Voltage Divider

Concept and formula

Quick example

With Vin = 12 V, R1 = 1 kΩ and R2 = 2.2 kΩ, Vout ≈ 8.25 V.

Try the interactive calculator →

What to check in a real design

• Consider the impedance of the load connected to Vout.
• Very low values waste current; very high values make the output more sensitive to noise.
• For accurate references or changing loads, add an op-amp buffer.

Intuition: the voltage is shared in proportion

Picture a ladder from 0 V up to V_in. Two resistors in series split that height into two sections, and each section is proportional to its resistor’s value. If R1 and R2 are equal, the middle point sits exactly halfway; if R2 is three times R1, it sits at three quarters of the height. The formula V_out = V_in · R2 / (R1 + R2) is just that proportion.

The key point is that the output depends on the ratio between the resistors, not on their absolute values: 1 kΩ with 2 kΩ and 100 kΩ with 200 kΩ give the same voltage. What changes is the current drawn and the ability to supply current to a load.

Where the formula comes from

By Kirchhoff’s current law, with no load on the output, the same current I flows through R1 and R2. By Ohm’s law, I = V_in / (R1 + R2). The voltage across R2 is V_out = I · R2, and substituting gives V_out = V_in · R2 / (R1 + R2). Gustav Kirchhoff stated his circuit laws in 1845, while still a student; together with Ohm’s law they are the foundation of all circuit analysis used today.

The divider as seen by the load: Thévenin

To the load, a divider looks like an ideal voltage source of V_in · R2 / (R1 + R2) with a series resistance equal to R1 ∥ R2. This is the Thévenin equivalent, and it explains why the output sags when you connect a load: the load current causes a drop across that internal resistance. As a rule of thumb, the load should be at least 10 times larger than R1 ∥ R2 to keep the error small.

Example 1: the potentiometer, an adjustable divider

A potentiometer is a divider with a sliding contact: the wiper splits the resistive track into two parts that always add up to the total value. With a 10 kΩ pot between 0 and 5 V and the wiper 30 % of the way from ground, R2 = 3 kΩ and R1 = 7 kΩ, so V_out = 5 × 3 / 10 = 1.5 V. Analog volume knobs, joysticks and many position sensors work this way.

Example 2: reading a thermistor or a photoresistor

A microcontroller cannot measure resistance directly, but it can measure voltage. Put a 10 kΩ NTC thermistor (at 25 °C) on top and a fixed 10 kΩ resistor below, powered from 5 V: at 25 °C the output is 2.5 V. If the thermistor warms up and its resistance falls to 5 kΩ, the output rises to 5 × 10 / (5 + 10) ≈ 3.33 V. The ADC reads that voltage, and the program works out the resistance and, from the sensor’s curve, the temperature. Convert the reading with the ADC calculator.

Example 3: when the instrument changes the measurement

A 100 kΩ / 100 kΩ divider on 10 V should read 5 V. With a digital multimeter of 10 MΩ input impedance, R2 is in parallel with 10 MΩ (≈ 99.0 kΩ) and the reading is ≈ 4.98 V, an error of only 0.5 %. With an old 20 kΩ/V analog meter on its 10 V range (200 kΩ input), R2 ∥ 200 kΩ ≈ 66.7 kΩ and the reading drops to 4.0 V. The circuit didn’t change; the instrument did. The Thévenin resistance here is 50 kΩ, far too high for a 200 kΩ instrument.

When not to use a divider

A divider is not a power supply. If you try to run a 3.3 V module from 5 V with two resistors, the voltage will shift every time the module’s current changes, and power is wasted in the resistors. To power circuits, use a linear or switching regulator; keep dividers for signals, references and measurements.

Real-world applications

• Measuring batteries and supplies with a low-voltage ADC.
• Logic level shifting from 5 V to 3.3 V on input lines.
• Resistive sensors: thermistors, photoresistors, strain gauges and humidity sensors.
• Transistor biasing and reference voltages for comparators.
• Regulator feedback: the adjust pin of many regulators sets the output voltage through a divider.

Work out your resistors with the voltage divider calculator and, if you need to combine resistors to reach a value, use the parallel resistance calculator.