Work out the NTC thermistor accuracy you get from a resistor divider once the thermistor, resistor, reference, ADC, self-heating and firmware are all counted. See every contributor to thermistor temperature accuracy across your range, the budget at any temperature, and copy a C lookup table for the exact circuit.
10 kΩ ±1 %, B25/100 = 3988 K ±1 %, dissipation factor about 1.5 mW/K in air, −55 to 155 °C. R-T table 8016 from the datasheet. Datasheet
43 points, -55 to 155 °C · R25 = 10 kΩ · B25/85 = 3974 K
Power for a 1 °C rise; the datasheet value is usually in still air.
The ADC voltage falls as temperature rises.
Also used for Rp.
Thick film is often ±100, thin film ±25 or better.
Optional. Linearizes the curve at the cost of sensitivity.
Below 100 % when a GPIO powers the divider only to sample.
Microchip MCP3208-B with VREF tied to the divider supply: INL ±1 LSB, offset ±3 LSB, gain error ±5 LSB, leakage ±1 µA (datasheet maximums). Datasheet
ADC reference = divider supply: supply errors cancel.
Flows through the divider’s source impedance.
Your estimate; budgeted at 3σ.
The error budget below is for this temperature. Click the chart to move it.
Worst case
±2.25 °C
at 85 °C; sum of every contributor
RSS
±0.92 °C
at 85 °C; root-sum-square
Resolution
0.022–0.089
°C per LSB (worst at 85 °C)
Self-heating
+0.18 °C
peak NTC power 272 µW
Divider current
298 µA
peak, at 85 °C where the NTC is lowest
ADC source impedance
9.07 kΩ
max; codes 3713 to 397 (81 % of span)
⚠ Self-heating reaches 0.18 °C. Murata sizes its maximum operating current for a 0.1 °C rise; raise the series resistor, lower the excitation or switch the divider on only while sampling.
Error contributors across temperature
Stack height is the worst case; the dashed line is the RSS. Click or tap to inspect a temperature.
Error budget at 25 °C
NTC at 10 kΩ, ADC node at 1.65 V (code 2048), 0.022 °C per LSB. Error band -0.87 to +1.04 °C.
| Contributor | Spec | Error (°C) | Share of worst case |
|---|---|---|---|
| Series resistor tolerance | ±1 % | ±0.23 | 22 % |
| NTC R25 tolerance | ±1 % | ±0.23 | 22 % |
| Self-heating | 1.5 mW/°C | +0.18 | 17 % |
| ADC input leakage | ±1 µA × source impedance | ±0.14 | 13 % |
| Series resistor tempco | ±100 ppm/°C, board 0 to 70 °C | ±0.10 | 9.8 % |
| ADC offset | ±3 LSB | ±0.067 | 6.4 % |
| ADC gain error | ±0.122 % of full scale | ±0.056 | 5.3 % |
| ADC INL | ±1 LSB | ±0.022 | 2.1 % |
| Quantization | ±½ LSB | ±0.011 | 1.1 % |
| ADC noise (3σ) | 0.5 LSB rms ÷ √16 × 3 = ±0.375 LSB | ±0.0084 | 0.8 % |
| Lookup table interpolation | 65 entries, linear | ±0.0034 | 0.33 % |
| NTC B tolerance | ±1 % (±39.7 K) | ±0 | 0 % |
| Worst case (sum) | ±1.05 | ||
| RSS | ±0.42 |
Firmware lookup table (C)
ADC code to 0.01 °C, linear interpolation. Worst interpolation error in range: 0.11 °C.
/* NTC lookup table: 12-bit ADC code -> temperature in 0.01 degC.
* TDK B57861S0103F040, NTC to GND, Rs = 10 kohm.
* ratiometric (ADC reference = divider supply).
* 65 entries, one every 64 codes, linear interpolation;
* clamped to -40.00 .. 105.00 degC.
