Electric Calculator for hardware engineers
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Resistor voltage divider

Find the voltage at the mid-point of a resistor divider. In a real design the resistors and the supply both have tolerances, so the mid-point voltage is not a single number either.

Diagram: Resistor voltage divider
V
Ω
Ω

SI prefixes accepted (4k7 / 1M / 10m / 220). Upper-case M = mega, lower-case m = milli

Voltage
2.7211V
Max voltage2.9057 V
Min voltage2.5381 V
Voltage range0.3675 V p-p
Advanced — Supply tolerance, R1 tolerance, R2 tolerance
±%
±%
±%

Derived values

Division ratio
0.825
R2 / (R1 + R2)
Divider current
57.895 µA
Vcc / (R1 + R2)
Series resistance
57 kΩ
R1 + R2
Divider dissipation
191.05 µW
Vcc² / (R1 + R2)

The output impedance (R1∥R2) is 8.246 kΩ. When driving an ADC sampling input or an op-amp, a higher value contributes more error.

History
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Formula

Mid-point voltage: Vout = Vin × R2 / (R1 + R2)
Maximum with tolerance: Vin_max × R2_max / (R1_min + R2_max)
Minimum with tolerance: Vin_min × R2_min / (R1_max + R2_min)

Design notes

The divider is the basic way to make an arbitrary voltage. It scales a signal into an MCU's ADC range, sets a sensor's operating point and monitors battery voltage.

Things to watch:
• The output impedance is R1∥R2 — the voltage moves when the load changes
• Where accuracy matters, use tight-tolerance resistors (1% or 0.1%)
• This calculator rolls the supply tolerance into the error budget as well

When you need this

For reference voltages, supply monitoring, switching converter feedback and level shifting. The real purpose is not the nominal output but how far it moves once resistor tolerance and supply variation are included.

How tolerance propagates

The ratio R2/(R1+R2) depends only on the ratio of the resistors, so errors in the same direction cancel. What hurts is opposite-direction error.

With two ±1% resistors, the worst-case ratio error is about ±1% (R1 high, R2 low). Supply tolerance then multiplies on top. A ±5% supply gives roughly ±6% total on the output.

Temperature coefficient can matter more than tolerance. Ordinary thick-film chip resistors are ±100–200ppm/K, which is up to 2.5% across −40 to +85°C. Movement shared by both resistors cancels, but that only holds if they are the same type in the same thermal environment. For accuracy, use the same series and size and place them together.

Choosing the resistance

ResistanceCurrent (3.3V halved)Suits
1 kΩ rangeabout 1.6 mANoise-immune; wasteful on always-on equipment
10 kΩ rangeabout 165 µAGeneral purpose; the usual ADC choice
100 kΩ rangeabout 16 µABattery equipment; watch trace capacitance and leakage
1 MΩ rangeabout 1.6 µAVery low power; board contamination leakage starts to matter

Feeding an ADC, check that the divider's output impedance (R1 in parallel with R2) is below what the ADC requires. Successive-approximation ADCs charge a sampling capacitor, so a high source impedance reads low. Below 10kΩ is safe; above that, add a capacitor at the output.

Worked example: measuring 3.3V with an ADC

  1. Vcc = 3.3V, R1 = R2 = 10kΩ, supply tolerance ±5%, both resistors ±1%.
  2. Nominal output is 1.65V.
  3. Maximum 1.7498V, minimum 1.5518V, a span of 0.198V.
  4. That is ±6% about the centre — far larger than a 12-bit ADC's 0.8mV resolution.
  5. If the goal is measuring the supply itself, this error is fatal. But use the supply as the ADC reference and supply variation cancels between numerator and denominator, leaving only the ±1% resistor error.

Step five is the one that pays off in practice: changing what you measure against cuts the error six-fold without changing a single component.

Common mistakes

  • Loading the tap. This is the unloaded value. Anything drawing current from the midpoint pulls it down. Check that the load resistance is at least 100 times R2.
  • Very high resistance on converter feedback. In the hundreds of kilohms, trace capacitance adds phase shift and destabilises the loop. Keep FB routing short and add a feedforward capacitor if needed.
  • Exceeding the voltage rating on high-voltage dividers. Chip resistors have a maximum working voltage per element (around 50V for 0603). To divide hundreds of volts, use several in series to share it.
  • Not accounting for E-series rounding. Rounding the ideal value to E24 already introduces up to 2% error. Do the tolerance analysis on the rounded values.

Frequently asked questions

How do I reduce error when measuring the supply with an ADC?
Use the supply itself as the ADC reference. The divider output scales with the supply and so does the ADC full scale, so the variation cancels, leaving only resistor tolerance. If you need an absolute measurement instead, use a voltage reference IC.
How much does 0.1% buy over 1%?
It divides the worst-case ratio error by ten. But 0.1% parts are thin-film and cost five to ten times more. In most designs the temperature coefficient and the reference accuracy dominate anyway — check those first.
Can I put a capacitor on the tap?
It is effective against noise, but it slows the response, so watch the time constant if you need to track changes. It is set by R1 in parallel with R2 and the capacitor: 10kΩ in parallel (5kΩ) with 100nF is 0.5ms.
Which resistor is which?
R1 is the high side (to the supply) and R2 the low side (to ground). The output is the voltage across R2.

Standards and references

  • IEC 60115-1 — Generic specification for fixed resistors; tolerance and temperature coefficient.
  • IEC 60063 — Preferred number series (E24 / E96).

Last updated: 2026-08-29