Standard Operating Procedure 

North Carolina Standards Laboratory 

SOP 25 

Calibration of Liquid-in-Glass and Digital 

Thermometers 

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 The accuracy of a temperature probe is determined by comparing the test 

results for the unknown to those of a traceable laboratory standard when both 

are immersed in a comparison bath. Any probe having calibration points within 

a -30 °C to 660 °C temperature range may be calibrated using this procedure. 

The term “probe” refers to either a resistance thermistor, Platinum Resistance 

Thermometer (PRT), Resistance Temperature Detectors (RTD) thermometer, 

thermocouple probe, or a Liquid-in-Glass (LIG) thermometer. 

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. 

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. 

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 

(%) 

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 

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2 

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. 

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 a comparison bath or ice point and reading of the 

standard, check standard, and test thermometer(s). 

This method is applicable to all liquid-in-glass and digital thermometers 

provided that the uncertainty requirements can be met. 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 metrologist checks the condition of the submitted probe(s). All 

thermometers must have a serial number etched/engraved on it. The North 

Carolina Metrology Lab will not calibrate thermometers without serial numbers. 

Probes with defects such as excessive wear, etc. will not be calibrated. The 

metrologist may attempt to fix problems, and if successful, will proceed to 

calibrate the probe. Specific guidance on the subject of repairing defective 

liquid-in-glass thermometers can be found in NIST Special Publication 1088, 

Maintenance, Validation, and Recalibration of Liquid-in-Glass Thermometers. 

Digital thermometers or systems are not adjustable using this procedure. 

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

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

test probes’ readings are compared to the standard’s reading to determine the 

test probes’ corrections. The check standard verifies the precision and accuracy 

of the calibration. If the check standard detects an out-of-control situation, the 

metrologist attempts to discover the source, corrects it if possible, and repeats 

the calibrations 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 

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traceable to the SI and having an expanded uncertainty less than 1/10 

of the unknown's smallest division and appropriate for the test 

thermometer’s temperature range. If more than one pair of standard / 

check standard meet these criteria, select the most durable and least 

expensive standard. Appropriate standards typically include a platinum 

resistance thermometer or the dry well, all depending upon the range 

and required accuracy. 

2.3.2 A comparison bath, or ice point bath, with a standard deviation no 

greater than 1/10 of the test thermometer’s smallest division. 

2.3.3 A viewing device such as a CCTV monitor and camera with a zoom lens. 

NOTE: These are comparison devices. Calibration is not required. Any 

systematic bias will be canceled. 

2.3.4 Sufficient clamping fixtures to hold the thermometers; 

2.3.5 Dry ice for repairing separated columns or gas bubbles in the bulb; 

2.3.6 Suitable magnifying device for examining liquid-in-glass thermometers; 

2.3.7 Calibrated environmental equipment to 

relative humidity laboratory conditions; 

monitor temperature and 

2.3.8 Stopwatch or other timing device to observe the time of each 

measurement (calibration not required; this is used to ensure sufficient 

elapsed time for stabilization between readings). 

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2.4 Procedure 

2.4.1 Determine the points to be calibrated as specified by the customer. If it 

is an ASTM thermometer, the specifications, test methods, calibration 

points, stem temperatures and any special procedure are listed in ASTM 

Specifications E-1 and E-77. The order of obtaining data related to the 

calibration points, check standard readings, and stem correction is not 

critical; but in all data gathering efforts the lowest temperature reading 

on the thermometer should take place first with subsequent readings in 

order according to the ascending values. If the unknown standard is 

digital the stem correction data will not apply. 

2.4.2 If the thermometer is a liquid-in-glass thermometer, use a magnifying 

device and check for foreign material in the capillary (i.e. glass chip, 

oxides of mercury, or dirt), chipped or cracked capillary, a separated 

column, gas in the bulb, a distorted capillary, divisions numbered 

incorrectly, irregular division spacing or marks, or division wear. 

2.4.2.1 If the test thermometer’s divisions are worn off but the 

etching is still present, trace the etching with a black 

permanent marker to restore appearance. 

2.4.2.2 Refer to NIST Special Publication 1088, Maintenance, 

Validation, and Recalibration of Liquid-in-Glass 

Thermometers for specific steps and guidance on repairing a 

separated column or removing bubbles in the bulb. Reject 

the thermometer for any reason listed in section 2.4.2 if 

repairs attempts are unsuccessful or not performed. 

