Hong Life CalculatorsUnderstanding the voltage divider calculator — concept and principle
A voltage divider uses two resistors in series to produce a fraction of an input voltage. It is one of the most common circuits in electronics: scaling a battery voltage down for a microcontroller's analog input, setting a bias point, or reading a sensor such as a thermistor or light-dependent resistor. This calculator gives the output voltage, the current through the divider and the division ratio, with or without a load.
How it is calculated
- Output voltage: V_out = V_in · R2 / (R1 + R2)
- Divider current: I = V_in / (R1 + R2)
- Ratio: R2 / (R1 + R2)
R1 is the top resistor (from V_in to the output) and R2 the bottom one (from the output to ground). If a load R_L is connected across the output, R2 is replaced by R2 ∥ R_L = R2·R_L / (R2 + R_L). Enter 0 for no load.
The principle
With no load, the same current flows through R1 and R2, set by the total resistance: I = V_in / (R1 + R2). The voltage across R2 is then I · R2, which gives the formula. The output is the input scaled by the share of the total resistance that R2 represents. A load draws extra current from the output node and acts in parallel with R2, lowering the effective bottom resistance and therefore the output voltage.
Worked example
- Inputs: V_in = 12 V, R1 = 10,000 Ω, R2 = 4,700 Ω, no load.
- Total resistance = 10,000 + 4,700 = 14,700 Ω.
- Current = 12 / 14,700 = 0.000816 A = 0.8163 mA.
- Ratio = 4,700 / 14,700 ≈ 0.3197.
- V_out = 12 × 0.3197 ≈ 3.837 V (3.836734694).
If a 10 kΩ load were connected, R2 ∥ R_L ≈ 3,197 Ω and V_out would drop to about 2.91 V.
| Load (Ω, 0 = none) | Output voltage (V) |
|---|---|
| 0 | 3.836734694 |
| 1 | 0.0011996248 |
| 2 | 0.0023984997 |
| 3 | 0.0035966253 |
| 4 | 0.0047940024 |
| 5 | 0.0059906317 |
| 6 | 0.0071865138 |
How to read the result
The unloaded output is the best case. For the output to stay within about 1% of the calculated value, the load should be roughly 100 times larger than R2 or more. Lower resistor values make the divider "stiffer" against loading but waste more current; here the divider dissipates 12 V × 0.8163 mA ≈ 9.8 mW. In battery devices, values in the tens to hundreds of kilohms are common to save power, while the input being driven, such as an ADC, may need a lower source resistance.
Common mistakes
- Swapping R1 and R2, which gives V_in − V_out instead of V_out.
- Using a divider as a power supply for a motor, LED string or other varying load; use a regulator instead.
- Ignoring resistor tolerance: two ±5% resistors can shift the ratio by several percent.
Frequently asked questions
How do I choose R1 and R2 for a target output?
Pick R2, then R1 = R2 · (V_in / V_out − 1). For 12 V to 3.3 V with R2 = 10 kΩ, R1 ≈ 26.4 kΩ.
Can I use a potentiometer as a divider?
Yes. The wiper splits the track into R1 and R2, so the output varies from 0 to V_in as you turn it.
Does a voltage divider work with AC?
With resistors only, yes, the ratio is the same for AC. Capacitors or inductors make it frequency-dependent.
Sources: P. Horowitz and W. Hill, The Art of Electronics, Cambridge University Press · J. W. Nilsson and S. A. Riedel, Electric Circuits, Pearson