Voltage Divider Calculator: Loaded, Thevenin and ADC-Ready
The only US calculator with three solve modes, E12+E24+E96 values for both resistors simultaneously, 4-band color codes for R1 and R2 in one view, Thevenin equivalent output, ADC digital count mapping, and a visual load-effect chart. Backed by NIST and IEC 60063 standards.
RL is connected in parallel with R2. The “10x rule” says RL should be at least 10 times R2 to keep loading error under 10 percent. The chart shows you exactly how Vout degrades as RL decreases.
Shows the integer value your Arduino (10-bit, Vref=5V) or Raspberry Pi ADC reads at the calculated Vout. Ideal for battery monitoring dividers and sensor voltage scaling.
Calculate Voltage Divider to see Vout, E-series values for R1 and R2, dual color codes, Thevenin equivalent, loading analysis, and the Vout vs load curve.
How a Resistor Voltage Divider Works: The Physics Behind the Formula
A voltage divider is one of the oldest and most useful circuits in electronics. The idea is simple: connect two resistors in series between a voltage source and ground, and the voltage at the junction between them is a fraction of the input. That fraction is determined entirely by the ratio of the two resistors, which is exactly what makes the circuit so predictable and so useful.
The physics behind this is Ohm’s Law combined with Kirchhoff’s Voltage Law. In a series circuit, the current through both resistors is identical because there is only one path for current to flow. The voltage drop across each resistor equals that current times the resistor’s value. Since the total voltage drop must equal the input voltage, the output at the junction is the portion of Vin that falls across R2.
A quick real-world sense check: if R1 equals R2, then Vout is exactly half of Vin. If R2 is much larger than R1, Vout is close to Vin. If R2 is much smaller than R1, Vout is close to zero. You can verify these extremes mentally without a calculator, which is a good habit for catching wiring errors on a breadboard before you even pull out your multimeter.
The Three Solve Modes: Choose What You Know
In practice, you do not always know R1 and R2 and want Vout. Often you have a specific target voltage and need to find the right resistor combination. This calculator has three modes to match every starting point. Find Vout mode is the classic forward calculation: you know the resistors and need the output voltage. Find R2 mode is for when you have a specific target voltage and you have already chosen R1 from your parts drawer. Find R1 is the reverse: you have R2 specified (perhaps by the circuit it feeds into) and need R1 to set the divider ratio. All three modes show E-series standard values for both resistors, so you can immediately cross-reference against the Digi-Key or Mouser catalog.
Why Load Resistance Kills Voltage Divider Accuracy
Here is the thing about a voltage divider that every textbook mentions but very few people fully internalize until they have been burned by it: the output voltage changes the moment you connect anything to it. The formula Vout = Vin x R2/(R1+R2) assumes nothing is drawing current from the Vout node. The instant you connect a microcontroller input, a sensor, or any load, you have added a third resistor in parallel with R2, and the divider is no longer the circuit you calculated.
The combined resistance of R2 in parallel with RL is always less than R2 alone, which means the actual Vout is always lower than the unloaded calculation. How much lower depends on the ratio of RL to R2. When RL is 10 times R2, the parallel combination is about 9.09 times lower than R2, and the error in Vout is roughly 9 percent. When RL is 100 times R2, the error drops to about 1 percent. This is why the Vout vs Load Resistance chart in this calculator is so valuable: it shows you the exact shape of this degradation curve for your specific resistor values, not just a rule of thumb.
The Thevenin Equivalent: What the Load Actually Sees
The Thevenin theorem, established by French engineer Leon Charles Thevenin in 1883 and now a fundamental tool of US electrical engineering education as referenced in IEEE standards, allows you to simplify any linear circuit into a single voltage source and a single series resistance. For a voltage divider, the Thevenin voltage (Vth) is the unloaded output voltage, and the Thevenin resistance (Rth) is R1 and R2 in parallel. This is critical because Rth is the source impedance that the load sees. Any load RL forms a further voltage divider with Rth, which is why a low-impedance load pulls the output down so much: both Rth and RL divide Vth, reducing the voltage reaching the load. If you need a stable Vout regardless of load, the solution is an operational amplifier voltage follower (unity-gain buffer) inserted between the divider output and the load, which presents essentially infinite impedance to the divider while driving the load from a near-zero source impedance.
How This Voltage Divider Calculator Works: Six Steps Explained
Knowing what happens inside a calculator builds your intuition for troubleshooting real circuits. Here is exactly what this tool does when you click Calculate.
Step 1: Voltage and Resistance Calculation Using Big.js
All core arithmetic uses Big.js arbitrary-precision floating-point math to avoid the rounding errors that plague standard JavaScript calculations. For example, dividing 1 by 3 in JavaScript returns 0.3333333333333333, which carries a small floating-point error. Big.js computes this as 0.3333333… to arbitrary precision and only rounds at the final output stage. For voltage dividers in precision circuits, where you might be targeting 1.800000V and the error compounds across multiple calculations, this matters.
