Standard Operating Procedure

North Carolina Standards Laboratory

SOP 70

Calibration of PRTs and Thermistors

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Document ID 30898 Revision 2 Approved by Effective Date 29 Jul 2013

Page 1 of 21 Issued By NCDA&CS Qualtrax Published Date

Provided as a resource for laboratories performing thermometry calibrations on 23 July 2021 by 

the North Carolina Metrology Laboratory. Changes made to this document after this date were 

not authorized nor approved by North Carolina metrology staff.

1 Introduction

1.1 Previous versions of this procedure were known as SOP 25a, Calibration of 

Platinum Resistance Thermometers (PRTs) and Thermistors.

This procedure details the method to test and calculate coefficients for PRTs 

and thermistors using Fluke 9938 “MET/TEMP II” software. Test results for the 

unknown are compared to those of a traceable laboratory standard when both 

are immersed in a comparison bath at temperatures ranging from -30 o

C to 230 o

C (Mercury Triple Point to Tin Freezing Point).

1.2 Prerequisites

1.2.1 Valid calibration certificates with appropriate values and uncertainties 

must be available for all the standards used in the calibration. All 

standards must have demonstrated metrological traceability to the 

international system of units (SI), which may be to the SI, through a 

National Metrology Institute such as NIST. 

1.2.2 Standards must be evaluated to ensure that standard uncertainties for 

the intended level of calibration are sufficiently small. Reference 

standards should not be used to routinely calibrate customer standards 

using this procedure and should be reserved for the use of calibrating 

working standards only. 

1.2.3 Verify that all equipment that is used is in good operating condition with 

sufficiently small process standard deviation as verified by a valid 

control chart.

1.2.4 Verify that the operator is experienced in temperature measurement 

techniques, with a special emphasis on using the Met/Temp II software 

and developing ITS-90 compliant calibration data.

1.2.5 Laboratory facilities must comply with the following minimum 

conditions to meet the expected uncertainty possible with this 

procedure and to comply with the manufacturer’s operating conditions.

Table 1. Environmental conditions.

Temperature Requirements During a Calibration Relative Humidity

(%)
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Temperature Requirements During a Calibration Relative Humidity

(%)

Lower and upper limits: 18 °C to 23 °C

Maximum changes: ± 5 °C / 12 h and ± 3 °C / h 40 to 60 ± 10 / 4 h

1.3 Safety

Review all applicable JSAs prior to performing this procedure. The danger of 

severe burns and freezing should be minimalized to the fullest extent possible.

2 Methodology

2.1 Scope, Precision, Accuracy

This procedure is based upon the procedures demonstrated and described in the 

"Precision Thermometry Workshop" conducted by the NIST Temperature Group 

(March 2001). Multiple thermometers may be calibrated at the same time using 

this procedure. The procedure consists of an examination of the test probe(s), 

preparation of comparison baths, configuration of both hardware and software, 

calculation of coefficients, and measurement assurance.

This method is applicable to all resistance-based thermometry devices. The 

achievable precision using this procedure is appropriate. The accuracy 

achievable with this procedure depends on the accuracy of the calibration of the 

working standards and the precision of the intercomparison.

2.2 Summary

The test probe(s), a standard, and a check standard are immersed in a 

temperature comparison bath and allowed to come to thermal equilibrium. A 

Fluke Superthermometer is used to read input of all probes. Fluke “MET/TEMP 

II” software is used to gather the test probes’ resistances at various 

temperatures controlled by a working standard Platinum Resistance 

Thermometer (PRT). The “MET/TEMP II” software also calculates coefficients 

for the probes. Coefficients for the unknown standard derived from the results 

of the procedure are entered into the test device display and the indication is 

compared to that of the standard in the temperature bath for verification 

purposes.

The check standard monitors the precision and accuracy of the process. If the 

check standard detects an out of control situation, the metrologist attempts to 
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discover the source, corrects it if possible, and repeats the calibration if 

necessary. 

2.3 Apparatus/Equipment

2.3.1 Two standard temperature indicating devices, one used as the standard, 

the other used as the check standard, both with calibration certificates 

traceable to the SI and having an expanded uncertainty appropriate for 

the test thermometer’s temperature range. Appropriate standards

typically include a platinum resistance thermometer. 

2.3.2 A comparison bath(s) with a standard deviation suitable to perform this 

procedure.

2.3.3 Sufficient clamping fixtures to hold the thermometers;

2.3.4 Calibrated environmental equipment to monitor temperature and 

relative humidity laboratory conditions;

2.3.5 A Superthermometer, Multiplexer, Met/Temp II software and laptop, 

and a Smart Switch for RS-232 communications during the calibration 

process. 

