# Thermometer Calculator

Calculate temperature from resistance or resistance from temperature given calibration values for:

• PRT using Callendar-Van Dusen equation
• PRT using ITS-90
• Thermistor using Steinhart-Hart equation

Save and load thermometer coefficients. Convert CVD coefficients between a-b-c and α-δ-β equations. ## Usage

This app has three calculators for three different calculations. The calculator is selected by touching the spinner at the top and choosing one of the three options.

Each calculator has a set of input coefficients. These are the calibration coefficients for the specific thermometer you wish to calculate for. For an uncalibrated industrial platinum resistance thermometer, use the default coefficients on the Callendar-Van Dusen calculator.

The last two numbers for each calculator are temperature and resistance. These are both inputs and outputs. Enter a temperature to calculate the resistance or enter resistance to calculate the temperature.

The calibration coefficients can be saved and later restored. To save touch the menu button, select save, and enter a name for the coefficients. To load touch the menu button, select load, and choose your coefficients from the list. Each caluculator has a separate list of saved coefficients.

## The Math

All math is performed with double precision floating point numbers. For non-programmers that means around 15 significant digits.

### Callendar-Van Dusen

The Callendar-Van Dusen equation is directly calculated from temperature to resistance. The equation used depends on whether coefficients are in a-b-c or alpha-delta-beta format. Both equations are shown here.

R = R0 + R0*alpha*(t-delta(t/100-1)(t/100))
R = R0 * [ 1 + AT + B(T^2)+C(T-100)(T^3)]

When calculating from resistance to temperature two methods are used. When R>R0 (i/e temperature above 0C) there is a direct solution. When R<R0 the temperature is estimated using Newton's method. The estimated temperature is used to calculate the resistance using the above equations and the estimate is repeated until the error in resistance is less than 0.39uOhms (1uK).

T = (-A + sqrt( A^2 - 4*B*(1-(R/R0)) ) / (2*B)

### ITS-90 PRT

While the ITS-90 is very specific on some points, it says little about how to actually get temperature measurements from PRT resistance. First let me describe the case of converting temperature to resistance. First, you must convert from temperature to resistance ratio (denoted Wr) using the ITS-90 reference function. Next, based on the subrange, calibration coefficients, and Wr you calculate the deviation function. The output is the expected deviation (in resistance ratio) between the calibrated PRT and the reference function. Now add the two together to get the W for this calibrated sensor. Finally, multiplying by the resistance at the triple point of water gives you the resistance at the input temperature.

Now, finding temperature from resistance is a bit harder. The ITS-90 defines an inverse of the reference function. Unfortunately, this equation is only accurate to within 0.13mk. Add to that the trouble of inverting all of the deviation functions and it is easier (and 130 times as accurate) to use Newton's Method.