# Online Calculators for Thermistor Beta, Temp. Coefficient, and R-Temp

**Ametherm** today introduced a new calculators page to its website. Offering a convenient and time-saving resource, the online calculators allow design engineers to quickly determine the beta value of NTC thermistors, in addition to their temperature coefficient and resistance temperature (R-temp) characteristics using the Steinhart-Hart Equation.

A thermistor's beta value indicates the shape of the curve representing the relationship between the device's resistance and temperature. Beta value is used to calculate temperature coefficient of the thermistor, which in turn, is used in calculating the temperature accuracy of the thermistor.

The temperature coefficient of a thermistor is used when calculating its tolerance in terms of temperature. With Ametherm's Temperature Coefficient (Alpha) Calculator, designers can determine the tolerance at any temperature for any given beta value.

With the Steinhart and Hart Calculator, the temperature for any given resistance can be calculated using coefficients based on three measurements — low-, mid-, and high-temperature.

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:

Where:

- T is the temperature in Kelvin
- R is the resistance at temperature 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.)

First, measure the thermistor at three different temperatures. The temperatures should be evenly spaced and at least 10 degrees apart. Use the three temperatures to solve three simultaneous equations using these steps:

Knowing A, B and C for a thermistor allows you to use the Steinhart and Hart equation in two ways.

1) If resistance is known and temperature desired then use Equation 1 above.

2) If temperature is known and expected resistance is desired, use Equation 5 below:

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