Why Use Even/Odd Rounding?

Why not simply round every exact 5 upward?

The reason becomes clearer when many measurements are processed statistically.

If every exact halfway value always rounds upward, the rounding process can introduce a small systematic upward tendency over many observations.

Even/odd rounding distributes exact halfway cases in both directions depending on the retained digit.

NIST GLP 9 explains that the even/odd method can provide greater balance in repeated rounding and help avoid long-term bias in mean values where these cases matter statistically.

That does not mean conventional rounding is universally incorrect.

And this is where NIST GLP 9 becomes especially useful for calibration laboratories.

NIST GLP 9 Recognizes Three Rounding Approaches

NIST’s GLP 9 – Rounding Expanded Uncertainties and Calibration Values is particularly relevant because it addresses calibration laboratory reporting directly.

The document identifies three rounding options commonly used by calibration and testing laboratories and says the laboratory should document which method or methods it uses.

They are:

The existence of these three options is an important point.

It would therefore be misleading to say:

“NIST requires all laboratories to use half-to-even rounding.”

That is not what GLP 9 says.

Instead, NIST GLP 9 recognizes multiple approaches and emphasizes that the laboratory should establish and document its chosen method.

Option A: Even/Odd Rounding

Consider:

U = 3.450 lbf

to be reported with two significant digits.

Because the retained digit is 4—an even number—the exact halfway case remains:

U = 3.4 lbf

Now consider:

U = 3.550 lbf

The retained digit is 5—an odd number—so it increases:

U = 3.6 lbf

NIST GLP 9 provides this exact type of example for its Option A method.

Option B: Standard Spreadsheet Rounding

GLP 9’s Option B recognizes standard rounding practices used by common spreadsheet software.

For positive uncertainty values, an exact halfway example such as:

3.450

will generally become:

3.5

rather than 3.4.

For the overwhelming majority of values that are not exact halfway cases, Options A and B will usually produce the same result.

For example:

3.447 → 3.4

and:

3.453 → 3.5

under either approach.

It is the exact tie case where the distinction becomes visible.

Option C: Always Round the Uncertainty Up

Option C takes a different approach.

Rather than rounding to the nearest value, the uncertainty is increased to the next reporting increment whenever additional non-zero digits remain beyond the desired significant digits.

For example:

2.341 lbf

would normally become:

2.3 lbf

under conventional or even/odd rounding.

Under the conservative round-up approach:

2.341 → 2.4 lbf

Likewise:

0.084024 lbf

may ordinarily be reported as:

0.084 lbf

but with the conservative uncertainty-up method it becomes:

0.085 lbf

NIST GLP 9 discusses this method as an option for uncertainty reporting and notes potential applications involving maximum permissible errors, tolerances, risk assessments, guardbanding, and accreditation-scope values.

The advantage is obvious: the reported uncertainty is not reduced by the rounding operation.

The tradeoff is that the reported uncertainty may be slightly more conservative than nearest-value rounding would produce.

Which Method Should a Calibration Laboratory Use?

There is no universal answer that can be reduced to “Method A is always correct” or “Method B is always correct.”

What matters is that the laboratory has a technically defensible and consistently applied procedure that also satisfies applicable accreditation requirements.

NIST GLP 9 expressly recommends that laboratories document the rounding method they use.

A laboratory procedure might therefore establish one method for routine uncertainty reporting and clearly explain its application in software, spreadsheets, uncertainty budgets, and certificate-generation systems.

Consistency matters especially when different tools perform rounding differently.

A laboratory may calculate uncertainties using:

Excel, Python, laboratory-management software, instrument software, custom calibration software, database functions, or other computational tools.

Those systems do not necessarily use identical rounding logic in every circumstance.

A written laboratory policy prevents the software package from silently determining the laboratory’s metrological policy.

Do Not Round Intermediate Uncertainty Calculations

This is one of the most important practical rules in the entire subject.

Suppose a laboratory has an uncertainty budget containing reference-standard uncertainty, repeatability, resolution, environmental effects, alignment effects, interpolation effects, and other contributors.

It may be tempting to round every contributor to two significant digits before combining them.

That is not what the two-significant-digit reporting rule means.

The laboratory should retain sufficient precision during its calculations.

NIST GLP 9 specifically warns against rounding intermediate values because doing so can introduce rounding errors into the final result. Rounding should occur after the final expanded uncertainty has been determined.

The preferred workflow is therefore:

Full-precision uncertainty components

→ calculate combined standard uncertainty

→ apply the appropriate coverage factor

→ determine expanded uncertainty

→ then round the final value for reporting

The difference is important.

The rule controls what appears on the certificate. It should not unnecessarily reduce the numerical precision of the laboratory’s internal calculations.

Round the Measurement Result to Match the Uncertainty

After the expanded uncertainty has been rounded, there is another reporting step that is sometimes overlooked.

The reported measurement value, correction, or error should normally be rounded to the same decimal position as the least significant digit in the uncertainty.

NIST GLP 9 explicitly describes this approach.

Consider a force calibration calculation:

Result = 10,000.03748 lbf

Expanded uncertainty = 2.37483 lbf

First, round the uncertainty:

2.37483 → 2.4 lbf

The uncertainty extends to the tenths-of-a-pound position.

The reported result should therefore also be expressed to that position:

10,000.03748 → 10,000.0 lbf

The certificate can then report:

10,000.0 lbf ± 2.4 lbf

rather than:

10,000.03748 lbf ± 2.4 lbf

The latter mixes a highly detailed displayed measurement value with a much coarser statement of uncertainty.

