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SOP 49

Standard Operating Procedure 

for

Calibration of Environmental Monitoring Standards by Direct Comparison

1 Introduction

Purpose 

The purpose of this procedure is to use calibrated environmental 

sensors/instruments as short-term transfer standards immediately after its 

calibration to perform downstream calibration of internal laboratory 

environmental sensors/instruments for calibration, verification that 

measurement results continue to be stable, or for validation of extending 

calibration intervals. The procedure may be suitable for sensors/instruments 

that are used for laboratory monitoring where a larger uncertainty may be 

acceptable and possibly for other calibration uses provided the application and 

required uncertainties are evaluated and found to be acceptable.

Range and Scope

Detailed measurement ranges, standards, equipment, and uncertainties for this 

SOP are generally compiled in a separate document in the laboratory (e.g., 

traceability hierarchy, uncertainty tables). Uncertainties of this process must be 

assessed (Section 5.5) to determine if they are sufficiently small for the 

standards to be used in downstream calibrations or if uncertainties are only 

suitable for laboratory monitoring applications. 

Limitations 

The temperature range is limited from 15 °C to 25 °C if based on typical 

laboratory conditions; the range in air may be from 5 °C to 95 °C if a wider 

range of calibrated standards and whether an oven, temperature bath, or ability 

to vary conditions are available/possible. Barometers are compared under 

various laboratory ambient pressures. Relative humidity is compared over 

during several days with various ambient laboratory humidity conditions unless 

a humidity chamber is available or the laboratory can vary conditions. 

If multiple points are obtained during varying conditions observed in the 

comparisons, such as through use of a temperature bath/oven or use of relative 

humidity salt solutions, only the range of measurements between multiple 

calibration points may be considered suitable for calibration applications, 

provided the uncertainty is sufficiently small. If the prior calibration(s) of the 

instrument being calibrated demonstrated a best fit linear response where all 

offsets from nominal were within the stated uncertainty, a one-point calibration 

may be used. When a one-point calibration is used, such as at standard 
 

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environmental conditions only, the instrument should only be used for 

environmental monitoring and should also be verified again at one-fourth of the 

intended calibration interval to ensure ongoing accuracy and stability under 

laboratory environmental conditions.

Prerequisites

Staff must have suitable training and have demonstrated proficiency in 

comparison calibration measurements, e.g., those used in temperature, 

mass, volume, and dimensional parameters. 

Valid calibration certificates that are less than 30 days old, with 

appropriate values and uncertainties, must be available for all the 

standards used in this 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.

Exception: where the calibration of the standards is not less than 30 days 

old, enough laboratory data must be available to demonstrate historical 

stability of the instrument to the limits needed for this calibration. 

Standards must be evaluated to ensure that standard uncertainties for the 

intended level of calibration are sufficiently small. The uncertainties 

resulting from this procedure may be suitable for monitoring laboratory 

conditions but not suitable for use in calibration processes unless the 

uncertainties of the standard calibration and the resolution of the 

standard are sufficiently small (i.e., the uncertainty of the instruments 

used as a standard must have better resolution than the instruments being 

calibrated if they are to be used as downstream measurements for 

calibrations). 

Maintain environmental conditions within the limits noted in Table 1. 

These limits are not critical for this calibration; the limits are 

recommended based on good laboratory environmental control 

practices. 

Table 1. Suggested Environmental limits for calibrations.

Temperature

Range

Temperature 

Stability Relative Humidity Relative Humidity Stability

18 °C to 23 °C ± 1 °C 40 % to 60 % ± 2 %

2 Methodology

Summary

Laboratory environmental sensors/instruments are used as transfer standards to 

calibrate internal environmental sensors/instruments owned by the laboratory 
 

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using direct comparison procedures over a series of days. Results are used to 

provide for calibration, evaluation of the calibration status, or stability of 

measurement results to support calibration intervals. 

Equipment / Apparatus

Limits given in this section are used to evaluate the final calibration results from 

this procedure when sensors/instruments will be used to provide corrections in 

subsequent calibrations (e.g., buoyancy corrections in mass or gravimetric 

volume calibrations; air density corrections used in dimensional calibrations). 

In this case, the calibrated uncertainty limits of the sensors/instruments to be 

used as standards must be significantly smaller than limits stated in this section 

(e.g., by enough so that conformity statements to these limits may be made 

based on measurement results and calculated uncertainties). See NISTIR 6969, 

SOP 2 for recommended limits for calculating air density.

When the following limits are not attainable, the final measurement results and 

uncertainties may be evaluated for suitability for use as laboratory monitoring 

sensors/instruments. Monitoring limits might consider 1 % of the air density 

limits as shown in SOP 2. 

