Steinhart-Hart equation

The Steinhart-Hart equation is a model of the resistance of a semiconductor at different temperatures. The equation is:

${1 \over T} = A + B \ln(R) + C (\ln(R))^3 \,$

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where:

$T$ is the temperature (in kelvins)
R is the resistance at T (in ohms)
$A$ , $B$ , $C$ , and $D$ are the Steinhart-Hart coefficients which vary depending on the type and model of thermistor and the temperature range of interest. The $D$ coefficient is frequently neglected because it is typically much smaller than the other coefficients.

Uses of the equation

The equation is often used to derive a precise temperature of a thermistor since it provides a closer approximation to actual temperature than simpler equations, and is useful over the entire working temperature range of the sensor. Steinhart-Hart coefficients are usually published by thermistor manufacturers.

Where Steinhart-Hart coefficients are not available, but three accurate measures of resistance are made at precise temperatures, then the coefficients may be derived by solving three simultaneous equations.

Developers of the equation

The equation is named after John S. Steinhart and Stanley R. Hart who first published the relationship in 1968^[1]. Professor Steinhart (1929-2003), a fellow of the American Geophysical Union and of the American Association for the Advancement of Science, was a member of the faculty of University of Wisconsin-Madison from 1969-1991[1]. Dr. Hart, a Senior Scientist at Woods Hole Oceanographic Institution since 1989 and fellow of the Geological Society of America, the American Geophysical Union, the Geochemical Society and the European Association of Geochemistry, [2] was associated with Professor Steinhart at the Carnegie Institution of Washington when the equation was developed.