What is the voltage divider formula?
VOUT = VIN × R2 / (R1 + R2), where R2 is the resistor between the output and ground.
CIRCUIT DIAGRAM EXAMPLE
Voltage Divider Circuit Diagram and Formula
Two resistors in series across a supply give a fixed fraction of that supply at the point between them. Dividers set reference voltages, scale a battery voltage down for an ADC input and bias transistors.
How this circuit works
R1 and R2 form one series path from 12 V to ground, so the same current flows through both: 12 V / (10 kΩ + 4.7 kΩ) ≈ 0.82 mA. Each resistor drops a share of the supply in proportion to its resistance, so R2 gets 4.7 / 14.7 of it.
That gives VOUT = 12 V × 4.7 kΩ / 14.7 kΩ ≈ 3.84 V. Only the ratio of the two resistors sets the output voltage. Their absolute size sets how much current the divider wastes and how firmly it holds the output when something is connected.
The formula assumes nothing draws current from VOUT. A load sits in parallel with R2, lowers the effective bottom resistance and pulls the output down. A 47 kΩ load, ten times R2, lowers it to about 3.59 V, roughly 6 % low; a load close to R2 changes it far more.
That is why a divider makes reference and measurement voltages, not power. To run a circuit from a lower voltage, use a regulator such as the 7805 in the bridge rectifier example.
Formulas
- Output voltage
VOUT = VIN × R2 / (R1 + R2) = 12 V × 4.7 kΩ / 14.7 kΩ ≈ 3.84 V- Divider current
I = VIN / (R1 + R2) = 12 V / 14.7 kΩ ≈ 0.82 mA- Loaded output
VOUT = VIN × (R2 ∥ RL) / (R1 + R2 ∥ RL)R2 ∥ RL = R2 × RL / (R2 + RL). With RL = 47 kΩ the output falls to about 3.59 V.
- Output resistance
Rout = R1 ∥ R2 = 10 kΩ × 4.7 kΩ / 14.7 kΩ ≈ 3.2 kΩWhat a load sees looking back into the divider. Lower means the output sags less.
Working with your own values? The voltage divider calculator does the sums.
Voltage divider calculatorParts list
| Ref | Part | Value | What it does |
|---|---|---|---|
| R1 | Resistor | 10 kΩ | Top resistor, from the supply to the output. |
| R2 | Resistor | 4.7 kΩ | Bottom resistor, from the output to ground. The output is taken across it. |
| V1 | DC voltage source | 12 V | 12 V DC supply. |
Netlist
Recovered from the drawing itself: every pin on each net below is joined by a wire, a junction or a shared supply or ground symbol.
| Net | Connects |
|---|---|
| GND | V1.-, R2.2 |
| N1 | V1.+, R1.1 |
| VOUT | R1.2, R2.1 |
Common mistakes
- Powering a load from a divider. The output sags as soon as the load current is comparable to the divider current.
- Swapping R1 and R2. The output becomes 12 V × 10 kΩ / 14.7 kΩ ≈ 8.16 V instead of 3.84 V.
- Feeding an ADC from very large resistors. Many microcontroller ADCs expect a source resistance of about 10 kΩ or less unless a capacitor sits at the pin; check the datasheet.
- Forgetting resistor tolerance. With 5 % parts the output can be several percent off, so use 1 % resistors for measurement dividers.
Frequently asked questions
How do I choose the resistor values?
Pick the ratio for the output you need, then scale both resistors so the divider current is small but still about ten times larger than any current the load draws.
Can I use a voltage divider to get 5 V from 12 V?
Only for a signal or reference that draws almost nothing. For anything that draws real current, use a linear regulator such as a 7805 or a buck converter.
Can I measure a battery voltage with an Arduino through a divider?
Yes. Scale the battery's highest voltage below the ADC reference: 20 kΩ over 10 kΩ divides 12.6 V down to 4.2 V for a 5 V Arduino.
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