Voltage Divider Formula
This is a quick reference for the voltage divider formula, also known as the voltage divider formula. The voltage divider formula allows us to easily calculate the output voltage of any divider circuit or any circuit with resistors in series. A voltage divider consists of resistors in series with a measurement or reference voltage between them. For a complete discussion, see our lesson on voltage dividers.
V_{out}=V_{in}\frac{R_2}{R_1+R_2}In the case of a circuit with more than two resistors:
R1 is equal to the sum of the resistances of all resistors ‘above’ the measurement point and
R2 is equal to the sum of resistances of all resistors ‘below’ the measurement point
Rules of Thumb for the Voltage Divider Formula
- The closer R1 and R2 are to each other, the closer that that Vout will be to 1/2 Vin.
- The bigger R1 gets (compared to R2), the more Vout will approach zero (0). Vout gets closer to the voltage at the negative terminal of the source.
- The bigger R2 gets (compared to R1), the more Vout will approach Vin. Vout gets closer to the voltage at the positive terminal of the source.
The ‘rules of thumb’ for the voltage divider formula are often very helpful for developing intuition regarding the effects of manipulating a circuit by changing the resistance at different points. When analyzing a circuit, the rules of thumb can help estimate the effect of a resistor within a circuit. When designing a circuit, these rules can help estimate the value of a needed resistor. An in-depth analysis can be performed at a later time to determine the exact value.
Using the Voltage Divider Formula
The primary use of the voltage divider formula is to calculate the output voltage of a voltage divider circuit. However, voltage divider circuits are not the only situations in which the voltage divider formula is useful.
It turns out that the voltage divider formula is incredibly useful in many situations and across thousands of different types of circuits. This is because the voltage divider formula can be applied any time resistors are placed in series with a known voltage input.
There are many times when resistors are placed in series in a circuit. It’s often helpful to use the voltage divider rule as a quick calculation or estimation to determine what the voltage is (compared with ground) at that point in the circuit. In that way, the voltage divider rule is an incredibly useful equation to remember, and will likely present itself as a valuable tool in your arsenal.