Voltage Dividers: How They Work and How to Calculate Them

What is a voltage divider?

A voltage divider uses two series resistors to produce an output voltage lower than the input voltage. It is widely used for sensor signal level-shifting, generating analog reference voltages, and reading higher voltages with low-voltage ADCs.

Voltage divider formula

V_out = V_in × R2 / (R1 + R2)

• V_in: input voltage
• R1: top resistor (connected to V_in)
• R2: bottom resistor (connected to GND)
• V_out: output voltage across R2 (relative to GND)

Calculation examples

Practical applications

• Level shifting: Interface a 5V sensor output to a 3.3V microcontroller input by setting R1=2kΩ and R2=3.3kΩ, yielding approximately 3.3V.
• Potentiometer: A potentiometer is a variable voltage divider where the R1:R2 ratio changes continuously. Used for volume controls and angle sensors.
• Battery monitoring: Scale a higher voltage (e.g., 12V) down to an ADC range (0–3.3V) for a microcontroller to measure.

Important considerations

• Any load resistance connected to the output appears in parallel with R2, altering V_out. The load resistance should be at least 10× R2 for accurate results.
• Power dissipation: P = V_in² / (R1 + R2). Use values in the 10kΩ–100kΩ range to keep quiescent current low.

Key takeaways

• Formula: V_out = V_in × R2 / (R1 + R2)
• When R1 = R2, V_out = V_in / 2.
• Load impedance must be ≥10× R2 for accurate output.