NTC Thermistor Calculator

Resistance from temperature or temperature from resistance, with the Beta model or Steinhart–Hart coefficients — then the voltage divider around it: output voltage, ADC reading, sensitivity, and a fixed resistor chosen for the range you need to measure.

Last updated 22 Sep 2026

NTC thermistor and divider

R25 + Beta or A, B, C ⇄ °C, Vout, ADC

Thermistor model

R25, resistance at 25 °C (kΩ)From the part number or datasheet: 10 kΩ is the commonest.

B value (K)Datasheets quote B between two temperatures, e.g. B25/85 = 3977 K; B25/50 is a little lower. Use the figures from your part’s datasheet; typical values vary widely between manufacturers.

Steinhart–Hart A (× 10⁻³)Defaults: fitted by this page to Vishay’s NTCLE100E3103 (10 kΩ, B25/85 3977 K) curve at 0, 50 and 100 °C.

Steinhart–Hart B (× 10⁻⁴)

Steinhart–Hart C (× 10⁻⁷)

Find

Temperature (°C)

Measured resistance (kΩ)

Divider supply voltage (V)

Where the thermistor sits

Fixed resistor

Fixed resistor (kΩ)

ADC resolution

ADC reference (V), 0 = the divider supply0 means ratiometric: the ADC reference is the same supply as the divider, so supply changes cancel.

Range: lowest temperature (°C)

Range: highest temperature (°C)

The thermistor and the fixed resistor form a divider; its midpoint goes to the ADC input (which draws no current). The NTC is labelled with its resistance at the temperature above and turns amber, then red, as the power in it nears or passes 1 mW, where self-heating starts to matter. The dots show the divider current.

5.279kΩExample

10 kΩ NTC, B = 3977 K, at 40 °C; 10 kΩ fixed resistor from 3.3 V, NTC to ground, 12-bit ADC

Thermistor and divider equations

R = R₂₅ e^{B(1/T − 1/298.15)}; 1/T = A + B ln R + C ln³R; V_out = V_s × R ÷ (R + R_f); ADC = ⌊V_out ÷ V_ref × 2ⁿ⌋; three-point R_f = (R₂(R₁ + R₃) − 2R₁R₃) ÷ (R₁ + R₃ − 2R₂)

T: absolute temperature in kelvin (°C + 273.15)
B: the B (Beta) constant in kelvin, from the datasheet, measured between two temperatures such as 25 and 85 °C
A, B, C: Steinhart–Hart coefficients, from the maker or fitted to three points of the R-T table
R₁, R₂, R₃: NTC resistance at the lowest, middle and highest temperature of the range

Worked example

10 kΩ NTC, B = 3977 K, at 40 °C; 10 kΩ fixed resistor from 3.3 V, NTC to ground, 12-bit ADC
R = 10 kΩ × exp(3977 × (1/313.15 − 1/298.15)) = 5.279 kΩ
V_out = 3.3 × 5.279 ÷ (5.279 + 10) = 1.1401 V
ADC = ⌊1.1401 ÷ 3.3 × 4,096⌋ = 1,415
Sensitivity −30.26 mV/°C, so each ADC step is 0.027 °C
Vishay's own curve gives 5.33 kΩ at 40 °C: the Beta model reads 0.25 °C out there

Beta model against the manufacturer’s curve

Vishay NTCLE100E3103 (10 kΩ). The Beta model is exact at 25 °C and 85 °C, where B was measured, and drifts outside. The last column is the reading error if you convert with Beta (checked against the Steinhart–Hart fit).
Temperature	Vishay curve	Beta model, B25/85 = 3977 K	Difference	Temperature error
−20 °C	96.36 kΩ	107.1 kΩ	+11.1%	−1.85 °C
0 °C	32.55 kΩ	33.9 kΩ	+4.1%	−0.79 °C
10 °C	19.87 kΩ	20.27 kΩ	+2.0%	−0.41 °C
20 °C	12.49 kΩ	12.55 kΩ	+0.5%	−0.11 °C
25 °C	10 kΩ	10 kΩ	−0.0%	+0.01 °C
30 °C	8.059 kΩ	8.025 kΩ	−0.4%	+0.11 °C
40 °C	5.33 kΩ	5.279 kΩ	−1.0%	+0.25 °C
50 °C	3.605 kΩ	3.563 kΩ	−1.2%	+0.31 °C
60 °C	2.49 kΩ	2.463 kΩ	−1.1%	+0.30 °C
70 °C	1.753 kΩ	1.739 kΩ	−0.8%	+0.23 °C
85 °C	1.07 kΩ	1.07 kΩ	−0.0%	−0.01 °C
100 °C	677.3 Ω	684.9 Ω	+1.1%	−0.38 °C

