Engineering Reference
NTC Thermistor and Temperature-Coefficient Reference
Lookup reference for NTC R25, beta and Steinhart-Hart terms, resistance-temperature values, self-heating, TCR units, ppm conversion, and linear drift boundaries.
- NTC Example
- 10 kΩ, B3950
- TCR Basis
- Fraction per kelvin
- Updated
- September 28, 2026
NTC and Coefficient Terminology
| Term | Meaning | Unit | Boundary |
|---|---|---|---|
| R25 | Nominal resistance at 25°C | Ω, kΩ, or MΩ | Tolerance applies at the stated reference temperature |
| B or β | Beta material constant | K | Use the datasheet's stated temperature pair, such as B25/85 |
| A, B, C | Steinhart-Hart coefficients | Coefficient-specific | Coefficient convention must match resistance in ohms and natural logarithm |
| T0 | Reference absolute temperature | K | 25°C equals 298.15 K |
| D | Dissipation constant | mW/K | Temperature rise per dissipated milliwatt depends on installation |
| τ | Thermal time constant | s | Response time depends on medium, airflow, mounting, and sensor mass |
| α | Relative temperature coefficient | 1/K, %/K, or ppm/K | First-order fractional change per degree |
| a | Absolute temperature coefficient | value/K | Absolute change per degree in the quantity's native unit |
Derived 10 kΩ B3950 NTC Lookup
These illustrative nominal values are generated at build time with the same beta-equation function used by the NTC Thermistor Calculator: R = R25 exp[B(1/T − 1/298.15 K)]. They are not generic limits for every 10 kΩ thermistor.
| Temperature °C | Resistance Ω | R/R25 |
|---|---|---|
| -40 | 401859.72 | 40.18597 |
| -20 | 105384.69 | 10.53847 |
| 0 | 33620.60 | 3.36206 |
| 25 | 10000.00 | 1.00000 |
| 50 | 3588.18 | 0.35882 |
| 75 | 1491.68 | 0.14917 |
| 85 | 1086.67 | 0.10867 |
| 100 | 697.52 | 0.06975 |
| 125 | 358.83 | 0.03588 |
Model Selection
| Model | Inputs | Useful for | Boundary |
|---|---|---|---|
| Beta equation | R0, T0, β | Compact two-parameter resistance-temperature model | Accuracy depends on the thermistor and stated beta interval |
| Steinhart-Hart | A, B, C | Wider-range fitted model when coefficients are supplied | Do not mix coefficient sets or logarithm/resistance conventions |
| Two-point beta | R1, T1, R2, T2 | Derives an effective beta between two points | It is not automatically valid outside that interval |
| Linear TCR | X0, α, T0 | Small first-order drift estimate | Large spans or nonlinear devices require a fuller model |
Temperature-Coefficient Unit Conversion
| Fractional coefficient | Equivalent ppm | Equivalent percent |
|---|---|---|
| 1 × 10⁻⁶ /K | 1 ppm/K | 0.0001 %/K |
| 1 × 10⁻⁴ /K | 100 ppm/K | 0.01 %/K |
| 1 × 10⁻³ /K | 1000 ppm/K | 0.1 %/K |
| 1 × 10⁻² /K | 10,000 ppm/K | 1 %/K |
| 1 ppm/°F | 1.8 ppm/K | Temperature intervals only |
| 1 %/°F | 1.8 %/K | Temperature intervals only |
Linear TCR Examples
The table uses X = X0[1 + α(T − T0)] for a 10 kΩ reference value from 25°C to 85°C. It is a first-order drift illustration, not an NTC curve.
| TCR ppm/K | TCR %/K | Change over 60 K % | Final value from 10 kΩ |
|---|---|---|---|
| 25 | 0.0025 | 0.1500 | 10015.00 |
| 50 | 0.0050 | 0.3000 | 10030.00 |
| 100 | 0.0100 | 0.6000 | 10060.00 |
| 250 | 0.0250 | 1.5000 | 10150.00 |
Measurement and Error Boundaries
| Effect | Why it matters | Engineering response |
|---|---|---|
| R25 tolerance | Shifts the nominal resistance curve | Include it separately from beta or fit error |
| Beta tolerance | Changes curve slope across temperature | Use the specified beta interval and tolerance |
| Self-heating | Measurement power raises bead temperature | Reduce excitation or characterize dissipation in the installed medium |
| Lead resistance | Adds series resistance, especially at low R | Use suitable wiring and include lead error |
| ADC/reference error | Adds gain, offset, quantization, and reference drift | Budget the complete measurement chain |
| Interpolation | Sparse tables can hide nonlinearity | Use the manufacturer's recommended interpolation or coefficients |
| Aging and moisture | Can shift resistance over life | Use stability data for long-term error budgets |
Common Reference Mistakes
- Using Celsius instead of kelvin in the beta equation.
- Assuming every 10 kΩ NTC has the same beta curve.
- Ignoring the temperature pair attached to a beta value.
- Mixing Steinhart-Hart coefficients from another part or unit convention.
- Treating R25 tolerance as full-range temperature accuracy.
- Using a constant linear TCR across a strongly nonlinear NTC range.
- Confusing relative ppm/K with an absolute value-per-kelvin coefficient.
- Treating ppm/°F as numerically equal to ppm/K.
- Ignoring excitation-current self-heating.
- Assuming dissipation constant is independent of mounting and medium.
- Rounding resistance before inverse temperature conversion.
- Using this illustrative lookup instead of the selected part's datasheet.
Support reference
FAQ
What does R25 mean for an NTC thermistor?
R25 is nominal resistance at 25°C. Its tolerance does not by itself define accuracy across the full temperature range.
What is an NTC beta value?
Beta is a temperature constant in kelvin used by the exponential resistance model. A datasheet normally states the temperature pair over which it was characterized.
What does B25/85 mean?
It identifies an effective beta derived or specified between 25°C and 85°C. It should not be assumed identical to beta over every other interval.
Does NTC resistance increase with temperature?
No. For a standard NTC thermistor with positive beta, resistance decreases as temperature increases.
When should I use Steinhart-Hart instead of beta?
Use the supplied Steinhart-Hart coefficients when wider-range accuracy is needed and the coefficient convention is known. The beta model is simpler but usually more interval-dependent.
Why must thermistor equations use kelvin?
The beta relationship contains reciprocal absolute temperatures. Substituting Celsius values produces invalid results.
What is thermistor self-heating?
Measurement current dissipates I²R in the thermistor. Dividing power by the installed dissipation constant gives a first-order temperature-rise estimate.
What is temperature coefficient in ppm/K?
It is fractional change per kelvin multiplied by one million. A value of 100 ppm/K equals 0.01%/K.
Are ppm/K and ppm/°C equivalent?
Yes for temperature differences because a one-kelvin interval equals a one-degree-Celsius interval.
Are ppm/K and ppm/°F equivalent?
No. One degree Fahrenheit is 5/9 kelvin, so coefficient units must be converted consistently with the temperature interval.
Can a constant TCR model an NTC thermistor?
Only over a sufficiently narrow range as a local approximation. NTC resistance is strongly nonlinear and normally requires beta, Steinhart-Hart, or tabulated data.
Does this lookup replace a thermistor datasheet?
No. Use the actual part's resistance tolerance, beta or coefficient set, operating range, dissipation constant, time constant, and stability data.
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