Calculate output voltage of a resistive voltage divider circuit given input voltage and two resistor values.
Last reviewed: May 2026
A voltage divider is one of the most fundamental circuits in electronics — two resistors in series that produce an output voltage proportional to the input voltage. Despite its simplicity, the voltage divider appears in virtually every electronic device, from smartphone chargers and audio equipment to industrial control systems and sensor interfaces.1
The circuit works on a straightforward principle: when current flows through two resistors in series, the voltage drops across each resistor in proportion to its resistance. The output voltage, measured between the junction of the two resistors and ground, is a predictable fraction of the input voltage determined entirely by the ratio of the resistor values.
The core formula is Vout = Vin × R2 / (R1 + R2), where R1 is the resistor connected between the input voltage and the output node, and R2 is the resistor connected between the output node and ground. This formula assumes an ideal, unloaded divider — meaning no current is drawn from the output node. Understanding when this assumption holds and when it breaks down is critical for practical circuit design.2
The voltage divider equation derives directly from Ohm's law and Kirchhoff's voltage law. In a series circuit, the same current I flows through both resistors. By Ohm's law, I = Vin / (R1 + R2). The voltage across R2 (which is the output voltage) is V_R2 = I × R2 = Vin × R2 / (R1 + R2).
The ratio R2 / (R1 + R2) is called the divider ratio or attenuation factor. It always produces a value between 0 and 1, meaning the output voltage is always less than or equal to the input voltage. When R2 is much larger than R1, the output approaches the input voltage. When R1 is much larger than R2, the output approaches zero. Equal resistors produce exactly half the input voltage.3
| Vin | R1 | R2 | Vout | Divider Ratio | Current Draw |
|---|---|---|---|---|---|
| 12V | 10kΩ | 10kΩ | 6.00V | 0.500 | 0.6 mA |
| 5V | 10kΩ | 20kΩ | 3.33V | 0.667 | 0.167 mA |
| 12V | 8.2kΩ | 3.3kΩ | 3.44V | 0.287 | 1.04 mA |
| 3.3V | 4.7kΩ | 10kΩ | 2.24V | 0.680 | 0.224 mA |
| 24V | 47kΩ | 10kΩ | 4.21V | 0.175 | 0.421 mA |
| 5V | 1kΩ | 2kΩ | 3.33V | 0.667 | 1.67 mA |
The unloaded voltage divider formula assumes infinite load impedance — no current drawn from the output. In practice, any connected load draws current and reduces the effective R2 value, causing the actual output voltage to be lower than the formula predicts. This loading effect is the most common source of error in voltage divider applications.
When a load resistance R_L is connected in parallel with R2, the effective bottom resistance becomes R2_eff = (R2 × R_L) / (R2 + R_L). The loaded output voltage is Vout_loaded = Vin × R2_eff / (R1 + R2_eff). As a rule of thumb, the load impedance should be at least 10× the value of R2 for the output to remain within 10% of the unloaded value.4
The output impedance of a voltage divider equals R1 and R2 in parallel: Zout = (R1 × R2) / (R1 + R2). This is the Thevenin equivalent resistance seen by the load. Lower divider resistances produce lower output impedance (better load regulation) but increase current draw and power dissipation. Higher resistances save power but are more susceptible to loading and noise.
Microcontroller ADC level shifting: Many sensors output 0–5V signals, but modern microcontrollers (Arduino, ESP32, STM32) have 3.3V ADC inputs. A voltage divider with R1 = 10kΩ and R2 = 20kΩ converts a 5V signal to 3.3V safely. This is the single most common voltage divider application in hobbyist and professional electronics.1
Battery voltage monitoring: Monitoring a 12V or 24V battery with a microcontroller requires reducing the voltage to the ADC range. A divider with R1 = 100kΩ and R2 = 10kΩ scales 12V down to approximately 1.09V, well within a 3.3V ADC range. High-value resistors minimize current drain from the battery.
Transistor biasing: Voltage dividers set the DC operating point (bias) of transistor amplifier stages. The divider establishes a stable base voltage independent of transistor beta variation, making the circuit's performance predictable across manufacturing tolerances. This is the foundation of the voltage-divider bias configuration used in nearly all discrete amplifier designs.2
Potentiometers: A potentiometer is a variable voltage divider — the wiper position determines the ratio. Volume controls, position sensors, and joysticks all use this principle.
| Application | Recommended R Values | Rationale |
|---|---|---|
| Signal conditioning (sensors to ADC) | 10kΩ–100kΩ | Low current draw, minimal sensor loading |
| Audio circuits | 1kΩ–47kΩ | Balance noise and output impedance |
| Battery monitoring | 100kΩ–1MΩ | Minimize battery drain; high-impedance OK |
| Transistor biasing | 1kΩ–22kΩ | Low impedance for stability |
| LED circuits | Not recommended | Use a current-limiting resistor instead |
A voltage divider is not a substitute for a voltage regulator. Dividers provide a fixed voltage ratio but cannot maintain a constant output voltage under varying load conditions. If your application draws more than a few milliamps and requires a stable output, use a linear regulator (like the LM7805 or LM1117) or a switching regulator instead.