2.4.3 Determine the scale range and division size for thermometers. 

2.4.3.1 Read liquid-in-glass thermometers to 1/10th of the smallest 

division. Use a CCTV monitor and camera with a zoom lens to 

read liquid-in-glass thermometers. Read the standard to one 

place beyond the item under test. 

2.4.3.2 If the thermometer under test is digital, read the standards 

to one digit beyond the readability of the test thermometer, 

if possible. 

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2.4.4 Take an initial data reading for either stem correction, check standard 

readings, or calibration data. Using clamps or the well cover holding 

device, insert the working standard and check standard PRT into the 

applicable temperature bath. Place these standards as close as possible 

to each other and at the same depth, at least six inches, to minimize the 

effect of temperature gradients. Immerse liquid-in-glass thermometers 

as follows: 

2.4.4.1 Total immersion -- immerse all but 6 - 12 mm of the filled 

column; The meniscus should never be immersed in the bath 

fluid, since distillation of the mercury and other liquids can 

occur at high temperatures and cause droplets to condense 

at the top of the thermometer. After remaining at room 

temperature (20 °C) for 1 hour, these thermometers are 

calibrated starting at the lowest temperature requested and 

proceeding in sequence to the highest point. At each 

calibration point the thermometer must be pushed deeper 

into the calibration bath, along with the comparison 

standard, to maintain the proper immersion. If the 

thermometer has a contraction chamber, it must be 

immersed well below the surface of the bath medium. The 

contraction chamber contains a great deal of liquid and this 

liquid must be at the same temperature as the liquid in the 

bulb for the thermometer to give a correct reading. If there 

is a temperature gradient at the surface of the bath, as may 

be the case in some high temperature calibration baths, the 

contraction chamber must be placed below this gradient, 

even if this means changing the calibration point. If the 

thermometer being calibrated is too long and cannot be 

immersed to the proper depth, a stem temperature 

correction will have to be made as described in section 3.3. 

2.4.4.2 Partial immersion -- immerse to immersion line or the proper 

depth of immersion engraved or printed on the back (most 

thermometers have both). Like total immersion 

thermometers, calibration points are taken in the same 

sequence; the thermometer must remain at room 

temperature (20 °C) for 1 hour before calibrating; and a 

contraction chamber must be immersed properly. 

2.4.4.3 If no immersion type is listed, assume the thermometer is a 

total immersion type. 

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2.4.5 Allow approximately 15 to 20 minutes for thermal equilibrium after the 

point of noted stabilization. Cyclical patterns of heating and cooling 

should be noted on the display graph of the Superthermometer and 

should not display periods of increasing variance. In some cases, 30 

minutes of stabilization is required. If obtaining data related to the 

check standard, record the value in the appropriate control chart. If the 

value is outside of the control limits, the system is out of control. The 

source of this situation must be investigated, corrected and returned to 

in control status as indicated by the control limits. Measurement 

Assurance is discussed in further detail in section 4. 

2.4.6 If it is desired to document the behavior of a thermometer, the 

temperature of the lowest data point should be measured before 

testing and again within one hour after the measurement of the highest 

temperature point (when the temperature of the thermometer has 

come to room temperature), whenever possible. The second point 

should agree with the initial data point within the expected accuracy of 

the thermometer. This is an optional step and would likely only be used 

when a thermometer’s behavior during calibration is erratic. 

2.4.7 Assure that liquid in glass thermometers are plumb and such that the 

divisions and liquid column may be viewed through the camera lens. 

Also, assure that the camera is level and the lens is at the same height 

as the top of the liquid in the thermometer capillary. Adjust the zoom 

lens until the top of the liquid in the capillary is displayed on the 

monitor along with the last division mark completely covered by the 

liquid and the next division mark directly above the column. If the top 

of the liquid column is even with a division mark, read the temperature 

at that mark. Otherwise, adjust the zoom lens magnification and focus 

until the distance between the two divisions is as great as possible. 

Measure the distance (d1) between the two division marks surrounding 

the top of the liquid column and the distance (d2) from the top of the 

liquid column to the nearest division mark below it using gridlines (mm) 

superimposed on the monitor screen. Divide distance (d2) by distance 

(d1) to obtain the proportional decimal equivalent of the fractional part 

of a degree covered by the liquid. Add this number to the temperature 

of the last division completely covered by liquid. For all other 

temperature probes with digital indication, read the indication after the 

unit under test has stabilized at each calibration point. 

2.4.8 Dial indication thermometers are not common, but when presented for 

calibration, the vertical design will likely prohibit the use of the camera. 

In such cases alternative magnification may be performed though the 

use of a magnifying glass. 

