Voltage Divider Calculator and Formula

This interactive voltage divider calculator allows you to obtain the output voltage ($V_{out}$) of a passive voltage divider circuit immediately. Below, we explain the physical and mathematical theory behind this fundamental circuit.

What is a Voltage Divider?

A voltage divider (or potential divider) is a simple passive linear circuit that reduces an input voltage ($V_{in}$) to a fraction of it as output voltage ($V_{out}$).

It typically consists of two resistors in series ($R_1$ and $R_2$) connected to an input power supply. Voltage dividers are widely used in electronics to:

• Adapt signal levels for microcontrollers (such as ADC pins on Arduino or ESP32)
• Bias active components like BJT transistors and operational amplifiers
• Create stable reference voltages
• Interface 5V sensors with 3.3V microcontrollers

Voltage Divider Formula

The physical principle of a voltage divider is based on Ohm's Law and Kirchhoff's voltage laws. Since the same current flows through both resistors in series, the general formula is:

$V_{out} = V_{in} \times \frac{R_2}{R_1 + R_2}$

Where:

• $V_{out}$ — Output voltage at the midpoint between the two resistors (V)
• $V_{in}$ — Input supply voltage (V)
• $R_1$ — Top resistor (connected to $V_{in}$), in ohms (Ω)
• $R_2$ — Bottom resistor (connected to GND), in ohms (Ω)

Current through the divider:

$I = \frac{V_{in}}{R_1 + R_2}$

Solving for R1 given a target Vout:

$R_1 = R_2 \times \frac{V_{in} - V_{out}}{V_{out}}$

Step-by-Step Example: 5V Sensor to 3.3V ADC

A common real-world problem: you have an ultrasonic sensor (HC-SR04) that outputs 5V signals, but you want to read it on an ESP32 ADC pin that is limited to 3.3V.

Given: $V_{in} = 5\,\text{V}$, $V_{out} = 3.3\,\text{V}$, choose $R_2 = 20\,\text{k}\Omega$.

Find R1:

$R_1 = 20{,}000 \times \frac{5 - 3.3}{3.3} = 20{,}000 \times 0.515 = 10{,}303\,\Omega$

Use the nearest standard value: 10 kΩ (E12 series).

Verify:

$V_{out} = 5 \times \frac{20{,}000}{10{,}000 + 20{,}000} = 5 \times 0.667 = 3.33\,\text{V}$

Current through the divider: $I = 5\,\text{V} / 30\,\text{k}\Omega = 167\,\mu\text{A}$ — negligible.

Common Voltage Divider Pairs Quick Reference

Always verify by plugging your chosen standard values back into the formula, since the nearest E12/E24 resistor may shift $V_{out}$ by a few percent.

Loading Effect

When you connect a load resistance $R_L$ in parallel with $R_2$, the effective bottom resistance becomes:

$R_{eq} = \frac{R_2 \times R_L}{R_2 + R_L}$

And the actual $V_{out}$ drops to:

$V_{out,\text{loaded}} = V_{in} \times \frac{R_{eq}}{R_1 + R_{eq}}$

Rule of thumb: To minimize loading error to less than 10%, choose $R_L \geq 10 \times R_2$. For a microcontroller ADC pin (typically 100 kΩ–1 MΩ input impedance), a divider using 10 kΩ–20 kΩ resistors experiences negligible loading.

Power Dissipation

The power dissipated by the divider resistors as heat:

$P_{total} = \frac{V_{in}^2}{R_1 + R_2}$

For a 5V–to–3.3V divider with 10 kΩ + 20 kΩ:

$P = \frac{25}{30{,}000} \approx 833\,\mu\text{W}$

This is tiny — standard 1/8W resistors are more than adequate. However, for 12V systems with low-value resistors (e.g., 1 kΩ + 2 kΩ), power reaches 48 mW — still fine for 1/4W resistors, but worth checking.

Frequently Asked Questions

How does load resistance affect the voltage divider output?

When a load ($R_L$) is connected in parallel with $R_2$, it reduces the effective bottom resistance and pulls $V_{out}$ lower than the unloaded value. To keep the output stable, the divider's source resistance ($R_1 \parallel R_2$) must be much smaller than the load — ideally 10× or more. If the load impedance varies widely, consider a buffered divider using an op-amp voltage follower.

Can I use a voltage divider to power a motor or LED strip?

No. A resistive voltage divider is only suitable as a signal-level shifter or reference bias, not as a power supply. The output voltage collapses under load, and the power wasted in the resistors scales with current. Use a switching regulator (buck converter) or LDO regulator to step down voltage for power delivery.

What is the difference between a voltage divider and a Zener regulator?

A voltage divider produces an output that varies with load and input voltage. A Zener diode placed across $R_2$ clamps $V_{out}$ to a fixed reference voltage as long as the current through the circuit exceeds the Zener's minimum holding current. Zener regulators are still inefficient under heavy loads; for precision references, use a dedicated voltage reference IC (e.g., LM4040, TL431).

Why do I get a different voltage than the formula predicts?

The three most common causes: (1) the load draws enough current to change the divider ratio (loading effect), (2) you are measuring with a cheap multimeter whose internal resistance (~10 MΩ) participates in the divider at very high source impedances, or (3) the actual resistor values differ from nominal due to tolerance — check values with a multimeter.