NTC Thermistor Calculator
An NTC (Negative Temperature Coefficient) thermistor is a type of resistor whose resistance decreases as its temperature increases. These semiconductor devices are highly temperature-sensitive and find applications in thermostats, temperature sensors, and protection systems.
The Beta equation
The resistance at a given temperature is calculated using the Beta equation:
R(T) = R0 x exp(B x (1/T - 1/T0))
Where:
- R0 — reference resistance in ohms (typically at 25 C)
- T0 — reference temperature in Kelvin
- B (Beta) — characteristic constant of the thermistor
- T — target temperature in Kelvin
The formula works by comparing the inverse of the absolute (Kelvin) temperatures of the target and reference points. The Beta constant amplifies the differences for precise modelling.
Parameters
- Reference resistance (R0): the nominal resistance at the reference temperature, typically 10k ohms at 25 C
- Reference temperature (T0): usually 25 C (298.15 K)
- Beta constant (B): provided in the thermistor datasheet, typically 3000-4000 for common NTC devices
- Target temperature (T): the temperature at which you want to know the resistance
Worked example
For a typical 10k NTC thermistor (B = 3950, R0 = 10,000 ohms at 25 C):
| Temperature (C) | Temperature (K) | Resistance (ohms) |
|---|---|---|
| 0 | 273.15 | 32,650 |
| 10 | 283.15 | 19,900 |
| 20 | 293.15 | 12,490 |
| 25 | 298.15 | 10,000 |
| 30 | 303.15 | 8,055 |
| 40 | 313.15 | 5,325 |
| 50 | 323.15 | 3,600 |
| 60 | 333.15 | 2,488 |
| 70 | 343.15 | 1,752 |
| 80 | 353.15 | 1,256 |
| 90 | 363.15 | 915 |
| 100 | 373.15 | 677 |
The steep resistance curve at lower temperatures gives excellent resolution for solar thermal monitoring, where tank temperatures of 20-80 C are typical.
Steinhart-Hart equation
The Beta equation assumes a simplified two-point model of the thermistor's resistance-temperature curve. For wider temperature ranges or higher accuracy, the Steinhart-Hart equation uses three coefficients:
1/T = A + B x ln(R) + C x (ln(R))^3
Where A, B, and C are coefficients determined by calibrating against three known temperature points. The Steinhart-Hart model fits the real NTC curve more closely than the Beta equation, particularly at temperature extremes.
Our firmware supports both methods per sensor — if a Beta value is configured, the Beta equation is used. If Beta is set to zero, the Steinhart-Hart coefficients are used instead. Each sensor also supports a per-channel calibration offset, applied after conversion, to correct for systematic errors.