Using an NTC thermistor

An NTC (negative temperature coefficient) thermistor is a resistor whose value falls steeply as it warms, by about 4.5% per degree near room temperature. It is the cheapest accurate temperature sensor there is. Two numbers identify most parts: R25, the resistance at 25 °C, and B, which describes how fast it falls. The Beta model R = R25 × exp(B(1/T − 1/T25)) is exact at the two temperatures B was measured at and close in between. For the example part, Vishay’s NTCLE100E3103 (10 kΩ, B25/85 = 3977 K), it gives 5.279 kΩ at 40 °C where Vishay’s curve says 5.33 kΩ, a reading error of 0.25 °C. At 0 °C the error grows to −0.79 °C.

Steinhart–Hart fits the curve with three coefficients, 1/T = A + B ln R + C (ln R)³, and follows a real thermistor to a few hundredths of a degree over a range of 100 °C or more. The default coefficients were fitted to Vishay’s curve at 0, 50 and 100 °C and stay within 0.05 °C of it from −20 to 125 °C. If the maker gives no coefficients, fit your own to three points of the datasheet’s resistance table; the page shows the B25/85 your coefficients imply, as a check.

Reading it with an ADC. The usual circuit is a voltage divider: the NTC and a fixed resistor between the supply and ground, with the junction going to an ADC input. With the ADC referenced to the same supply (ratiometric), the supply voltage cancels out of the reading. In the example, 40 °C gives 1.1401 V and a 12-bit reading of 1,415; the output moves 30.26 mV per degree, so one ADC step is 0.027 °C.

Choosing the fixed resistor. The divider’s output against temperature is an S-shaped curve. Making the fixed resistor equal to the thermistor’s resistance at the middle of your range makes the output change fastest at that temperature, which is the best choice for resolving small changes around one set point. For a straighter line over the whole range, choose the resistor that puts the mid-range output exactly half-way between the outputs at the ends (the three-point formula above). Over 0 to 100 °C the output of a 10 kΩ divider strays up to 22.0% of its span from a straight line through its ends; the mid-range choice (3.563 kΩ) cuts that to 7.6%, and the three-point choice (2.797 kΩ) to 5.5%, close to the 5.1% that the best possible single resistor (about 2.9 kΩ, found by search) achieves. Over a narrower 0 to 50 °C range the three-point divider is within 2.0% of its span, about 1 °C, which is why simple thermostats get away with a straight-line conversion. For the best accuracy, convert each reading with the Steinhart–Hart equation or a lookup table instead of relying on linearity.

Self-heating. The divider current warms the thermistor. The datasheet’s dissipation constant, in mW/K, says how many degrees each milliwatt adds; keep the power in the thermistor to a small fraction of it, or power the divider only while reading. For the divider arithmetic in general, see the voltage divider calculator.

Frequently asked questions

How do I convert thermistor resistance to temperature?

With the Beta model, 1/T = 1/298.15 + ln(R ÷ R25) ÷ B, with T in kelvin. With Steinhart–Hart, 1/T = A + B ln R + C (ln R)³. Subtract 273.15 for °C. Choose the second mode above.

What is the B value of a thermistor?

A constant, in kelvin, describing how steeply the resistance falls with temperature. It is measured between two temperatures, so datasheets write B25/50 or B25/85. The example part’s B25/85 is 3,977 K.

What resistor should I use with a 10k thermistor?

For best resolution around one temperature, the thermistor’s resistance at that temperature (10 kΩ for 25 °C). For the straightest output over a range, the three-point value: 2.797 kΩ for 0 to 100 °C with a 3977 K part.

Is the Beta equation accurate enough?

Within a few tenths of a degree between the two temperatures B was measured at, and worse outside. For better than about 0.5 °C over a wide range, use Steinhart–Hart coefficients or the maker’s table.

What is 10k NTC resistance at 0 °C?

For Vishay’s NTCLE100E3103 (B25/85 3977 K), 32.55 kΩ from its table; the Beta model gives 33.9 kΩ. Other 10 kΩ parts with different B values differ considerably.

Related calculators

References

Steinhart JS, Hart SR. Calibration curves for thermistors. Deep-Sea Research 1968;15:497–503.
Vishay BCcomponents. NTCLE100E3 NTC thermistors, radial leaded, datasheet rev. 07-May-2025: NTCLE100E3103, R25 10 kΩ, B25/85 3977 K, R-T characteristic and coefficients.
Microchip Technology. ATmega328P datasheet, ADC conversion result: ADC = V_IN × 1024 ÷ V_REF (10-bit).