The Steinhart-Hart Equation

If you are working with thermistors then you are probably vaguely familiar with the Steinhart-Hart equation. Simply put, this mathematical equation allows for people to measure temperature within thermistors. This equation allows for precise temperature control. This equation works better than simple equations to gauge temperature. This is due to the accuracy of the equation because it factors in the range of the whole sensor. Many company who create these products also put out official Steinhart-Hart coefficients. A coefficient is a single number that you are able to apply to multiply variables. Usually, you will take a coefficient and add, multiple, subtract, or divide the variables that you are working with. The Steinhart-Hart equation is very specific.

This means that:

T equals temperature in kelvin

R equals the resistance of T. This is done in ohms

A, B, and C are the coefficients of the equation. These three numbers vary depending style and model of the thermistor, as well as, the range of temperature you need to achieve.

Sometimes the Steinhart-Hart coefficients cannot be found, but they can still be derived. There are three ways to accurately measure resistance at a specific temperature. This method of determining coefficients is to solve three simultaneous equations, which is also known as a system of equations. It is a specified amount of set equations, and finding common solutions solves them.

If you flip or invert the equation you will be able to get the resistance of semiconductors. This is only possible when the temperature for the reverse equation is already had.

Two people are responsible for this equation, and they are John Steinhart and Stanley R. Hart. The equation was published for the first time in 1968. The published piece is called "Calibration Curves for Thermistors, Deep Sea Research, and Oceanographic Abstracts." John Steinhart was a professor at the University of Wisconsin-Madison, and he did this from 1969 to 1991. Stanley Hart worked with Steinhart at the American Geophysical Union. The two were associated at the Carnegie Institute of Washington, and this is where they were able to work and develop their equation. Since its publication in 1968, many people and companies have used the equation, so that they can get the most out of their thermistors. Even if you aren't great at math, companies who sell and make these products should be able to help you through the process.

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