The Steinhart–Hart equation is a model of the resistance

Electrical resistance

The electrical resistance of an electrical element is the opposition to the passage of an electric current through that element; the inverse quantity is electrical conductance, the ease at which an electric current passes. Electrical resistance shares some conceptual parallels with the mechanical...

 of a semiconductor

Semiconductor

A semiconductor is a material with electrical conductivity due to electron flow intermediate in magnitude between that of a conductor and an insulator. This means a conductivity roughly in the range of 103 to 10−8 siemens per centimeter...

 at different temperature

Temperature

Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

s. The equation is:


where:

• is the temperature (in kelvins)
• R is the resistance at T (in ohms)
• , , and are the Steinhart-Hart coefficients which vary depending on the type and model of thermistor
  Thermistor
  A thermistor is a type of resistor whose resistance varies significantly with temperature, more so than in standard resistors. The word is a portmanteau of thermal and resistor...
  
   and the temperature range of interest. (The most general form of the applied equation contains a term, but this is frequently neglected because it is typically much smaller than the other coefficients, and is therefore not shown above.)

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, they can be derived. Three accurate measures of resistance are made at precise temperatures, then the coefficients are derived by solving three simultaneous equations

Simultaneous equations

In mathematics, simultaneous equations are a set of equations containing multiple variables. This set is often referred to as a system of equations. A solution to a system of equations is a particular specification of the values of all variables that simultaneously satisfies all of the equations...

.

Inverse of the equation

To find the resistance of a semiconductor given the temperature the inverse of the Steinhart–Hart equation must be used. See the Application Note, "A, B, C Coefficients for Steinhart-Hart Equation".
where

Developers of the equation

The equation is named after John S. Steinhart and Stanley R. Hart who first published the relationship in 1968. Professor Steinhart (1929–2003), a fellow of the American Geophysical Union

American Geophysical Union

The American Geophysical Union is a nonprofit organization of geophysicists, consisting of over 50,000 members from over 135 countries. AGU's activities are focused on the organization and dissemination of scientific information in the interdisciplinary and international field of geophysics...

 and of the American Association for the Advancement of Science

American Association for the Advancement of Science

The American Association for the Advancement of Science is an international non-profit organization with the stated goals of promoting cooperation among scientists, defending scientific freedom, encouraging scientific responsibility, and supporting scientific education and science outreach for the...

, was a member of the faculty of University of Wisconsin–Madison

University of Wisconsin–Madison

The University of Wisconsin–Madison is a public research university located in Madison, Wisconsin, United States. Founded in 1848, UW–Madison is the flagship campus of the University of Wisconsin System. It became a land-grant institution in 1866...

 from 1969 to 1991.http://www.secfac.wisc.edu/senate/2004/0405/1775(mem_res).pdf Dr. Hart, a Senior Scientist at Woods Hole Oceanographic Institution

Woods Hole Oceanographic Institution

The Woods Hole Oceanographic Institution is a private, nonprofit research and higher education facility dedicated to the study of all aspects of marine science and engineering and to the education of marine researchers. Established in 1930, it is the largest independent oceanographic research...

 since 1989 and fellow of the Geological Society of America

Geological Society of America

The Geological Society of America is a nonprofit organization dedicated to the advancement of the geosciences. The society was founded in New York in 1888 by Alexander Winchell, John J. Stevenson, Charles H. Hitchcock, John R. Proctor and Edward Orton and has been headquartered at 3300 Penrose...

, the American Geophysical Union, the Geochemical Society

Geochemical Society

The Geochemical Society is a nonprofit and international scientific society for the purpose of encouraging the application of chemistry to solve problems involving geology and cosmology...

 and the European Association of Geochemistry

European Association of Geochemistry

The European Association of Geochemistry is a pan-European organization founded to promotes geochemical research. The EAG organizes conferences, meetings and educational courses for geochemists in Europe, including the Goldschmidt conference which it co-sponsors with the North American Geochemical...

, http://www.whoi.edu/science/GG/people/shart/cv.htm was associated with Professor Steinhart at the Carnegie Institution of Washington when the equation was developed.