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An NTC (Negative Temperature Coefficient) thermistor is a resistor whose resistance falls as temperature rises. The relationship is non-linear, so two models are used: the simple Beta equation (accurate over a modest range from one reference point and a B-value) and the more precise Steinhart-Hart equation (three coefficients, accurate over a wide range).
| Model | Equation |
|---|---|
| Beta — T from R | 1/T = 1/T0 + (1/B)·ln(R/R0) |
| Beta — R from T | R = R0·eB(1/T − 1/T0) |
| Steinhart-Hart | 1/T = A + B·ln(R) + C·(ln R)³ |
All temperatures are in kelvin (K = °C + 273.15). R0 is the rated resistance at T0 = 25 °C — for example a "10k NTC" is 10 kΩ at 25 °C with a typical B of 3950 K.
A temperature-sensitive resistor whose resistance decreases as temperature increases (Negative Temperature Coefficient). It is widely used for cheap, sensitive temperature measurement.
A material constant (in kelvin) that describes how steeply the thermistor's resistance changes with temperature. Common NTCs have B around 3000–4000 K; a typical 10k NTC is 3950 K.
The reference resistance at the reference temperature, almost always 25 °C (298.15 K). A "10k NTC" has R0 = 10 kΩ at T0 = 25 °C.
With the Beta equation: 1/T = 1/T0 + (1/B)·ln(R/R0), then convert kelvin to °C by subtracting 273.15.
The Beta model is simple and fine over a limited range near the reference. Steinhart-Hart, with three coefficients, is far more accurate across a wide temperature range.
They are fitted from three known resistance-temperature points (or given in the datasheet). Once you have A, B, and C, the equation converts any resistance to temperature.
The equations are physical relationships that only work on the absolute (kelvin) scale. Always convert: K = °C + 273.15, and back with °C = K − 273.15.
The measuring current dissipates power in the thermistor and warms it slightly, biasing the reading. Use a small sense current or pulsed measurement to minimise it.
Put it in a voltage divider with a fixed resistor, read the divider voltage with the ADC, compute the thermistor resistance, then use these equations to get temperature.
NTC resistance falls with temperature (used for sensing); PTC resistance rises with temperature (used for resettable fuses and inrush/overheat protection).
Usually one equal to the thermistor's nominal value (e.g. 10 kΩ for a 10k NTC), which centres the divider's sensitivity around your temperature of interest.
With a good model and calibration, ±0.1–0.5 °C is achievable over a moderate range — excellent for the cost, though thermocouples or RTDs suit wider ranges.
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