Calibrated barometer with sufficiently small resolution, stability, and 

uncertainty (See NISTIR 69691, SOP 2, e.g., accurate to ± 66.5 Pa (0.5 

mm Hg)) to determine barometric pressure. 1

Calibrated thermometer with sufficiently small resolution, stability, and 

uncertainty (see SOP 2, e.g., accurate to ± 0.10 °C) to determine air 

temperature.1

Calibrated hygrometer with sufficiently small resolution, stability, and 

uncertainty (see SOP 2, e.g., accurate to ± 10 percent) to determine 

relative humidity.1

Procedure

Identify a sensor/instrument that was recently calibrated by an 

accredited supplier and where the calibration certificate has been 

evaluated to ensure suitable measurement results and uncertainties are 

available. Verify that the standard and any constants from calibration 

reports have been entered into their respective devices correctly (if 

applicable). This instrument will be used as the standard, S, for this 

comparison procedure. 

 1 NISTIR 6969, Selected Laboratory and Measurement Practices, and Procedures to Support Basic Mass Calibrations. SOP 2, Applying Air 

Buoyancy Corrections. 
 

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Equilibrate the standard and the instrument to be calibrated, X, for 2

hours to 4 hours in a suitable laboratory environment. If the instruments 

have been outside of a laboratory environment, allow a 24 hour 

equilibration time. 

2.3.2.1 Electronic equipment should be plugged in and warmed up as 

specified in their operating manuals.

2.3.2.2 Ensure that all barometers are at the same elevation and that 

station pressure values are used (not sea-level pressures).

2.3.2.3 All thermometers involved in the calibration should be placed in 

a stable medium (determined by sensor type). If a temperature 

oven or bath is available, it is preferred. However, a solid block 

or closed air system may be used for probes restricted to air;

immersed block in water that is equilibrated to laboratory 

conditions may be used for liquid-compatible probes.

Option A. Obtain and record observed measurement values for the 

Standard, S, and Unknown, X, for temperature St, Xt,, for pressure, SP, 

XP, and for relative humidity SRH, XRH, as shown on the Appendix A data 

sheet for Option A. Record observations over a period of three days, 

taking care to record or convert to similar measurement units. Record 

the measurements of each parameter within 30 s of each other to 

minimize potential drift due to laboratory environment or human 

influence factors in the measurement results. If additional degrees of 

freedom are needed, for example, where pooled standard deviations are 

not available, this process may be extended over more days. (Do not 

perform all three sets of observations on the same day). 

Option B. If excess drift is suspected or observed in either the 

instruments or the environment, use two sets of observations in reverse 

order (S1, X1, X2, S2) on each day (double substitution) for temperature, 

pressure, and relative humidity. Record data as shown on the Appendix 

A data sheet for Option B.

3 Calculations (Measurement Equations)

Perform the following calculations for each measurement parameter that is being calibrated 

(temperature, pressure, relative humidity) as applicable.
 

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Calculate the three observed measurement differences, dn, for each of the 

measurement parameters spread out over three different days:

To calculate the observed difference for Option A, use Eqn. 1 for 

temperature, pressure, and relative humidity observations (obs).

n obs obs dX S = − Eqn. (1)

To calculate the observed difference for Option B, use Eqn. 2 for 

temperature, pressure, and relative humidity observations as numbered.

11 2 2

2 n

XSXS d −+ − = Eqn. (2)

Calculate the mean value for the observed measured differences, dd̅.

Calculate the correction for each instrument parameter (temperature, 

barometric pressure, relative humidity as applicable), Cx, using the correction 

for the reference standard, Cs, taking care to ensure the correct sign and 

reference value is used. Note: some corrections, especially in thermometry, are 

not additive to the nominal value. 

CCd x s = + Eqn. (3)

4 Measurement Assurance

Three replicate comparisons are performed during the measurement process to 

calculate a replicate standard deviation.

Replicate standard deviations are tracked on a standard deviation chart for this 

process and the replicate process standards deviation are pooled over time. 

Calibration repeatability is evaluated against the limits on the chart and assessed

based on the limits of uncertainty needed for subsequent calibration and use in 

the laboratory. Where repeatability and final uncertainties are too large, a better 

calibration method or calibration source are essential. 

Where a check standard instrument is available, values for that instrument may 

be tracked over time. However, if instruments are not identical in type and 

resolution, the variability of a check standard may not be a suitable duplication 

for an unknown standard to use the standard deviation of the check standard for 

the process repeatability. The value of the check standard may provide a 

suitable check on the stability of measurement results over time. 
 

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5 Assignment of Uncertainty

Uncertainty for the standard, us.