Voltage dividers are appropriate for signal conditioning (microampere to low-milliampere loads), reference voltage generation for comparators, and measurement applications. For power delivery — driving motors, LEDs, charging circuits, or powering ICs — always use a proper regulator that maintains output voltage regardless of load current.5
While the basic voltage divider formula uses resistances, the same principle extends to AC circuits using impedances. In an AC voltage divider, components can include resistors, capacitors, and inductors. The generalized formula becomes Vout = Vin × Z2 / (Z1 + Z2), where Z represents complex impedance. This is the foundation of many analog filter circuits, audio crossover networks, and signal conditioning stages.
A capacitive voltage divider uses two capacitors instead of resistors. Unlike resistive dividers, capacitive dividers are frequency-dependent — the impedance of a capacitor is Z_C = 1/(2πfC), which decreases with increasing frequency. This means the divider ratio changes with signal frequency, making capacitive dividers useful in frequency-selective circuits like high-pass and low-pass filters. At DC (f = 0), capacitors have infinite impedance and block all current, so capacitive dividers do not work for DC signals at all.5
For applications requiring very large voltage reductions — such as measuring high voltages (hundreds or thousands of volts) with low-voltage electronics — multi-stage voltage dividers can be cascaded. However, each stage loads the previous one, so the overall ratio is not simply the product of individual stage ratios. Careful impedance analysis is required, or buffer amplifiers can be placed between stages to prevent loading.
In high-voltage measurement applications, specialized high-voltage resistor dividers use precision resistors rated for kilovolts. These dividers must account for stray capacitance between resistors and the enclosure, voltage coefficient of resistance (some resistors change value slightly with applied voltage), temperature coefficient drift, and creepage and clearance distances for safety. Professional-grade high-voltage dividers from manufacturers like Fluke and Tektronix achieve accuracy specifications of 0.01% or better, enabling precise measurement of voltages up to 100 kV or more for use in power system monitoring, electrical safety testing, and scientific research applications.4
When designing a voltage divider for a real circuit, follow this workflow for reliable results. First, determine the required output voltage and the acceptable tolerance range. Second, calculate the ideal ratio R2/(R1+R2). Third, select standard E-series resistor values that closely approximate this ratio — the E96 series (1% tolerance) offers 96 values per decade, while the E24 series (5% tolerance) offers 24 values. Fourth, verify that the chosen values do not exceed the power rating of your resistors by calculating P = V²/R for each component. Fifth, check that the current draw through the divider (Vin / (R1 + R2)) is acceptable for your power budget. Finally, if the divider feeds a load, verify that the loaded output voltage still meets your requirements using the parallel resistance formula for R2 and the load.3
Standard resistors have 5% tolerance (gold band) or 1% tolerance (brown band). In a voltage divider, resistor tolerances compound — worst case, both resistors could deviate in opposite directions. For a divider with 5% resistors targeting 3.3V from 5V, the actual output could range from 3.10V to 3.51V. For applications requiring better than 2% voltage accuracy (like precision ADC reference voltages), use 1% or 0.1% tolerance metal film resistors.3
→ Start with the desired ratio, then pick values. Calculate R2/(R1+R2) for your target Vout, then choose standard resistor values that closely match this ratio. Use a resistor calculator or E-series chart to find available values.
→ Keep load impedance above 10× R2. If your load resistance is less than 10 times R2, the output voltage will sag significantly. Either reduce R1 and R2 values or add a buffer amplifier (op-amp voltage follower) between the divider and the load.
→ Use 1% resistors for precision applications. The extra cost of 1% tolerance resistors is negligible (pennies) and eliminates the largest source of error in voltage divider circuits.
→ Calculate power dissipation. P = Vin² / (R1 + R2). Standard ¼W resistors can handle up to 250 mW. For low-value resistors with high input voltages, verify that neither resistor exceeds its power rating.
See also: Ohm's Law · Resistor Color Code · LED Resistor · Power Calculator · Frequency Calculator