2.4 Procedure – Configuration Steps

2.4.1 Check the probe carefully for foreign material and wear, i.e., nicks, dirt, 

frayed wires prior to beginning the Procedure process.

2.4.2 To prepare a test, configure the communications port, reference probe 

and module, scanner, heat sources and equipment as described in the 

configuration menu section of the Fluke 9938 “MET/TEMP II” User’s 

Guide. Step-by-step instructions follow below.

Fig. 1

Open a new test by clicking on the icon shown in Figure 1. 

2.4.3 The dropdown menu will appear at the top of the screen as shown in 

Figure 2 and will provide the following menu options.
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Fig. 2

2.4.4 Select the File dropdown menu and click on the Open option. The 

Configuration screen will be similar to the one shown in Figure 3, but 

since new configurations are always able to be added or removed, these 

exact configurations may not be present.

Fig. 3

 

2.4.5 Once a configuration is selected, a screen titled Equipment Info will 

automatically open. A total of six fields (Steps) are required to be filled 

in with appropriate information for a calibration configuration to be 

valid. Any steps that are in blue indicate that the step is fulfilled and 

does not require any further data input; likewise, any step that is red

indicates an absence of required information for the calibration. Steps 

five and six will always appear red since the software intentionally 

blocks the carrying over of data in these steps when a configuration is 

saved. See the Equipment Info screen as shown in Figure 4.
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Fig. 4

2.4.6 Click on Step 5, Set-points. A Set-point Configuration will appear as 

shown in Figure 5. In order to meet ITS-90 calculation requirements, the 

following parameters must be followed:

1) A minimum of five set points is required for calculations

2) One of the set points must be 0 °C 

3) Two to ten points must be selected between the Mercury Triple 

Point (-38.8344 °C) and the Gallium Melting Point (29.7646 °C)

4) Two to ten points must be selected between the Water Triple 

Point (0 °C) and the Tin Freezing Melting Point (231.928 °C)

For a reference that describes the parameters above, see the Fixed 

Points and Ranges of the ITS-90 graph. 
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Fig. 5

2.4.7 Automatic generation of set-points is the simplest means to complete 

this portion of the configuration. If automatic generation is not used, 

then the “Insert Set-point” radio button can be selected to manually 

enter each set-point. In the example shown in Figure 6, six set-points 

have been selected with a range of 20 °C between each set-point and 

with a starting set-point of 0 °C. This example would be a typical setup 

for any thermistor. The “Prompt for heat source conflicts” option is 

useful but not required, as heat source “bath” selection can occur at 

later steps.
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Fig. 6

2.4.8 After the previous step is complete and “OK” is selected, a new window 

will appear as shown in Figure 7. This window is similar to the one 

shown in section 2.4.6 except the fields are mostly complete. The 

Window, Tolerance, Duration, and Uncertainty should populate 

automatically based upon default settings. The Uncertainty value should

be verified to be accurate based upon the latest published laboratory 

scope. The software has a lower limit of 10 mK for the uncertainty, so 

reporting anything lower than this is not possible. The “Heat Source to 

use” option will always default to the first available bath. This setting 

can be verified as correct or needing to be changed by clicking on “OK” 

and going back to the screen shown in step 2.4.5. Step 4, Heat Sources, 

will reveal the order of the baths established by the default settings.

Each set-point must be individually clicked on to verify that the settings 

are correct.
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Fig. 7

2.4.9 As shown in section 2.4.8, selecting the 40.00 °C set-point will allow the 

insertion of the 25.00 °C set-point as required for a typical thermistor 

calibration. This is done by clicking on the “Insert Set-point” radio 

button and manually filling in the required information. In addition, the 

“Enable proportional band” should be enabled and the values entered 

according to the recommendations published in the bath user’s manual. 

This completed step is shown in Figure 8.
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Fig. 8

2.4.10 Once the previous step is complete and “OK” has been selected, the 

final step of the configuration process is to complete step 6, Test 

Probes. As shown in Figure 9, select the appropriate channel based 

upon the desired channel placement of the unknown standard. Note 

that this selection must be on the Multiplexer (channels five through 

fourteen), as the first four channels are reserved for the standard, check 

standard, and connection from the Superthermometer to the 

Multiplexer. If the unknown standard has been previously calibrated, all 

of the remaining information fields will populate automatically. If the 

unknown standard is new, then all of the fields must be completed.
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Fig. 9 

2.4.11 Select the Customer radio button and a screen as shown in Figure 10

will appear. In most cases the dropdown option Recalibration will apply, 

unless this is a new unknown standard with no previous history 

available. The Customer order ID should represent the customer 

Purchase Order. The Customer name can be selected from the 

dropdown menu if they are a returning customer.

