The voltage divider consists of two series connected resistors used to drop the input voltage by a set amount. It is an application of Ohm’s Law. This post shows the derivation of the voltage divider equation and concludes by demonstrating the hazard of circuit loading. Part 2 provides a generalized equation for systems with three or more resistors.
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Last updated: 23 December, 2025
TL;DR
- The output voltage is set by the resistor ratio, not the resistor value.
- Every voltage divider is loaded either by the next circuit or by your meter.
- Dividers with high value resistors droop more than those with low values resistors. However low value resistors are difficult to drive and inefficient.
What is a voltage divider?
A voltage divider is a two-resistor series circuit:
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Figure 1 shows the standard form with input in the top and output taken from the junction of R1 and R2.
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For the resistive divider, the output voltage is always less than the input voltage.
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The output voltage is determined by the ratio of the resistors not their absolute values.
Figure 1: Schematic for the standard form of the voltage divider.
Tech Tip: The circuit shown in Figure 1 does not include a load on the output signal. Any load connected to the output will disturb the circuit resulting in a lower than anticipated output voltage.
Quick solutions
DigiKey’s online calculator (Figure 2) provides a quick way to solve the voltage divider equation. There is also a tab (not shown) for situations when a voltage divider is operating under load.
Figure 2: The DigiKey voltage divider calculator may be used to quickly solve a voltage divider problem.
Voltage Divider Equation Derivation
The voltage divider is a shortcut that allows us to use a single equation to solve for the system. If we dig deeper, we discover the two underlying equations have been combined.
Current flowing in the circuit is defined by:
I = \frac{V_{in}}{R_1 + R_2}
Voltage across resistor R2 is defined as:
V_{R2} = I \times R_2
If we combine the equations, we see that:
V_{R2} = V_{out} = \frac{V_{in}}{R_1 + R_2} \times R_2
As a final step, we rearrange the equations to obtain the familiar (standard) form of the voltage divider formula:
V_{out} = V_{in}\times \frac{R_2}{R_1 + R_2}
This form is preferred as it clearly shows that the output voltage is proportional to the ratio of the resistors: {R_2}/{(R_1 + R_2)}
Expanding the resistive voltage divider to calculate Vin, R1, or R2
The voltage divider is a system with 4 variables. Given any three, we can calculate the fourth as demonstrated by the following four equations. As a practical algebra exercise, you should be able to derive each equation from the standard form of the voltage divider equation.
V_{out} = V_{in}\times \frac{R_2}{R_1 + R_2}
V_{in} = \frac{V_{out} \times (R_1 + R_2)}{R_2}
R_1 = \left(\frac{V_{in}}{V_{out}} - 1\right) \times R_2
R_2 = \frac{V_{out} \times R_1}{V_{in} - V_{out}}
In practice it may be simpler and less error prone to keep the voltage divider in standard form (1st equation) and then perform the algebra. There is something to be said for consistency. Also, the person grading your solution may not be thinking about the voltage divider in terms of the three additional equations.
Voltage droop with divider loading
A classic design error is to think about the voltage divider in terms of an isolated system. Specifically, it fails to consider the loading on the voltage divider. This load could be an external circuit or even something as innocuous as a voltmeter or oscilloscope probe.
This loading effect is best demonstrated in Figure 3. Here we see a collection of independent voltage dividers consisting of the R1/R2 pair, the R3/R4 pair, and the R5/R6 pair. The output voltage of each divider is measured using a voltmeter featuring a simulated 1 MΩ input resistance. The resistor pairs are chosen to increase by a factor of 10 for every stage as we move from (left to right).
In our ideal (unloaded) calculations, each resistor pair yields a 5 VDC output. In the real world we observe a droop in voltage for the higher resistor pairs. The 1 kΩ pair yields a 5.00 VDC reading while the 100 kΩ pair yields a 4.76 VDC reading.
Figure 3: This circuit presents three individual voltage dividers where the voltage is measured using a 1 MΩ input impedance voltmeter. Observe that the high resistance R5 / R6 pair has a significant voltage drop.
Tech Tip: The input resistance or impedance of a voltmeter or oscilloscope probe may load down the circuit. The DigiKey calculator does include an option for calculating the output voltage for a loaded voltage divider.
Next steps
We could continue this conversation to include Thevenin’s Theorem. The Figure 3 example would be particularly insightful as it provides a convenient way to visualize the circuit. We could also expand our voltage divider to encompass reactive elements such as inductors and capacitors. The challenge increases when we allow the frequency to change. If we make those allowances, the simple resistive voltage divider transforms into a filter such as this representative low-pass device. Perhaps we can explore these concepts another day.
Parting Thoughts
You will be tempted to use the online calculators for your homework.
Don’t!
The resistive voltage divider encapsulates the early lessons in electronics. As a student of electronics, you will be tasked to solve thousands of related problems. You will grok electronics by working through these problems enthusiastically and looking for those relationships / applications outside the immediate problem. With that intuitive understanding you will see the impact of loading on the voltage divider and no longer be surprised when the voltage is lower than expected. This same concept arrives fully formed in the future when we explore filters and the detrimental impact of circuit loading.
Be sure to read this follow up article involving voltage divider calculations involving three or more resistors.
Please leave your comments and suggestion in the space below. Also, be sure to answer the questions and critical thinking questions at the end of this note.
Best wishes,
APDahlen
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About this author
Aaron Dahlen, LCDR USCG (Ret.), serves as an application engineer at DigiKey. He has a unique electronics and automation foundation built over a 27-year military career as a technician and engineer which was further enhanced by 12 years of teaching (interwoven). With an MSEE degree from Minnesota State University, Mankato, Dahlen has taught in an ABET-accredited EE program, served as the program coordinator for an EET program, and taught component-level repair to military electronics technicians.
Dahlen has returned to his Northern Minnesota home, completing a decades-long journey that began as a search for capacitors. Read his story here.