Step 2: E-Series Standard Value Lookup for Both Resistors
After computing the exact resistance values (either calculated or entered), the tool searches the full E12, E24, and E96 tables (expanded across all decades from 1 ohm to 1 megaohm per IEC 60063) to find the nearest standard values above and below each calculated resistor. For each E-series candidate, the tool also computes what Vout would actually be with that standard value, so you can immediately see the tradeoff between using 9.1k ohms (slightly below) versus 10k ohms (slightly above) as R1 and the resulting Vout change.
Step 3: Load Analysis and Thevenin Calculation
When you enable the load resistance panel, the tool computes R2_effective as the parallel combination of R2 and RL using the formula (R2 x RL)/(R2 + RL). It then recalculates Vout_loaded using R2_effective in place of R2. The loading error percentage is (Vout_unloaded – Vout_loaded)/Vout_unloaded x 100. The Thevenin resistance is computed as R1||R2, and the Thevenin voltage is the unloaded output.
Step 4: ADC Digital Count Mapping
The ADC mode shows you what integer value your microcontroller analog input will read. The formula is ADC_count = round(Vout/Vref x (2^n – 1)), where n is the ADC bit depth. For a 10-bit Arduino (ADC = 1023 maximum, Vref = 5V), a Vout of 2.5V gives a count of 511. An important nuance: the Arduino’s ADC reference is the supply voltage by default (5V for Uno, 3.3V for 3.3V boards), but you can change it to an internal 1.1V or external reference. Always match the Vref setting in this calculator to your microcontroller’s actual reference voltage for an accurate count.
Step 5: Power and Current Analysis
The quiescent current (the current flowing through the divider itself when no load is connected) is Vin/(R1+R2). The power dissipated in R1 is the voltage drop across R1 multiplied by the current: (Vin – Vout) x Iq. The power in R2 is Vout x Iq. Total power is Vin x Iq. For battery-powered designs this is critical, as a 10k/10k divider from a 5V USB supply draws 250 microamps continuously. For a coin cell with 200mAh capacity, that divider alone would drain the battery in roughly 33 days without any other load.
Step 6: Vout vs Load Resistance Chart
The Chart.js visualization sweeps RL from 5 percent of R2 (severe loading, Vout drops significantly) to 2000 times R2 (essentially open-circuit, Vout near the unloaded value) across a logarithmic scale. This curve shape is the same for any voltage divider: it is always a hyperbola that asymptotically approaches Vout_unloaded as RL increases. The chart shows you at a glance where your circuit falls on that curve and how much margin you have before loading error becomes problematic.
Three Real US Engineering Examples with Complete Calculations
A maker in Portland is monitoring a 12V SLA battery with an Arduino Uno. The 10-bit ADC maxes out at 5V, so the 12V battery voltage needs scaling down to the 0 to 5V range.
Ratio needed: 5/12 = 0.4167
Using R1=22kΩ, R2=15kΩ:
Vout = 12 × 15000/(22000+15000) = 4.865V (at 12V)
ADC count at 12V: round(4.865/5 × 1023) = 996
ADC count at 11V (low battery): 913
Loading: Arduino ADC input impedance ~100MΩ, loading error less than 0.01%
An automation engineer in Detroit needs to scale a 0-10V industrial process signal down to 0-3.3V for a Cortex-M4 microcontroller input. The signal source has a 600-ohm output impedance.
R1 = 20kΩ, R2 = 10kΩ:
Vout = 10 × 10/(20+10) = 3.333V ✓
Rth = 20kΩ||10kΩ = 6.67kΩ
MCU input Z = 1MΩ, loading error = 0.66%
E24 values: R1=20kΩ, R2=10kΩ (exact E24 values!)
A startup engineer in Austin needs to interface a 5V UART signal from a legacy sensor to a Raspberry Pi GPIO pin rated at 3.3V maximum. A simple divider is the no-IC solution.
Using R1=1kΩ, R2=2kΩ:
Vout = 5 × 2000/(1000+2000) = 3.333V ✓
Pi GPIO input impedance ~50kΩ
R2_eff = 2k||50k = 1923Ω, Vout_loaded = 3.234V
Loading error = 3%: acceptable for UART logic levels
E24: R1=1kΩ, R2=2kΩ (exact E24 values)
Six Expert Tips for Voltage Divider Design in US Projects
Understanding Attenuation in Decibels for Audio and RF Applications
The decibel (dB) attenuation field in this calculator uses the voltage ratio formula: attenuation = 20 x log10(Vout/Vin). A ratio of 0.5 (half the voltage) corresponds to -6.02 dB of attenuation. A ratio of 0.1 gives -20 dB, and 0.01 gives -40 dB. In US audio engineering and RF systems, gain and loss are always expressed in decibels rather than linear ratios because decibels are additive: a -6 dB stage followed by another -6 dB stage gives -12 dB total, which is much easier to work with than multiplying 0.5 by 0.5 to get 0.25. The attenuation reading is particularly useful when you are designing a voltage divider for use as a simple attenuator pad in an audio test setup, where you need to know the signal level reduction in the same dB units your audio analyzer expects.
