Calculate The Gain Vout Vin of The Following Voltage Divider

A voltage divider is a simple circuit that produces an output voltage (Vout) that is a fraction of the input voltage (Vin). This calculator helps you determine the voltage gain (Vout/Vin) of a voltage divider circuit given the resistor values.

What is a voltage divider?

A voltage divider is a fundamental circuit configuration that consists of two resistors connected in series between a voltage source and ground. The output voltage is taken between the two resistors. This circuit is widely used in electronics for voltage scaling, signal conditioning, and bias voltage generation.

The voltage divider principle is based on Ohm's Law and the principle of voltage division. The output voltage is proportional to the ratio of the two resistors and the input voltage.

Voltage divider formula

The voltage gain (Vout/Vin) of a voltage divider can be calculated using the following formula:

Vout/Vin = R2 / (R1 + R2)

Where:

Vout is the output voltage
Vin is the input voltage
R1 is the resistance of the first resistor
R2 is the resistance of the second resistor

This formula shows that the voltage gain is determined solely by the ratio of the two resistors, not by the actual values of the resistors or the input voltage.

How to calculate voltage gain

To calculate the voltage gain of a voltage divider:

Identify the values of resistors R1 and R2 in ohms (Ω)
Apply the voltage divider formula: Vout/Vin = R2 / (R1 + R2)
The result will be a dimensionless ratio representing the voltage gain

For example, if R1 = 1000Ω and R2 = 2000Ω, the voltage gain would be 2000 / (1000 + 2000) = 0.6667, or 2/3.

Note: The voltage divider formula assumes ideal conditions with no current flowing through the output terminals. In practice, there may be small deviations due to resistor tolerances and other factors.

Example calculation

Let's calculate the voltage gain for a voltage divider with R1 = 1 kΩ and R2 = 2 kΩ:

Vout/Vin = 2000Ω / (1000Ω + 2000Ω) = 2000 / 3000 ≈ 0.6667

This means the output voltage will be approximately 66.67% of the input voltage. For example, if Vin = 5V, Vout ≈ 3.33V.

You can verify this calculation using our interactive calculator in the sidebar.

FAQ

What is the maximum voltage gain of a voltage divider?: The maximum voltage gain occurs when R1 = 0Ω, making Vout/Vin = 1 (100% of Vin). In practice, R1 can never be exactly zero, but it can be made very small compared to R2.
What happens if R1 = 0Ω in a voltage divider?: If R1 approaches zero, the voltage divider becomes a simple connection of R2 to ground, and Vout = Vin * (R2 / R2) = Vin. The voltage gain approaches 1.
Can a voltage divider be used as a voltage regulator?: While a voltage divider can provide a stable reference voltage, it cannot provide significant current to a load. For voltage regulation, more sophisticated circuits like voltage regulators are needed.
What is the power rating of resistors in a voltage divider?: The power rating of resistors should be chosen based on the maximum expected power dissipation, which depends on the input voltage and current. For most applications, 1/4W or 1/2W resistors are sufficient.
How does temperature affect voltage divider performance?: Resistors have a temperature coefficient that causes their resistance to change with temperature. For precise applications, temperature-compensated resistors or other compensation techniques may be needed.