arm becomes R2 ∥ R_L and the output drops. How far it drops depends on the divider's output resistance, R1 ∥ R2, against the load. Thévenin's theorem is the tool for this: the divider looks like a source of V_out behind R1 ∥ R2. A load 100 times that resistance costs about 1 %; a load equal to it halves the output. Meter loading is the same effect showing up on your multimeter.

The worst-case range assumes both resistors sit at opposite ends of their tolerance, R1 high and R2 low, then the reverse. When R1 and R2 are equal, 1 % parts give a 1 % spread on the output. The pair finder tries each standard value of R1, solves for the R2 that would give the exact output (allowing for the load when there is one), and tests the standard values either side of it. It keeps pairs whose total lands within about a factor of three of the total you asked for.

The ratio fixes the output; the size of the resistors fixes everything else. Low values make a stiff divider that shrugs off a load but wastes current and warms up. High values sip current, which matters on a battery, but a load or even the input current of an ADC pulls them around. A few kilohms to a few tens of kilohms suits most signal work. For battery monitoring people go to hundreds of kilohms and add a small capacitor across R2 for the ADC to draw from. The power dissipation lesson covers the heat side.

• Check the output with the real load connected. A 10 MΩ multimeter barely loads a divider, so the open reading looks right while the circuit it feeds sees less.
• Use 1 % resistors. With 5 % parts the tolerance spread is several times bigger than the error from rounding to standard values.
• On a high-value divider feeding an ADC, put 10 to 100 nF across R2. The ADC samples from the capacitor and the reading stops jumping about.
• For 5 V to 3.3 V logic, a divider is fine on slow lines such as a UART at ordinary baud rates. On fast SPI or anything in the megahertz range, the resistors and the pin capacitance round off the edges; use a level-shifter chip there.
• On higher input voltages, check R1, which carries most of the voltage. Look at its wattage and its maximum working voltage, which is low on small SMD packages.