NTC calculator

Negative temperature coefficient resistors (NTCs) are widely used as temperature sensors for their low cost, their availability in many different shapes and wide nominal resistance values (roughly from 1 Ω to 10 MΩ).

Picture of a NTC
Picture of a tiny NTC, R25 = 6.8 kΩ and B25/100 = 4200 K.

The resistivity of the vast majority of electrical conductors (metals) normally increases as the temperature rises; they have a positive temperature coefficient (PTC). But this resistivity change is pretty small: for example, the resistivity temperature coefficient of copper is only 0.0039 K-1. Of course, this phenomenon is used to measure the temperature, but the small signals involved add complexity to the circuit.

Semiconductors, on the other hand, are an exception: their resistivity goes down as the temperature increases and the change is significant. For example, the temperature coefficient of un-doped silicon is –0.075 K-1. It's therefore possible to build simple and very sensitive temperature sensors that will give very large signals.

The downside is that their resistance is not a linear function of the temperature as one can see in the two plots below (which refers to an NTC specified R25 = 6.8 kΩ and B25/100 = 4200 K). Even by restricting the temperature range (say from 0 to 50 °C), still the function can hardly be approximated by a line. As explained before, in an NTC the resistance decreases as the temperature increases.

Resistance as a function of temperature Resistance as a function of temperature (zoom 0-50°C)
Variation of the resistance as a function of temperature, both axes are linear.

As one can see in the plots below, the resistance varies as the exponential of the inverse of the absolute temperature (same NTC as above). As one would expect, by plotting the resistance with a logarithmic scale and the inverse of the temperature (1/T) the function become a straight line.

Logarithm of resistance as a function of temperature Logarithm of resistance as a function of the inverse of the absolute temperature
Variation of the resistance as a function of temperature, with logarithmic resistance axis (both plots) and inverse temperature axis (right plot only).

NTCs have two major parameters: the nominal resistance R25, which is their resistance at the standard temperature of 25 °C (T25 = 25 °C = 298.15 K) and their constant B25/100 which somehow represents the "temperature coefficient".

With these parameters the resistance (or the temperature) can be calculated as follows:

R(T) = R_25 * e ^ ( B_25_100 * ( ( 1/T ) - ( 1 / T_25 ) ) )          T(R) = 1 / ( ( ln( R / R_25 ) / B_25_100 ) + ( 1 / T_25 ) )          T_25 = 298.15 K

The following calculator uses the above equations to calculate the resistance of the temperature of a known NTC. Just enter the known temperature or resistance and press the corresponding "calculate" button. If the parameters of the NTC are not known, they can be calculated with just two measurements.

Temperature and resistance:
R = Ω
T = °C
NTC parameters:
B25/100 = K  
R25 = Ω  

NTCs are widely used temperature sensors because of their low cost, their availability in many sizes and shapes. With modern micro-controllers, is now easy to program the above explained equations and get a direct readings in °C (or any other temperature unit) without the need of complex analog linearizing circuits.

There are a few other downsides that should be mentioned: first the working temperature range is limited to about –50 to +150 °C. This depends, of course, on the particular model of NTC, but because the majority of NTCs use silicon, these limits cannot be exceeded. Than, because of the logarithmic change of resistance, the wider the temperature range accepted by the circuit, the lower the precision.

NTCs are usually not factory calibrated: the actual R25 and B25/100 can vary from one NTC to another and some sort of circuit adjustment is always required to do absolute temperature readings.

A last note: by using an NTC as a temperature sensor, one should be careful in not running to much current though it, since the current will heat the NTC and introduce a measurement error. For this reason, high value NTCs (10 kΩ or more) are better for thermometers.

Small values NTCs are normally not used as temperature sensors but they make very good inrush current limiters. When a circuit is switched on with an NTC in series, the NTC is initially cold, offering a few Ω of resistance, limiting the inrush current and preventing, for example, the fuse from blowing. As soon as the current starts flowing, the NTC heats up and its resistance drops in the mΩ range letting the main current through undisturbed.