EngineeringFormulaElectrical Engineering
Voltage Divider Calculator
Calculate the output voltage of a two-resistor voltage divider.
A voltage divider uses two resistors in series to produce a smaller output voltage from a larger input voltage. The output is taken across R2, the resistor nearer the ground/reference end of the pair. Enter the input voltage and the two resistor values to calculate the output voltage.
Vin · Voltage supplied to the top of the divider.
R₁ · Resistor between the input and the output node.
R₂ · Resistor between the output node and ground - the output is measured across this one.
Solution
Enter the required values to calculate the output voltage.
Vout = Vin × R2 / (R1 + R2)
Formula Sheet
- VoutOutput Voltage
- VinInput Voltage
- R₁R1
- R₂R2
Variables & Units
| Symbol | Variable | Description | Common Units |
|---|---|---|---|
| Vout | Output Voltage | Voltage measured across R2. | V |
| Vin | Input Voltage | Voltage supplied to the top of the divider. | V, mV, kV |
| R₁ | R1 | Resistor between the input and the output node. | Ω, kΩ, MΩ |
| R₂ | R2 | Resistor between the output node and ground - the output is measured across this one. | Ω, kΩ, MΩ |
How to Use This Calculator
- 01Enter the Input Voltage supplied to the divider.
- 02Enter R1 (the resistor between the input and the output node) and R2 (the resistor between the output node and ground, across which the output is measured).
- 03Select Calculate to see the resulting output voltage.
- 04Increase R2 relative to R1 to raise the output voltage closer to the input; increase R1 relative to R2 to lower it.
How the Formula Works
Because R1 and R2 are in series, the same current flows through both, so the input voltage splits between them in proportion to their resistance - the larger resistor drops the larger share of the voltage. The fraction of the input voltage that appears across R2 is R2 divided by the total resistance: Vout = Vin × R2 / (R1 + R2).
This means the output voltage depends only on the ratio of R1 to R2, not their absolute values - a 1 kΩ/2 kΩ pair and a 10 kΩ/20 kΩ pair produce exactly the same output fraction. Absolute resistance still matters for other reasons (like how much current the divider draws, or how much the output sags under load), which this calculator doesn't model.
Worked Example 01
Scaling 12 V down for a sensor input
Known
- Input Voltage (Vin): 12 V
- R1: 1 kΩ
- R2: 2 kΩ
Formula
Vout = Vin × R2 / (R1 + R2)
Substitution
Vout = 12 × 2,000 / (1,000 + 2,000)
Result
Vout = 8 V
With R2 twice the size of R1, two-thirds of the 12 V input appears across R2, giving an 8 V output.
Worked Example 02
Equal resistors halve the input voltage
Known
- Input Voltage (Vin): 5 V
- R1: 10 kΩ
- R2: 10 kΩ
Formula
Vout = Vin × R2 / (R1 + R2)
Substitution
Vout = 5 × 10,000 / (10,000 + 10,000)
Result
Vout = 2.5 V
Equal resistors always split the input voltage exactly in half, regardless of their absolute value.
Applications
- 01Scaling a sensor or reference voltage down to fit a microcontroller's input range
- 02Setting a bias or reference point in an analog circuit
- 03Estimating the resistor ratio needed to hit a target output voltage
Assumptions
- 01R1 and R2 are ideal, linear (ohmic) resistors in series.
- 02The divider's output is unloaded - nothing downstream is drawing current from the output node.
- 03The circuit is a steady-state DC circuit, or a purely resistive AC divider.
Where This Model Stops
- 01Does not account for loading - connecting a load to the output draws additional current and pulls the actual output voltage below this calculated value; the effect is larger the closer the load's resistance is to R2.
- 02Not valid for dividers using reactive components (capacitors, inductors) - those require an AC impedance analysis instead of plain resistance.
References
- [1]
Voltage divider
Standard electrical engineering and physics fundamentals
Vout = Vin × R2/(R1+R2), for a two-resistor series divider under no-load conditions.
Frequently Asked Questions
Why does only the resistor ratio matter, not the absolute values?
Vout = Vin × R2/(R1+R2) depends only on the ratio R2/(R1+R2) - scaling both resistors by the same factor leaves that ratio, and therefore the output voltage, unchanged. Absolute values still matter for current draw and how much the output sags under load.
What happens if I connect a load to the output?
This calculator assumes an unloaded (open-circuit) output. A real load draws current through R2, effectively placing another resistor in parallel with it, which lowers the actual output voltage below this calculated value. The lighter the load's current draw relative to the divider's own current, the smaller that effect is.
Which resistor should be R1 and which should be R2?
R1 is the resistor between the input voltage and the output node; R2 is the resistor between the output node and ground, and the output voltage is measured across R2. Swapping the two labels swaps which fraction of the input voltage you get.