Two models for NTC thermistors
An NTC thermistor’s resistance falls steeply and non-linearly as temperature rises. Datasheets describe this curve in one of two ways, and the calculator supports both.
The Beta model uses two datasheet values: the resistance R₀ at a reference temperature T₀ (almost always 25 °C, written R₂₅) and the constant β:
R = R₀ · exp[β (1/T − 1/T₀)]
Temperatures are in kelvin. The model is exact at T₀ and reasonably accurate near it, but β is only constant over a limited range. Datasheets usually state the range β was fitted over, for example “B25/85 = 3950 K”, meaning between 25 and 85 °C.
The Steinhart–Hart equation fits three calibration points exactly:
1/T = A + B·ln R + C·(ln R)³
With three well-spaced points, it typically stays within a few hundredths of a degree across a range of 100 °C or more, much better than a single β.
Worked example: 10 kΩ, β = 3950
The most common NTC in electronics is 10 kΩ at 25 °C with β = 3950 K. At 50 °C the Beta model gives 3588.18 Ω. The calculator also shows:
- Temperature coefficient α = −β / T² = −3.783 %/°C at 50 °C. Each degree changes the resistance by almost 4 %, about ten times the sensitivity of a platinum RTD.
- Slope dR/dT = −135.7 Ω/°C
- Resistance ratio R/R₀ = 0.35882
Over a wider range, the same thermistor measures 33,620.6 Ω at 0 °C and 697.5 Ω at 100 °C. Going the other way, 5 kΩ corresponds to 41.46 °C.
Fitting Steinhart–Hart coefficients
Enter three temperature and resistance pairs. “Fill R₁–R₃ from the Beta model” pre-fills the resistances from the Beta values above, which is useful when you only have a datasheet; replace them with measured values when you calibrate. The calculator then shows:
- The coefficients A, B and C, with full precision for copying into firmware
- The equivalent β between the first and last point
- A converter that uses the fitted equation in both directions
Choose points that span your working range: for 0 to 85 °C, use something like 0, 25 and 85 °C. Points close together make the fit sensitive to measurement noise. If C comes out negative, the calculator warns you; that usually means the three points are not from the same part, or one reading is wrong.
Choosing and using NTCs
- Self-heating. The measuring current heats the thermistor. Datasheets give a dissipation constant in mW/°C. Keep the measuring power well below it, typically under a tenth of a milliwatt for small beads.
- Tolerance. Common tolerances are ±1 %, ±3 % or ±5 % on R₂₅ and ±1 % on β. At 25 °C a ±1 % resistance tolerance is roughly ±0.25 °C.
- Divider design. In a voltage divider, a fixed resistor equal to the thermistor’s resistance in the middle of the range gives the best sensitivity there.
Common mistakes
Using β outside the range it was fitted over. A β quoted for 25–85 °C gives growing errors below 0 °C or above 100 °C. Use Steinhart–Hart with calibration points across your range.
Mixing up temperature units. Both equations need kelvin. The calculator handles this, but firmware often doesn’t.
Confusing B25/50 and B25/85. The same part has slightly different β values for different temperature pairs. Use the one matching your range.
Frequently asked questions
What does “10K 3950” mean?
R₂₅ = 10 kΩ and β = 3950 K. Both values are needed; many parts share 10 kΩ but differ in β (3435, 3380 and 3950 are all common).
How accurate is the Beta model?
Within roughly a degree over a few tens of degrees around T₀ for typical parts, getting worse further out. For better accuracy, calibrate three points and use Steinhart–Hart.
Can I use PTC thermistors?
No. PTC thermistors (switching types) don’t follow these equations.
Is there a resistance table?
Use the Steinhart–Hart converter or the Beta converter to generate any value, or enter your part’s values and step through temperatures with the arrow keys.