The uncertainty for the standard is obtained from the calibration certificate for 

the reference standard that is used for this calibration. Determine the degrees of 

freedom for the standard by reviewing the calibration certificate. If a coverage 

factor of 2 is stated, an estimate of 500 degrees of freedom may be used for the 

standard (this is an estimated value and other reasonable estimates may be 

used).

Uncertainty for the process, sp.

The uncertainty for the standard deviation of the process is obtained from the 

replicate standard deviation. 

Since the degrees of freedom are very small for this calibration (2), a higher 

coverage factor may be needed (See Appendix A in NISTIR 6969, SOP 29). A 

greater number of replicate observations may be obtained for an equal number 

of days, e.g., 7 observations obtained over 7 days, or 10 observations obtained 

over 10 days to increase the degrees of freedom for this component. 

Use a pooled replicate standard deviation where possible. A pooled value of the 

replicate standard deviation will provide greater degrees of freedom to be used 

for calculating the coverage factor for the uncertainty. 

Where the standard deviation is less than the resolution of the instrument, use 

an uncertainty for the process, up, of the larger of either the calculated standard 

deviation, sp, or the value calculated from the following formula. The 

laboratory may also round up to the nearest resolution of the instrument. 

resolution

3 p u = Eqn. (4)

Uncertainty for other components, uo.

Where instrument history or stability information are available, additional 

components should be considered in the evaluation of the uncertainty. The 

estimate of drift during a calibration interval may be treated as a rectangular 

distribution. While this will increase the uncertainty, it will provide a more 

realistic assessment of uncertainty to be used when evaluating the suitability of 

this procedure. 
 

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Table 2. Example Uncertainty Budget Table.

Uncertainty Component 

Description Symbol Source Typical Distribution

Uncertainty of the standard 

used as a reference 

(temperature, pressure, relative 

humidity)

us Calibration certificate

Expanded 

divided by the 

coverage 

factor, k

Standard deviation from 

replicate measurements sp

Standard deviation from replicate 

measurements, 

Pooled standard deviation where data 

is available from similar instruments

Normal

Standard deviation from 

replicate measurements – when 

standard deviation is less than 

resolution

up

Estimated process uncertainty based 

on resolution of the instrument being 

calibrated

Rectangular or 

rounded up to 

nearest 

resolution

Estimates of drift uo

Historical evaluation of stability in the 

instruments (where available) Rectangular

Calculate the combined and expanded uncertainty following the procedure in 

NISTIR 6969, SOP 29. Use appropriate effective degrees of freedom using the 

Welch-Satterthwaite equation as noted in NISTIR 6969, Section 8 or from the 

Guide to the Expression of Uncertainty in Measurement.

Evaluate the expanded uncertainty. 

Determine whether the measurement results and uncertainties will meet 

requirements for corrections needed for calibrations (e.g., per SOP 2), for 

monitoring laboratory conditions, or for other intended application and use. 

6 Certificate

Report results according to SOP 1, ISO/IEC 17025, and applicable customer requirements.

Report the mean values of the temperature, pressure, relative humidity (as appropriate). Include 

the range of environmental conditions observed during the calibrations and report the estimated 

calculated uncertainties. Report the reference calibration certificate and date for the instrument 

used as the standard. Include a suitability statement to the effect of whether the calibration may 

be used for calibration corrections and/or for monitoring laboratory environmental conditions. 

Note: If this is an internal calibration and/or not covered by the scope of accreditation or 

recognition, follow accreditation body requirements regarding any additional statements that 

may be required when such measurements are not covered by the Scope. 
 

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Appendix A – Data Sheet

Laboratory data and conditions:

Operator Laboratory Conditions Before After

Date Range Temperature

Replicate standard deviation of the 

process, from standard deviation 

chart, sp

Pressure

Degrees of Freedom Relative Humidity

Standard(s) data:

ID Nominala Correctionb Measurement 

Units 

Expanded Unc:

From cal. 

certificate

Unc. 

k factor Unc. Units

S – temperature

S – pressure

S – relative humidity

a selected reference value from the calibration certificate nearest to normal laboratory conditions.

b taking care to determine directionality as appropriate

Identification of the standards, serial number:

Identification of the standards, calibration source:

Identification of the standards, date of calibration:

Measurement Observations, Option A (Record Units in Column Headings):

Dates St_____ Xt_____ SP_____ XP_____ SRH _____ XRH _____

1

2

3

Measurement Observations, Option B (Record Units in Column Headings):

Temperature_____ Pressure_____ Relative Humidity_____

Dates S1 X1 X2 S2 S1 X1 X2 S2 S1 X1 X2 S2

1

2

3