Fig. 10
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2.4.12 Select “OK” and then “OK” again on the screen as shown in Figure 9. 

This should take you to the screen as shown in Figure 4. Select the 

“Start Test” radio button to begin the test sequence.

2.5 Procedure – Calibration Sequence 

2.5.1 The first confirmation screen will look like the example in Figure 11. The 

number of readings can be modified, if desired, in the programming 

configuration menu.

Fig. 11 

2.5.2 The next confirmation screen is a verification of the data to be 

presented on the ITS-90 Report of Calibration. The name of the 

Metrologist, designation of a Full range or Partial range calibration, Test 

number, and ambient (environmental) conditions can be entered here.
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Fig. 12 

2.5.3 Once “OK” has been selected on the previous screen, the calibration will 

begin. The first question in this sequence involves the unit readout of 

the standard and the unknown standard. The standard must be set to °C 

and the unknown standard must be set to ohms. Modify the unit 

readout if needed.

Fig. 13 

2.5.4 Once “OK” has been selected on the previous screen, the second

question in this sequence involves the confirmation that the probes are 

placed in the correct bath and ready to begin the calibration process. 
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Fig. 14 

2.5.5 Once the calibration begins, the process is automatic. When the 

program has determined stabilization has occurred (as defined in 

section 2.4.8) a prompt as shown in Figure 15 will appear. Data entries 

are permanent once the “OK” radio button is pressed. 

Fig. 15 

2.5.6 Continue the calibration process and follow the prompts during the 

process. Once all of the data has been collected, a notification will 

appear stating “The test has been completed. Select Close Test from the 

File menu”.

2.6 Procedure – Calculating the Coefficients 

2.6.1 Select the Utilities dropdown menu and scroll down to the Coefficients 

and Tables selection. Once this is clicked a new configuration screen will 

appear with new dropdown menu options.

2.6.2 Either select Coefficients from the dropdown menu or select the icon 

shortcuts. Follow these guidelines for determining coefficient 

calculation.
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1) Platinum Probe uses ITS-90 calculations and Subranges 5 and 9

2) Thermistors use Polynomial 3rd Order

3) The laboratory does not currently have the capabilities to 

produce coefficients for thermocouples 

2.6.3 After clicking “OK” the next screen will direct the user to select a test 

number for calculation of coefficients as shown in Figure 16. 

Fig. 16 

2.6.4 Click continue. The next screen will appear as the one shown in Figure 

17. Press the “Select All” radio button and then press the “Calculate”

radio button. After reviewing the data, experienced users may elect to 

deselect one reading for the calibration curve to fit the model. This 

should only be done if one reading is out of line with the other readings 

and all of the other points fit the curve. Recalibration is a preferred 

option rather than this method in order to substantiate accurate

readings.
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 Fig. 17 

2.6.5 The next screen will appear as the one shown in Figure 18. Click the 

“Save” radio button. 

Fig. 18 

2.6.6 The software will direct back to the main screen. From the File 

dropdown menu, select Export Coefficients. Select the correct test 

number, select the “Export” radio button, and then a new Save As 

screen will appear. Save the text file (EXPORT.TXT). Close this step by 

clicking on the “OK” radio button.

2.6.7 The software will then redirect back to the main screen. Follow a similar 

sequence as in section 2.6.6, except select Export Data. Highlight the 

test number and select the “Export” radio button. Save the file as in 

step 2.6.6. Note that even though the text files are named the same, the
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data within these files is processed separately, and both text files are 

required for proper printing of the ITS-90 report.

2.6.8 The software will then redirect back to the main screen. Under the File 

dropdown menu, select Print Reports and Tables. Select the proper test 

number and then click on the “Print” radio button. 

2.6.9 The first page of the Report of Calibration will display. Clicking on the 

printer icon at the top of the screen will print the first page. To print the 

subsequent pages, click on the Close icon at the top of the screen. 

2.6.10 When all pages of the report have printed, click on the Close icon again 

and the program will return to the previous Print Reports and Tables 

screen. Select the “Cancel” radio button and then the Close option 

under the File dropdown menu. The Met/Temp II program can be closed 

by selecting the red X in the upper right corner. 