* Open thermistor reads near code 4095, shorted near code 0:
* check for those before trusting the result.
* Generated by https://www.protoflow.ai/tools/ntc-accuracy-calculator
*/
#include <stdint.h>
#define NTC_ADC_MAX 4095u
#define NTC_LUT_SHIFT 6u
static const int16_t ntc_lut[65] = {
10500, 10500, 10500, 10500, 10068, 9261, 8613, 8074,
7609, 7201, 6838, 6510, 6210, 5933, 5675, 5433,
5205, 4990, 4784, 4588, 4399, 4217, 4042, 3872,
3706, 3545, 3388, 3234, 3083, 2934, 2788, 2643,
2500, 2358, 2216, 2076, 1936, 1796, 1656, 1515,
1373, 1231, 1087, 940, 792, 641, 487, 329,
166, -1, -175, -356, -545, -744, -955, -1182,
-1427, -1695, -1993, -2333, -2732, -3223, -3877, -4000,
-4000,
};
int16_t ntc_centi_celsius(uint16_t code)
{
if (code > NTC_ADC_MAX) code = NTC_ADC_MAX;
uint16_t i = (uint16_t)(code >> NTC_LUT_SHIFT);
int32_t frac = (int32_t)(code & 63u);
int32_t a = ntc_lut[i];
int32_t b = ntc_lut[i + 1u];
return (int16_t)(a + ((b - a) * frac) / 64);
}
It depends on the whole circuit, and mostly on the parts around the ADC rather than the ADC itself. A 10 kΩ ±1 %, B ±1 % NTC with a 10 kΩ ±1 % series resistor on a 12-bit ratiometric ADC has a worst case of ±1.05 °C at 25 °C (RSS ±0.42 °C) and ±2.25 °C at 85 °C, where the thermistor's B tolerance takes over. Each error is found by moving one part to its limit and converting the ADC code back to temperature; worst case adds them, RSS root-sum-squares them.
The firmware turns an ADC code into a resistance and the resistance into a temperature. The calculator runs exactly that chain, with the thermistor model you pick.
With an R-T table, the calculator interpolates between neighboring points with their local B value, the method in TDK's application note. For the Vishay 10 kΩ table at 5 °C steps that stays within 0.015 °C of Vishay's own extended Steinhart-Hart formula.
The last form is the ratiometric case (Vref = Vexc): the supply drops out, which is why a ratiometric divider has no excitation or reference term. With the NTC on the supply side, swap R and Rs.
Each contributor is found by perturbation, not by a linear sensitivity formula. At every temperature the circuit is evaluated twice more with one parameter at its + and − limit; both codes are converted back with the nominal model (what the firmware does), and the larger deviation is that contributor's error. Nonlinear effects near the ends of the range are therefore included.
| Contributor | How it is perturbed |
|---|---|
| NTC R25 tolerance | R(T) × (1 ± tol) |
| NTC B tolerance | R(T) × exp(±ΔB (1/T − 1/298.15 K)), ΔB = tol × B25/85 of the curve |
| Self-heating | NTC at T + P/δ, P = V_NTC² / R_NTC × duty (one-sided: always reads high) |
| Series resistor tolerance | Rs × (1 ± tol) |
| Series resistor tempco | Rs × (1 ± TC × max|T_board − 25 °C|), or × |T − 25 °C| when it sits with the NTC |
| Parallel resistor | Rp × (1 ± (tol + TC × ΔT)) |
| Excitation and reference (separate reference only) | Vexc × (1 ± tol), Vref × (1 ± tol) |
| ADC offset, INL | code ± LSB |
| ADC gain error | code × (1 ± gain) |
| ADC noise | code ± 3σ/√N (N = samples averaged) |
| Quantization | code ± ½ LSB |
| ADC input leakage | V_ADC ± I_leak × (Rs ∥ R_NTC) |
| Lookup table | largest |table − exact| over the code segment, inside the operating range |
Assumptions: errors are independent of each other, tolerance limits and 3σ noise are treated as equivalent bounds for the RSS, the averaged ADC noise is Gaussian, and self-heating uses the average power, which holds when the excitation pulses are short against the thermistor's thermal time constant (seconds for most parts). Quantization is kept at ±½ LSB even with averaging; with enough noise to dither, the real figure is smaller. Self-heating is solved for the temperature where the power balances; a rise above 100 °C, or a thermistor that runs away, is reported as an error instead of a number.