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3 

2.4.9 Read and record the temperature on the standard followed by the 

check standard and the first test thermometer (Because the metrology 

lab’s standard and check standard are digital and can be read nearly 

simultaneously with the test thermometer, there is no need to take a 

second reading of the standard). Repeat this procedure for each of the 

thermometers being calibrated at that temperature, then adjust and 

stabilize the bath at the next calibration point. Follow the preceding 

sequence for each calibration point. 

Calculations 

3.1 Symbols 

Table 2. Symbols used in this procedure. 

Symbol Description 

Ks 

Test thermometer’s stem correction, X. 

Note: If a test thermometer reads a low 

temperature, the correction is positive. If a 

test thermometer reads a high 

temperature, the correction is negative. 

k Differential expansion coefficient of liquid 

of unknown, X 

n 

Number of thermometer scale degrees 

adjacent to the auxiliary thermometer bulb, 

i.e., the number of degrees from the degree 

mark at the surface of the bath medium to 

the meniscus (for total-immersion), or from 

the immersion line to the meniscus (for 

partial-immersion) of the unknown, X 

tobs 

Observed mean temperature of the 

emergent stem (auxiliary thermometer 

reading) of the unknown, X 

tsp 

Temperature indication of the standard 

thermometer, S 

Ct Correction of the test thermometer, X 

Tstd 

Temperature indication of the standard 

thermometer, S 

Tt 

Temperature indication of the test 

thermometer, X 

3.2 To calculate a test thermometer’s correction, use the equation: 

Ct = Tstd - Tt Eqn. (1) 

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3.3 For total-immersion thermometers, a length of the liquid column often must be 

left emergent from the bath to view its meniscus. Therefore, an appreciable 

temperature gradient may exist around the thermometer stem near the surface 

of the bath. 

To calculate a total-immersion test thermometer’s stem correction, Ks, use the 

equation: 

Ks = kn (tsp -tobs) Eqn. (2) 

3.4 Partial-immersion thermometers must be calibrated and used at the same 

immersion depth; otherwise, a stem-temperature correction must be applied to 

the reading. 

To calculate a partial-immersion test thermometer’s stem correction, KS, use the 

equation: 

Ks = kn (tobs -tsp) Eqn. (3) 

Example: 

In figure A, the length of the emergent mercury column of the test 

thermometer is 120 mm. The center of the bulb of an auxiliary 

thermometer is placed adjacent to the test thermometer, 60 mm from 

the immersion line. In this example, the average observed stem 

temperature (tobs) is 33 °C, the specified mean temperature (tsp) is 45 °C, 

the coefficient of expansion of mercury in glass is 0.00016 (when 

graduations are in °C), and the difference from the immersion line to the 

mercury meniscus (n) is 35 degrees. 

Stem-temperature correction = 0.00016 n (tsp - tobs) 

= 0.00016 (35) (–45-33) 

= 0.07 °C 

Specific details on stem corrections and values for the differential expansion 

coefficient of the liquid can be found in ASTM E77, Inspection and Verification of 

Thermometers. 

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120 mm 

60 mm 

20° 

45°> 

25°> 

33°> 

15° 

Figure A. 

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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 

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. 

(Sc − S

t = c )

s p Eqn. (4) 

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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, 

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: 

d

s = ≈ 0.6d Eqn. (5) p

3 

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5.3 Uncertainty associated with propagation of Tripe 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 measuring grid (this applies to liquid-in-glass 

thermometers only). 

5.7 Uncertainty associated with readability of liquid-in-glass or digital thermometer. 

For liquid-in-glass thermometers, 1/10 of a division is used for the readability of 

the meniscus. For digital thermometry, one division of the digital display is 

considered the set value for this component. 

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

obtained from the manufacturer. 

5.9 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. 

5.10 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. 

5.11 Example components to be considered for an uncertainty budget table are 

shown in the following table. 

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Table 3. 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 measuring 

grid (5.6) uo From experimental data Normal divided by coverage factor 

Uncertainty associated with readability of 

liquid-in-glass or digital thermometer (5.7) uo Manufacturer Normal divided by coverage factor 

Uncertainty associated with bath stability 

(5.8) uo Manufacturer Rectangular 

Uncertainty associated with nonuniformity temperature gradients (5.9) uo Manufacturer or from 

experimental data Rectangular 

Uncertainty associated with bias (5.10) ud 

Control chart, proficiency 

tests 

See SOP 29 

5.12 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 nominal correction, 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. 

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. 

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