One important distinction: the formula 20 x log10(Vout/Vin) gives voltage attenuation in dB assuming equal source and load impedances. In a properly impedance-matched RF system (50 ohm or 75 ohm), this is equivalent to power attenuation in dB as well. However, a simple two-resistor divider does not maintain impedance matching, so while the voltage attenuation number is accurate, the power transfer is not the same as a properly designed attenuator pad. For impedance-matched RF attenuators, use a Pi or T network designed for your specific impedance.
Use High-Resistance Dividers for Battery-Powered Circuits
Every voltage divider draws current continuously even when the circuit is idle. Using 100k ohm and 100k ohm instead of 1k ohm and 1k ohm reduces quiescent current by 100 times without affecting the voltage ratio. For a 3V coin cell, the difference between a 2k total divider (1.5mA) and a 200k total divider (15 microamps) can be the difference between two days and six months of battery life.
Match Resistor Tolerance to Your Accuracy Need
E24 resistors at 5 percent tolerance mean both R1 and R2 can each vary by 5 percent in worst-case directions. In the worst case, your Vout could be off by about 10 percent from the calculated value. For precision reference voltages, use 1 percent E96 resistors. For a simple battery level indicator where 5 percent error is invisible to the end user, standard E24 parts from any US distributor are perfectly fine.
Add a Buffer Op-Amp for Load-Sensitive Applications
If your load changes (a microcontroller cycling between active and sleep modes draws different currents), Vout will fluctuate. An op-amp voltage follower like the LM358 or TLV2371 inserted between the divider output and the load presents near-infinite input impedance to the divider while driving the load from a low-impedance output. This eliminates loading error entirely and is the correct engineering solution for analog reference voltages rather than just using larger resistors.
Verify with a Multimeter Before Connecting Sensitive Loads
Before connecting a microcontroller or any load-sensitive component to a divider output, verify the unloaded Vout with a multimeter first. The multimeter input impedance is typically 10 megaohms, which causes negligible loading error even on high-impedance dividers. Once confirmed, connect the load and remeasure. If Vout drops significantly, your load is too heavy for the divider impedance and you need either lower-value resistors or a buffer stage.
Use Matched Resistors for Temperature-Stable Ratios
The voltage ratio is determined by the ratio of R1 to R2, not their absolute values. If both resistors have the same temperature coefficient (they come from the same manufacturing batch), their resistance changes track each other as temperature changes, keeping the ratio nearly constant. NIST TN-1298 documents this for precision DC divider applications: matched-pair resistors from the same vendor reel can achieve temperature stability far better than the individual component specification suggests.
Add a Bypass Capacitor for Noise Rejection
Adding a small capacitor (100nF to 10uF ceramic) from the Vout node to ground converts your resistor divider into an RC low-pass filter. This is standard practice in US circuit design for ADC input conditioning, where high-frequency noise on the analog input can alias into the digital reading. The cutoff frequency is 1/(2 x pi x Rth x C), where Rth is the Thevenin resistance of the divider. This calculator shows you Rth so you can calculate the filter cutoff directly without a separate tool.
Quick Reference: Common Voltage Divider Ratios for US Projects
The table below shows pre-calculated resistor pairs for common voltage scaling tasks in US engineering and maker projects. All values use E24 standard resistors. The “10x rule” column shows the minimum load resistance for less than 10 percent loading error. Verify with the calculator for your exact supply voltage and tolerance requirements.
| Use Case | Vin | Vout Target | R1 (E24) | R2 (E24) | Actual Vout | Min RL (10x rule) |
|---|---|---|---|---|---|---|
| 12V to 5V (Arduino mon.) | 12V | 5.0V | 15kΩ | 8.2kΩ | 4.234V | 82kΩ |
| 12V to 3.3V (MCU input) | 12V | 3.3V | 27kΩ | 10kΩ | 3.243V | 100kΩ |
| 5V to 3.3V (logic shift) | 5V | 3.3V | 1.0kΩ | 2.0kΩ | 3.333V | 20kΩ |
| 5V to 2.5V (half-supply) | 5V | 2.5V | 10kΩ | 10kΩ | 2.500V | 100kΩ |
| 5V to 1.8V (sensor Vref) | 5V | 1.8V | 18kΩ | 10kΩ | 1.786V | 100kΩ |
| 9V to 5V (battery mon.) | 9V | 5.0V | 7.5kΩ | 10kΩ | 5.143V | 100kΩ |
| 24V to 5V (industrial) | 24V | 5.0V | 43kΩ | 10kΩ | 4.528V | 100kΩ |
All values at zero load (open circuit). Actual Vout with E24 standard values may differ slightly from target due to preferred number rounding. Use the calculator for exact loading analysis. E24 per IEC 60063.