2.6.11 In order to determine if the calibration was successful and accurate

coefficients have been produced, all of the resistance values should be 

entered and plotted on that standard unknown’s history graph. Plotted 

points and uncertainties should overlap with previous values. If a 

particular data point does not overlap and it is outside the range of 

normal use of the customer, then the calibration can stand as is if it is 

limited to one such data point scenario. For more than one point as this, 

the unknown standard should be recalibrated. 

2.6.12 If consecutive calibrations of the unknown standard reveal a shift in the 

data point values and these two calibrations agree with uncertainty 

overlap, then the new data point values will be considered the new 

resistance and T(R) values. If more than two calibrations are required to 

meet the history stability of the standard unknown, then the customer 

should consider replacing the artifact as long term stability is 

questionable. 

2.7 Satisfaction Evaluation

An evaluation may be performed using the following definition: ITS-90 defines an 

instrument as satisfactory if it means the criteria that W(302.914 K) ≥ 1.11807 or 

W(234.3156 K) ≤ 0.844235. The value of W is calculated from the ITS-90 portion of 

the calibration certificate.
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3 Calculations

3.1 Since the Met/Temp II software is used for this procedure, no specific 

calculations or use of equations are performed outside the program, with the 

sole exception being the evaluation used for defining satisfactory instruments.

Evaluation using this equation after the calibration is not a requirement but can

be a useful tool. 

3.2 W can be calculated using the following equation:

W = (((Ωfpc1 – Ωfpc2) * fixed point cell value from nominal) + Ωfpc2) / RTPW

resistance 

 Eqn. (1)

Where, Ωfpc1 = higher value of resistance at the fixed point cell

 Ωfpc2 = lower value of resistance at the fixed point cell

 Ωfpcnom = resistance value of fixed point cell 

RTPW = resistance value at the Triple Point of Water provided in 

ITS-90 section of calibration certificate

Example: W(302.914 K) = (((28.366277 Ω– 28.356253 Ω) * 0.7640 °C) + 

28.356253 Ω)/ 25.366428 Ω 

4 Measurement Assurance 

4.1 Duplicate the process with suitable check standards for each nominal that is 

within the range of stem correction or unknown standard data gathering. See 

NISTIR 6969 SOP 9, Control Charts for Calibration of Mass Standards for general 

guidance on control charts; while these specifically reference mass control 

charts, many of the evaluations apply to the thermometry measurement 

assurance program.

4.2 Evaluate the value against the expected limits and plot the check standard value 

on the control chart to monitor changes over time. 

All values must be entered in the control chart, even if failing this statistic, unless 

a mistake (e.g., typographical error) is identified and corrected, to ensure the 

variability obtained for the process is not unduly reduced over time. The observed 

value of the check standard is compared to the accepted mean value of the check 

standard and divided by the standard deviation for the check standard 

observations over time. 

A t-test may be incorporated to check the observed value of the check standard 

against the accepted value using the following equation and a 95 % confidence 
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level. The t-statistic is calculated for stability analysis. This equation monitors

stability over time but should not be used to assess for bias. A calculated t-value 

less than two is within the warning limits of the process. A calculated t-value 

between two and three represents a value between the warning limits and 

control/action limits. A calculated t-value exceeding three represents a value 

outside of the control/action limits and suitable action must be taken. Calculated 

values of the t-statistic may also be monitored over time to determine the 

presence of drift.

( ) p

cc

s

SS

t − =

Eqn. (2)

4.3 Check standard measurement results obtained over time are used to calculate 

the standard deviation of the measurement process, sp.

4.4 The mean value of the check standard over time is also compared to an 

appropriate reference value of the check standard with respect to their 

applicable expanded uncertainties to evaluate bias and drift over time. 

Excessive drift or bias must be investigated and followed with suitable 

corrective action. See SOP 9, Section 3.5.3 and Section 8.16 for assessment 

methodology.

4.5 If check standards were already checked on a given day and found to be in 

control, additional evaluations may be conducted, but are not required.

5 Assignment of Uncertainty 

The limits of expanded uncertainty, U, include estimates of the standard uncertainty of 

the thermometry standards used, us, estimates of the standard deviation of the 

measurement process, sp, and estimates of the effect of other components associated 

with this procedure, uo. These estimates should be combined using the root-sumsquared method (RSS), and the expanded uncertainty, U, reported with a coverage 

factor of two (k = 2), to give an approximate 95 % level of confidence. See SOP 29 for the 

complete standard operating procedure for calculating the uncertainty. 

