NTC Thermistor Calculator

Three conversions, three ways to be wrong

A thermistor is the cheapest way to measure temperature and among the most awkward to get right, because three separate steps sit between the number firmware reads and the number a person wants.

That last one looks like a joke and is not. Using 273 puts every reading 0.15 °C out, which is well inside what a careless reviewer would accept and well outside what the part is capable of.

Read it as a ratio, not as a voltage

With the NTC to ground and a fixed resistor to the supply, the reading as a fraction of full scale gives the resistance directly:

R = Rfixed × ratio / (1 − ratio), where ratio = counts / fullScale

The supply voltage does not appear. On a ratiometric ADC — one whose reference is the same rail that feeds the divider — a supply that sags moves the divider output and the reference by the same factor, and the count does not change at all. That immunity is the main reason this circuit is used.

Code that converts counts to volts and then to ohms has thrown it away before the temperature is computed, and the reading starts drifting with the battery. It is a common shape in example code because volts feel more concrete than a ratio.

One detail inside that ratio is worth being exact about: full scale for an n-bit ADC is 2ⁿ − 1, not 2ⁿ. A 12-bit converter reads 0 to 4095, so half scale is 2047.5 and a reading of 2048 is just above the midpoint — which is why the calculator above answers 24.99 °C rather than 25.00 for a 10 kΩ part in a 10 kΩ divider. Dividing by 4096 is a small error at the middle and a growing one towards the top of the range.

Beta is the two-point model

1/T = 1/T₀ + ln(R/R₀) / B, with temperatures in kelvin.

One constant, exact at the reference temperature by construction, and exact at the second temperature it was fitted to. A datasheet quoting B25/85 is naming those two. Between and beyond them the real curve bends away, which is why a sensor calibrated at room temperature can read a degree out in a fridge and still be working perfectly.

Steinhart-Hart is the same equation with the curvature put back

1/T = A + B·ln(R) + C·ln(R)³

Look at what happens when C is zero: the equation becomes linear in ln(R), which is exactly the Beta equation rewritten. Beta is not an alternative to Steinhart-Hart, it is the C = 0 case of it.The cubic term is the curvature a real part has and a two-point fit cannot express.

Three coefficients need three measurements, and the fit passes through all three exactly. That makes the choice of points the whole job: three rows clustered around room temperature produce coefficients that are superb there and useless at the ends. Spread them across the range that matters.

The fixed resistor decides the resolution

Sensitivity peaks where the thermistor's resistance is near the fixed resistor's and falls away sharply either side. A 10 kΩ NTC with a 10 kΩ resistor resolves finely around 25 °C and coarsely at 100 °C, where the thermistor has dropped to a few hundred ohms and a whole ADC count covers a large temperature step.

Matching R25 is the reflex, and it is the right answer only if room temperature is what matters. For an oven or a battery pack running hot, size the fixed resistor to the thermistor's resistance in the middle of that range instead. The table above prices the trade.

Self-heating

Current through the thermistor warms it, and the reading follows the part up. Power divided by the dissipation constant on the datasheet — milliwatts per degree — gives the rise.

A 10 kΩ NTC in a 10 kΩ divider on 3.3 V dissipates about 270 µW, which with a typical 2 mW/°C constant is under a seventh of a degree. Tolerable. Halve the resistors for a stronger signal and the power quadruples, at which point the sensor is measuring its own current as much as the environment. Where that matters, the usual fix is to power the divider from a GPIO and switch it on only while sampling.

Getting the wiring backwards

With the NTC to ground, counts fall as it warms. With the NTC to the supply, they rise. Swap the legs and the reading still moves by the right amount, in the wrong direction — which looks like a wiring fault rather than a software one and gets debugged with a multimeter for far longer than it should.