Technicians and engineers often use thermistors to measure temperature in applications which require high accuracy. Thermistors operate by changing resistance as their temperature changes in a very predictable but non-linear way.
This characteristic allows them to provide higher accuracy than thermocouples or RTD’s. In order to ensure this high accuracy, thermistor calibration is an important consideration.
One challenge when using thermistors is calculating the temperature from the measured resistance value. To accomplish this, the Steinhart–Hart equation is used to convert a thermistor sensor’s resistance to temperature.
See the following project page on sourceforge to learn much more:
The project offers support for NTC thermistor calculations. The Steinhart-Hart equation is a mathematical model for these thermistors that seems to fit for a wide range of temperatures with high precision. Software to calculate the characteristic Steinhart-Hart coefficients based on temperature-resistance tables for given thermistors as well as functions allowing conversion of temperature values to resistance and vice versa is provided.
A model for the resistivity of a semiconductor as a function of the temperature was found by Steinhart and Hart 1968 (). The Steinhart-Hart law describes the absolute temperature T (in Kelvins) as a function of the NTC thermistor’s resistivity (in Ω) according to the formula
1/T = a0 + a1 · ln r + a3 · (ln r)3
The constants a0, a1 and a3, also called Steinhart-Hart coefficients, vary depending on the type of thermistor. To support developer when creating temperature measurement applications, thermistor manufacturer often supply these constants for their products. They also publicate tables where resistivity of thermistor products for a wider range of temperature values are listed.
This project provides software to
- calculate temperature value for a given resistance of an NTC thermistor with given Steinhart-Hart coefficients,
- calculate resistance value for a given temperature for an NTC thermistor with given Steinhart-Hart coefficients and
- evaluate Steinhart-Hart coefficients for an NTC thermistor descibed by a temperature-resistance table.
Apart from the standard Steinhart-Hart equation other forms have been found. For application with lower CPU power a simplified form of the Steinhart-Hart equation can be used.
1⁄T = a0 + a1 · ln r
On the other hand a quadratic term can be inserted into the formula to increase accuracy giving the extended Steinhart-Hart equation
1/T = a0 + a1 · ln r + a2· (ln r)2 + a3 · (ln r)3
An introduction to thermistors and the Steinhart-Hart polynom can be found at Wikipedia .
When compared against other methods, Steinhart-Hart models will give you much more precise readings across the sensors’ temperature ranges, often within a few hundredths of a degree.
Although the Steinhart-Hart equation is not universally known, it is useful in data logging applications such as measuring lake water temperatures, solar hot water systems, and skin temperature measurement.
Many high quality data loggers such as the dataTaker DT8x, Grant SQ20xx and VersaLog VL-TH allow you to enter the coefficients to automatically derive temperature from measured thermistor resistance. As part of our free tech support, we at CAS DataLoggers often provide help in this area for customers who call in asking how to perform the conversion.
Thermistor manufacturers don’t always provide users with Steinhart–Hart coefficients for their sensors; they may simply provide resistance versus temperature tables. In the case of a manufacturer-provided table, it’s not immediately obvious how to derive the necessary coefficients. Or, the user may want to perform self-validation of thermistors by measuring the resistance at several known temperature points and use this data to derive the Steinhart-hart coefficients.
To speed up the process, there are several Steinhart-Hart calculators online which allow you to enter the temperature and resistance values and then generate the coefficients.
You’ll find a link to our own online calculator, along with an example table, at the end of this article.
NTC Thermistors Steinhart and Hart Equation
The Steinhart and Hart Equation is an empirical expression that has been determined to be the best mathematical expression for resistance temperature relationship of NTC thermistors and NTC probe assemblies.
Deriving Steinhart-Hart Coefficients for Thermistor Calibration:
In cases where the Steinhart–Hart coefficients are not provided by your thermistor manufacturer or if you are doing thermistor calibration, you can derive them yourself. First, you’ll need three accurate resistance values (either from a table or measured) at three known temperatures and then insert them into the formula to derive the A, B and C coefficients.
The Steinhart-Hart equation is commonly defined as:
- T is the temperature (given in kelvins)
- R is the resistance at T (given in ohms)
- A, B, and C are the Steinhart–Hart Coefficients which differ according to your thermistor model/type and its particular temperature range
- Ln is the natural logarithm
The equation is sometimes presented as containing a term, but this results in a lesser value than the other coefficients and is therefore not as useful for obtaining higher sensor accuracy.
To find the Steinhart–Hart coefficients, you need to know at least three operating points. For this, we use three values of resistance data for three known temperatures.
Steinhart-Hart Temperature Calculator
Thermistor resistance is related to temperature in degrees Kelvin by the following formula:
1/T= A + B*ln(R/Rt) + C*ln(R/Rt)2 + D*ln(R/Rt)3
In the standard Steinhart-Hart equation the C parameter is set to zero. However, some manufacturers use all 4 coefficients. In the calculator below, you can specify whether to use this term or not, by just setting it to zero.
Subtract 273.15 to convert Kelvin to Celsius.
It’s wise to do a quick sanity check by putting in the coefficients and the same value for Rt and R. If the result isn’t 25 C then there is a problem with the coefficients.
Steinhart-Hart Calculator – The Steinhart–Hart equation is a model of the resistance of a semiconductor at different temperatures.
- T is the temperature (in Kelvin)
- R is the resistance at T (in ohms)
- A, B, and C are the Steinhart-Hart coefficients which vary depending on the type and model of thermistor and the temperature range of interest. (The most general form of the applied equation contains a (ln(R))2 term, but this is frequently neglected because it is typically much smaller than the other coefficients, and is therefore not shown above.)