Example: Force Calibration in Pounds-Force

Consider a load cell calibration where the laboratory calculates:

Applied force: 50,000.0000 lbf

Indicated force: 49,997.8364 lbf

The calculated indication error is:

−2.1636 lbf

Suppose the laboratory’s final expanded uncertainty calculation produces:

U = 3.4762 lbf

The expanded uncertainty is first reduced to the appropriate reporting precision:

3.4762 → 3.5 lbf

The error is then rounded to the same decimal position:

−2.1636 → −2.2 lbf

The certificate could therefore report:

Error: −2.2 lbf

Expanded uncertainty: 3.5 lbf

The internal calibration record can still retain:

−2.1636 lbf

and:

3.4762 lbf

for calculations, review, and traceability.

Reporting fewer digits does not mean the laboratory performed a less precise calculation.

It means the laboratory is communicating the result at a numerical resolution appropriate to its uncertainty.

Example: Force Calibration in Newtons

Now suppose an expanded uncertainty calculation produces:

U = 0.006742 N

The first significant digit is 6.

The second significant digit is 7.

Therefore the uncertainty might be reported as:

U = 0.0067 N

Notice that the four zeros before the 6 do not count as significant digits.

Now suppose the measured correction is:

0.018462 N

Because the uncertainty ends at the fourth decimal place:

0.0067 N

the correction should be rounded to the same decimal position:

0.0185 N

The reporting pair becomes:

Correction = 0.0185 N
U = 0.0067 N

This is a good illustration of why a blanket rule such as “always report uncertainty with two decimal places” would be incorrect.

What About Percentage or Relative Uncertainty?

The same principle applies when uncertainty is expressed relatively.

Suppose the calculated relative expanded uncertainty is:

0.012846 %

A two-significant-digit presentation might be:

0.013 %

Those digits are 1 and 3.

It should not automatically become:

0.01 %

simply because someone interprets the requirement as “two decimal places.”

Likewise:

0.24738 %

might become:

0.25 %

The rules concern the numerical significance of the uncertainty, not a fixed number of characters after a decimal point.

Avoid Truncation

Rounding and truncation are not the same operation.

Suppose:

U = 2.3987 lbf

Truncating to two significant digits gives:

2.3 lbf

Proper nearest-value rounding gives:

2.4 lbf

The difference is significant.

NIST GLP 9 specifically cautions against truncation in its discussion of standard spreadsheet rounding.

Truncation systematically removes information in one direction. For uncertainty values, that may even create a reported value lower than what an appropriate rounding procedure would produce.

Certificate Templates and Calibration Software Can Create Problems

Many reporting errors are not caused by a technician misunderstanding metrology.

They are caused by software formatting.

A database field may automatically display six decimal places.

A spreadsheet may use a ROUND function that does not match the laboratory’s documented tie-breaking convention.

A certificate template may force every uncertainty to three decimal places.

A custom application may calculate correctly but display too many digits.

A2LA has noted that excessive significant figures can occur when programs or certificate templates default to more digits than allowed.

For this reason, rounding requirements should be considered during the design and validation of calibration software—not only during final certificate review.

The laboratory’s procedure should define the rounding policy.

The software should implement that policy.

The certificate should display the resulting value correctly.

A Practical Laboratory Policy

A robust laboratory procedure can separate the subject into three questions:

1. How many significant digits will be reported?
For accredited calibration uncertainty, apply the applicable ILAC and accreditation-body requirements.

2. Which rounding method will be used?
Define whether the laboratory uses even/odd rounding, standard spreadsheet rounding, conservative upward rounding, or another justified approach where permitted.

3. When does rounding occur?
Retain adequate precision throughout calculation and round only when preparing the final reported value.

That simple structure prevents many certificate inconsistencies.

It also makes software validation much easier because the laboratory can test known boundary cases.

For example, a software validation set might deliberately include:

2.341
2.350
2.351
2.450
0.084024

These values reveal whether the software is using truncation, ordinary nearest rounding, even/odd rounding, or upward uncertainty rounding.

Why This Matters Beyond Formatting

Significant digits are sometimes treated as a cosmetic issue.

They are not.

The digits displayed on a calibration certificate communicate information about the measurement.

Too many digits can imply unsupported resolution.

Too few digits can unnecessarily discard useful information.

Inconsistent rounding can produce different reported results from the same underlying data.

Premature rounding can actually affect calculations.

And an accredited laboratory may create a nonconformance simply by reporting expanded uncertainty with more significant digits than the applicable accreditation requirement permits. A2LA has identified this as a recurring calibration-certificate issue.

Good rounding practice is therefore part of good measurement practice.

Final Takeaway

There are three separate concepts that should not be confused.

ILAC P14 addresses the reporting precision of expanded uncertainty: for the relevant accredited calibration context, the numerical value is limited to at most two significant digits.

NIST SP 811 explains established rounding mechanics, including the even/odd rule for exact halfway cases.

NIST GLP 9 brings the subject into calibration laboratory practice, describing even/odd rounding, standard spreadsheet rounding, and conservative uncertainty-up rounding; it also emphasizes documenting the selected method, avoiding intermediate rounding, and matching the reported measurement value to the decimal position of the uncertainty.

The practical sequence is therefore:

Calculate accurately → determine expanded uncertainty → apply the laboratory’s documented rounding method → report no more than the permitted significant digits → round the associated calibration value to a consistent decimal position.

That produces a calibration certificate that is not only cleaner, but also communicates the measurement result more appropriately.

You can also use the Metrioc Significant Figures Calculator to compare common rounding with the NIST SP 811 even/odd method for any number and selected number of significant figures.

Technical References

ILAC Policy Documents – ILAC P14
NIST SP 811 – Guide to the SI
NIST Good Laboratory Practices – GLP 9