5.1 The expanded uncertainty for the standard, U, is obtained from the calibration 

certificate. The combined standard uncertainty, uc, is used and not the 

expanded uncertainty, U, therefore the reported uncertainty for the standard 

will usually be divided by the coverage factor k. Where the coverage factor or 

confidence interval is not given, the laboratory should either contact the 

calibration provider to obtain the correct divisor or use a value of k = 2, 
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assuming that the expanded uncertainty was reported with an approximate 95 

% confidence interval (95.45 %).

5.2 Standard deviation of the measurement process from control chart 

performance (See SOP No. 9.) The value for sp is obtained from the control 

chart data for check standards using direct comparison measurements. If the 

standard deviation of the measurement process from the control chart is less 

than the resolution of the Superthermometer (less than 0.00001 °C), the 

laboratory may round up to the value of the Superthermometer division or use 

the larger of the standard deviation of the process or the following estimate for 

repeatability is used to represent the standard deviation of the process:

0.6

3 p

d s d = ≈ Eqn. (3)

5.3 Uncertainty associated with propagation of Triple Point of Water (TPW) cell. 

This is a fixed value that is established during the manufacturing and calibration 

of the cell.

5.4 Uncertainty associated with stability of the 1595A reference resistor

(Superthermometer) based upon bath being used at the time of calibration of 

unknown standards. This is a fixed value provided by the manufacturer.

5.5 Uncertainty associated with the bias of the measurement process from the TPW 

cell. This uncertainty component is a comparison of the thermometry standard 

against an intrinsic standard.

5.6 Uncertainty associated with bath stability. This component is a fixed value 

obtained from the manufacturer.

5.7 Uncertainty associated with non-uniformity temperature gradients. This 

component is either the value obtained from the manufacturer or the 

laboratory observed value derived from internal studies, whichever is higher. 

Actual laboratory data may reveal a degraded stability less than claimed by the 

manufacturer, depending on bath. 

5.8 Uncertainty associated with bias that is observed in the check standards as 

determined through analysis of the control charts. When bias is observed in the 

control charts, it must be assessed according to the equations provided in SOP 

29 and may be incorporated as an uncorrected systematic error using the 

equations in SOP 29.
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5.9 Example components to be considered for an uncertainty budget table are 

shown in the following table.

Table 2. Example uncertainty budget table.

Uncertainty Component Description Symbol Source Typical Distribution

Uncertainty of the standards (5.1) us Calibration certificate 

Normal divided by 

coverage factor

Accepted standard deviation of the 

process (5.2) sp

Control chart, standard 

deviation chart

Normal or 

estimated 

rectangular if actual 

sp is less than 

Superthermometer 

display resolution

Uncertainty of the propagation of the 

TPW Cell (5.3) uo

Calibration values from 

ITS-90 report

Normal divided by 

coverage factor

Uncertainty of the stability of the 1595A 

reference resistor (Superthermometer)

(5.4)

uo

Manufacturer supplied 

value in manual Rectangular

Uncertainty associated with bias of the 

measurement process from the TPW cell

(5.5)

uo Control chart Rectangular (also 

see SOP 29)

Uncertainty associated with bath stability

(5.6) uo Manufacturer Rectangular

Uncertainty associated with nonuniformity temperature gradients (5.7) uoManufacturer or from 

experimental data Rectangular

Uncertainty associated with bias (5.8) ud

Control chart, proficiency 

tests

See SOP 29

5.10 Draft a suitable uncertainty statement for the certificate. For example: 

The uncertainty reported is the root sum square of the standard uncertainty of 

the standard, the standard deviation of the process, and the uncertainty 

associated with other components corrections, multiplied by a coverage factor 

of 2 (k = 2) for an approximate 95 percent confidence interval. 
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NOTE: Where inadequate degrees of freedom are available, k, is determined using 

the appropriate degrees of freedom and the 95.45 % column in the table from 

Appendix A of NISTIR 6969, SOP 29. 

6 Certificate

6.1 Report results as described in SOP No. 1, Preparation of Calibration Certificates. 

Report the T(R) coefficient values, environmental conditions during the 

calibrations, and calculated expanded uncertainties with coverage factor(s). 

6.2 Conformity assessment.

Compliance to applicable tolerances is not considered in this type of 

thermometry calibration as the measurements are not performed to a 

tolerance. Acceptability for use is defined in section 3.2.

6.3 In cases where a system is presented for calibration, a statement must be 

included on the certificate noting if the calibration was performed on the 

individual components of the system or if the system was calibrated as one 

whole entity. 

6.4 A completed calibration packet includes the calibration certificate, the ITS-90 

Report, history graphs of the points of calibration, and an uncertainty budget.