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Resistor divider error: how far tolerance and loading push you from the design value

A divider built from R1 and R2 scales the voltage by R2/(R1+R2) on paper. In practice, tolerance, the load's input resistance, temperature and the ADC's sampling capacitor move the output a few percent, so check that the divider is not adding more error than the ADC's resolution.

Last updated: 2026-10-28 Resistor dividerErrorADCTolerance

Two ±1% resistors: a worst case of ±2% on the divider ratio

The error in the divider ratio R2 ÷ (R1 + R2) is largest when R1 and R2 drift in opposite directions. R1 at +1% and R2 at −1% pushes the ratio down; the reverse pushes it up.

For R1 = R2 (a 1/2 divider), 0.99 ÷ (1.01 + 0.99) = 0.495, or −1% against 0.5. For R1 = 9·R2 (a 1/10 divider), 0.99 ÷ (9.09 + 0.99) = 0.0982, or −1.8%. The smaller the divider ratio, the closer the error gets to ±2%. As a formula, relative error ≈ ±(R1 tolerance + R2 tolerance) × R1 ÷ (R1 + R2).

One LSB on a 12-bit ADC is 0.024% of full scale, so a 2% error is 82LSB.

The fixes are 0.1% resistors (ratio ±0.2%), calibration at manufacture with the measured ratio stored in firmware, or a design that does not need absolute accuracy, as in threshold detection.

Resistor tolerance and the worst-case divider-ratio error (1/10 divider, R1 = 9·R2)
Resistor toleranceWorst-case ratio errorEquivalent LSB (12-bit ADC)
±5%±9.0%±370LSB
±1%±1.8%±74LSB
±0.5%±0.9%±37LSB
±0.1%±0.18%±7LSB
Resistor tolerances and loading changing a voltage divider’s output
Resistor tolerances and loading changing a voltage divider’s output. AI-generated conceptual illustration; see the article’s diagrams and text for circuit details and conditions.
Divider ratio and worst-case errorA graph of the worst-case divider ratio error with two 1 percent resistors, plotted against the divider ratio as a falling straight line. The smaller the ratio, the closer the error gets to 2 percent: 1.8 percent for a 1/10 divider and 1 percent for a 1/2 divider. The right side repeats the calculations from the text and shows that 2 percent is 82 LSB on a 12-bit ADC. Worst-case ratio error with two ±1% resistors 2% 0 0 0.5 1 worst-case error ratio R2 / (R1+R2) 1/10 divider: 1.8% 1/2 divider: 1% smaller ratio: nearer ±2% 1/2: 0.99 / (1.01 + 0.99) = 0.495 1/10: 0.99 / (9.09 + 0.99) = 0.0982 ±2% worst case = 82LSB at 12 bits
Figure 1: with two ±1% resistors, the worst-case error approaches ±2% as the divider ratio gets smaller.

The load's input resistance lands in parallel with R2

The input resistance RL of whatever is connected to the divider output lands in parallel with R2 and pulls the ratio down. Load an R1 = R2 = 100kΩ divider with RL = 1MΩ and R2 ∥ RL = 90.9kΩ, so the ratio is 90.9 ÷ 190.9 = 0.476, or −4.8%.

To keep the error under 0.1%, make RL at least 1000 times R2. For R2 = 100kΩ that means RL = 100MΩ, where you would add an op-amp buffer. Making R2 smaller instead raises the divider current.

A SAR ADC connects a small capacitor (a few pF to a few tens of pF) to the divider output during sampling. If R1 ∥ R2 is high, the capacitor cannot fully charge within the sampling time and the reading comes in low. Keep R1 ∥ R2 within the datasheet's input-impedance limit, or put a 10 to 100nF capacitor at the output, though too large a time constant stops it tracking the input.

What loads a divider outputA schematic of Vin divided by R1 and R2, with the load's input resistance RL and, through a switch, an ADC sampling capacitor both connected in parallel at the output. On the right, a worked example of the resulting error. All loads sit parallel to R2 RL shifts DC ratio; Cs shifts it while sampling Vin R1 R2 Vout RL Load input R Sampling Cs ADC input R1 = R2 = 100kΩ, RL = 1MΩ R2 ∥ RL = 90.9kΩ, ratio 0.476 −4.8% vs. design value 0.5 Same divider, Cs = 10pF, 5µs sample R1∥R2=50kΩ, τ=0.5µs: charges in time R=500kΩ, τ=5µs: 37% short Fix RL ≥ 1000×R2, or 10-100nF at output Still short? Buffer with an op-amp
Figure 2: anything connected to the divider output lands in parallel with R2.