TDK B57861S0103F040 (10 kΩ ±1 %, B ±1 %, R/T table 8016), a 10 kΩ ±1 % 100 ppm/°C series resistor on a board at 0 to 70 °C, 3.3 V excitation, and an MCP3208-B at its datasheet limits, read ratiometrically from −20 to 85 °C. At 25 °C the worst case is ±1.05 °C (RSS ±0.42 °C). The largest terms are series resistor tolerance (±0.23 °C, 22 %), NTC R25 tolerance (±0.23 °C, 22 %), self-heating (+0.18 °C, 17 %) and ADC input leakage (±0.14 °C, 13 %).
At 85 °C the worst case grows to ±2.25 °C: the NTC B tolerance alone is ±0.71 °C, and each ADC code now spans 0.089 °C.
Same circuit with a 0.1 % 25 ppm/°C thin-film resistor and the divider powered 1 % of the time. At 25 °C the worst case falls to ±0.59 °C (from ±1.05 °C) and self-heating to 0.0018 °C. At 85 °C it only falls to ±1.79 °C, because the thermistor's own B tolerance (0.71 °C) is untouched. Past this point a better thermistor or a calibration buys more than a better resistor.
A Murata NCP15XH103F03RC 0402 NTC with 10 kΩ from a 3.3 V ±1 % regulator, read by an ADS1115 on its ±4.096 V range. The ADS1115 has its own reference, so the regulator's tolerance goes straight into the reading: ±0.53 °C of the ±1.40 °C worst case at 25 °C. It is worst where the divider sits near a rail: ±2.95 °C at −20 °C. Measuring the excitation on a second channel and dividing makes the reading ratiometric again; with that term gone the range worst case is ±1.90 °C.
Temperature a firmware Beta equation reports for the datasheet resistance, minus the true temperature. Vishay NTCLE100E3103 uses its B25/85 = 3977 K; TDK B57861S0103 (R/T 8016) uses its B25/100 = 3988 K. Both agree with the table at their two reference temperatures, to the rounding of the published B, and drift away from them.
| Temperature | Vishay R (table) | Beta error | TDK R (table) | Beta error |
|---|---|---|---|---|
| −40 °C | 332.1 kΩ | +2.99 °C | 336.5 kΩ | +2.94 °C |
| −20 °C | 96.36 kΩ | +1.71 °C | 97.07 kΩ | +1.70 °C |
| 0 °C | 32.55 kΩ | +0.76 °C | 32.65 kΩ | +0.77 °C |
| 10 °C | 19.87 kΩ | +0.40 °C | 19.9 kΩ | +0.41 °C |
| 25 °C | 10 kΩ | 0.00 °C | 10 kΩ | 0.00 °C |
| 40 °C | 5.33 kΩ | −0.24 °C | 5.327 kΩ | −0.27 °C |
| 60 °C | 2.49 kΩ | −0.31 °C | 2.488 kΩ | −0.39 °C |
| 85 °C | 1.07 kΩ | +0.01 °C | 1.072 kΩ | −0.25 °C |
| 100 °C | 677.3 Ω | +0.39 °C | 680 Ω | −0.01 °C |
| 125 °C | 338.7 Ω | +1.40 °C | 341.7 Ω | +0.67 °C |
| 150 °C | 182.6 Ω | +2.84 °C | 185.3 Ω | +1.67 °C |
The thermistor's own error, before any circuit: TDK B57861S0103F040 (R/T 8016, B25/100 = 3988 K ±1 %, so ΔB = ±39.9 K). The R25 term grows slowly as |α| falls; the B term is zero at 25 °C and dominates far from it.
| Temperature | α (%/°C) | From R25 ±1 % | From B ±1 % | Thermistor total |
|---|---|---|---|---|
| −40 °C | −6.65 | ±0.15 °C | ±0.56 °C | ±0.71 °C |
| −20 °C | −5.81 | ±0.17 °C | ±0.41 °C | ±0.58 °C |
| 0 °C | −5.11 | ±0.20 °C | ±0.24 °C | ±0.44 °C |
| 25 °C | −4.38 | ±0.23 °C | ±0.00 °C | ±0.23 °C |
| 50 °C | −3.81 | ±0.26 °C | ±0.27 °C | ±0.54 °C |
| 85 °C | −3.15 | ±0.32 °C | ±0.71 °C | ±1.03 °C |
| 100 °C | −2.92 | ±0.34 °C | ±0.92 °C | ±1.27 °C |
| 125 °C | −2.58 | ±0.39 °C | ±1.31 °C | ±1.70 °C |
The part alone: a 10 kΩ ±1 %, B ±1 % NTC (TDK B57861S0103F040) is within ±0.23 °C at 25 °C and ±1.03 °C at 85 °C, because the B tolerance grows away from 25 °C. The measurement adds the series resistor, the ADC and self-heating: with a 1 % resistor and a 12-bit ratiometric ADC the worst case is ±1.05 °C at 25 °C and ±2.25 °C at 85 °C.
Divide the resistance deviation by the size of the thermistor's sensitivity α: ΔT ≈ (ΔR/R) / |α|. At 25 °C a 10 kΩ, B = 3988 K part has α = −4.38 %/°C, so ±1 % of resistance is about ±0.23 °C. Vishay's NTCLE100E3 datasheet works the same example at 0 °C: ±5.97 % at 5.09 %/K is ±1.17 °C.
For the largest voltage swing over a range, use Rs = √(R(Tmin) × R(Tmax)): 10.2 kΩ for this 10 kΩ part from −20 to 85 °C. The best value for accuracy also weighs self-heating and where you need the most resolution; the calculator's "Find the best E96 value" button tests E96 values from a third of the thermistor's lowest resistance to three times its highest against the full error budget.
Yes. When the ADC reference is the same supply that drives the divider, the code depends only on Rs and the NTC, so the supply and reference tolerances cancel (TI's SLYT786 shows the algebra). It does not remove the ADC's own offset, gain error and INL, or the resistor and thermistor tolerances. In the ADS1115 example below, a 1 % excitation error alone costs ±0.53 °C at 25 °C.
The thermistor warms by ΔT = P / δ, where P is the power in it and δ the dissipation constant. A 10 kΩ NTC with 10 kΩ from 3.3 V dissipates 272 µW; at the TDK part's 1.5 mW/K that reads 0.18 °C high. Powering the divider only while sampling divides it by the duty cycle.
Use the manufacturer's R-T table (or Steinhart-Hart fitted to it) when you need better than about a degree away from 25 °C. The Beta equation fitted at 25 and 85 °C is off by 2.99 °C at −40 °C and 1.40 °C at 125 °C for the Vishay NTCLE100E3103; interpolating Vishay's own 5 °C table stays within 0.015 °C of its exact formula.
Worst case assumes every part sits at its limit in the worst direction at once; use it for safety limits and anything you must guarantee. RSS assumes the errors are independent and is a better guide to the spread across a production run. The real error of one unit is usually closer to RSS.
The thermistor's sensitivity falls (|α| is 3.15 %/°C at 85 °C versus 4.38 %/°C at 25 °C) and the divider compresses as its resistance drops far below Rs, so each ADC code spans more degrees and the B tolerance grows. In the default design the resolution falls to 0.089 °C per LSB at 85 °C.
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