Power dissipation and voltage rating: dividing a high voltage

Dividing 48V down to 4.8V with R1 = 90kΩ, R2 = 10kΩ draws 0.48mA and dissipates 21mW in R1, which is fine. With R1 = 9kΩ, R2 = 1kΩ the current is 4.8mA and R1 dissipates 207mW. That exceeds a 1608 (0603)'s 100mW rating, and a 3216 (1206, 250mW) falls short once you apply derating.

Voltage rating is also easy to overlook. The maximum working voltage of a chip resistor is commonly 50V for a 1005, 75V for a 1608, 150V for a 2012 and 200V for a 3216, and a part with more than its rating across it is unusable whatever its resistance. A 1608 as R1 in a 100V divider sees 90V, over its 75V rating.

Splitting R1 into two or three resistors in series is standard for high voltage. It spreads voltage and power, and limits the output jump if one resistor fails short.

Power and voltage rating in a high-voltage dividerLeft: a bar chart of the power in R1 when dividing 48 volts by 10. With R1 at 90 kilohms it is 21 milliwatts, under the 100 milliwatt rating of a 1608; at 9 kilohms it is 207 milliwatts, over 100 milliwatts and close to the 250 milliwatt rating of a 3216. Right: maximum working voltage of chip resistors, 50 volts for a 1005, 75 for a 1608, 150 for a 2012 and 200 for a 3216. R1 in a 100 volt divider sees 90 volts, so the 1005 and 1608 are over their ratings. Power and voltage rating when dividing a high voltage Power in R1 (48V divided by 10) 21mW 90k (0.48mA) 207mW 9k (4.8mA) 1608 rated 100mW 3216 rated 250mW Max working voltage vs voltage on R1 1005 50V 1608 75V 2012 150V 3216 200V 90V across R1 in a 100V divider
Figure 3: power in R1 against the rated power, and chip resistor maximum working voltage against the voltage across R1.

Temperature coefficient acts on the ratio

A chip resistor's temperature coefficient is ±100 to 200ppm/°C, up to ±1% over a 50°C swing. But the ratio depends on the difference between the R1 and R2 coefficients, and resistors of the same series and material barely change it. Trouble comes from mixing types (thick-film with thin-film, or different sizes) or from R1 alone self-heating in a high-voltage divider. With 0.1% resistors, match R1 and R2 as thin-film parts of ±25ppm/°C or better.

A resistor network with R1 and R2 in one package (ratio accuracy ±0.05%, coefficient mismatch ±5ppm/°C, for example) beats individual 0.1% resistors on ratio, and both halves stay at the same temperature.

Noise and leakage at high resistance

High resistance such as R1 = 1MΩ, R2 = 100kΩ cuts power but brings other problems. Thermal noise is 40nV/√Hz for 100kΩ, or 4µVrms over 10kHz: small next to a 12-bit ADC's 1LSB (0.8mV on 3.3V full scale), but it starts to matter at 16 bits (50µV). Board leakage matters too: flux residue or humidity puts tens to hundreds of MΩ in parallel with R2, and 100MΩ across a 100kΩ R2 is a 0.1% error.

Input bias current also counts. With a bipolar-input op-amp, or an ADC input leakage as high as 1µA, 1µA through R1 ∥ R2 = 90kΩ is a 90mV error (a CMOS input's few pA is negligible). A high-impedance node also picks up external noise, so add a capacitor at the output or keep the trace short.

Keeping the divider current between 10µA and 1mA balances these issues against power. For 3.3V that is a total of 3.3kΩ to 330kΩ.

Frequently asked questions

For an accurate divider ratio, what tolerance of resistor should I use?
It depends on the absolute accuracy you need. For ±10LSB or better on a 12-bit ADC, use ±0.1%. With ±1%, calibrate or use it where absolute accuracy does not matter.
Can a divider's output go straight into an MCU's ADC?
Yes, if R1 ∥ R2 is under the datasheet's input-impedance limit. Above that, put a 10 to 100nF capacitor at the output or buffer with an op-amp.
Can I use a 1608 resistor for R1 in a 48V divider?
A 1608 is typically rated at 75V, so 43V across it is within spec. For 100V or more, use a 2012 or larger, or split R1 into two in series.
Going to higher resistance saves power. Is there a ceiling?
Past R1 ∥ R2 = 100kΩ, watch loading, sampling capacitance, leakage and thermal noise. Above 1MΩ, assume a buffer and a guard ring.

Standards and references

  • IEC 60115-8 — Rated power, maximum working voltage, and temperature coefficient specifications for chip resistors
  • MCU vendors' datasheets and reference manuals — The relationship between ADC input impedance and sampling time, and input leakage current
  • Analog Devices, MT-004: The Good, the Bad, and the Ugly Aspects of ADC Input Noise — The relationship between front-end noise and resolution in ADC circuits

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