Type A vs Type B Uncertainty: What’s the Difference and When to Use Each

Type A and Type B uncertainty are not two kinds of error. They are two evaluation methods defined by the Guide to the Expression of Uncertainty in Measurement (GUM). This reference page explains the distinction, the formulas, citations, and the reporting conventions used by metrologists, engineers, and scientists. For a precision-and-rounding reference site, the key point is that the evaluation method determines how a standard uncertainty is obtained; the final combined and expanded uncertainties are then rounded and reported under the same significant-figures rules as any other measurement result.

Rule Statement

Under JCGM 100:2008 (GUM) Clause 2.3.2, a Type A evaluation of uncertainty is a method of evaluation based on the statistical analysis of a series of observations. Under Clause 2.3.3, a Type B evaluation is a method of evaluation based on means other than statistical analysis of a series of observations.

Both evaluations produce a standard uncertainty u_i, expressed as a standard deviation. The combined standard uncertainty u_c is the positive square root of the sum of squared standard uncertainties when inputs are independent: u_c = √(u_1² + u_2² + … + u_n²). Expanded uncertainty is U = k u_c, where k is a coverage factor.

Key point: Type A and Type B describe how you evaluated the uncertainty, not whether the underlying error is random or systematic. A systematic effect can be evaluated by Type A methods if repeated data are available; a random effect can be evaluated by Type B methods if only a certificate or specification is available.

Convention Comparison Table

Worked Examples

Example: length measurement. Repeated observations: 10.02, 10.01, 10.03, 10.00, 10.02 mm.

1. Mean = 10.016 mm.
2. Sample standard deviation s = 0.0114 mm (using n−1 = 4).
3. Type A standard uncertainty of the mean: u_A = s/√5 = 0.0051 mm.
4. Type B from calibration certificate: U = 0.02 mm, k = 2, so u_B1 = 0.02/2 = 0.0100 mm.
5. Type B from resolution: resolution 0.01 mm, half-width a = 0.005 mm, rectangular, so u_B2 = 0.005/√3 = 0.0029 mm.
6. Combined: u_c = √(0.0051² + 0.0100² + 0.0029²) = 0.0116 mm.
7. Expanded: U = 2 × 0.0116 = 0.0232 mm ≈ 0.023 mm (k = 2, about 95% for large degrees of freedom).

Report: 10.016 mm ± 0.023 mm (k = 2). The uncertainty has two significant digits; the measurement result is rounded to the same decimal place as the uncertainty, consistent with GUM Clause 7.2.6 and common ASTM E29 rounding practice.

Counter-Examples

The following errors are common in labs and engineering reports.

• Wrong: Type A is random error and Type B is systematic error. Right: The labels refer to evaluation method. A calibration correction evaluated from repeated readings is Type A if obtained statistically.
• Wrong: Add Type A and Type B uncertainties linearly: u_c = u_A + u_B. Right: For independent inputs, combine in quadrature: u_c = √(u_A² + u_B²).
• Wrong: Use the sample standard deviation s as the uncertainty of the mean. Right: For the mean of n independent observations, u_A = s/√n.
• Wrong: Treat Type B as a guess with no basis. Right: Type B must be based on traceable certificates, specifications, published data, or documented judgment.
• Wrong: Round each uncertainty before combining. Right: Carry extra digits through the calculation and round only the final reported uncertainty and result.

Standards Citation

The authoritative definitions are in JCGM 100:2008 (GUM), Clause 2.3.2 and Clause 2.3.3. Type A evaluation is detailed in Clause 4.2; Type B evaluation in Clause 4.3; combined standard uncertainty in Clause 5.1; expanded uncertainty in Clause 6.2; and reporting/rounding guidance in Clause 7.2.6. NIST TN 1297 gives a practical U.S. implementation, with Type A and Type B evaluation procedures in Sections 4.1–4.3. ISO/IEC Guide 98-3:2008 is the ISO publication of the GUM. ISO/IEC Guide 99:2007 (VIM) defines measurement uncertainty and related terms. For numerical rounding of results and uncertainties, ASTM E29-22 provides standard practice.

Common Mistakes

• Confusing the nature of the error with the method of evaluation.
• Forgetting that Type B contributions also require a standard uncertainty, not a tolerance or expanded uncertainty.
• Dividing by n instead of n−1 when calculating s from a sample.
• Using u = s instead of u = s/√n for the mean.
• Assuming all Type B distributions are normal.
• Using k = 2 automatically without considering degrees of freedom or required coverage probability.
• Reporting too many digits in U or in the measured value.
• Ignoring correlation between inputs that are not independent.

Quick Reference Table

Related Rules

Continue with these precision and rounding references:

• Combined Standard Uncertainty: Root-Sum-Square
• Coverage Factor k and Expanded Uncertainty
• Standard Error vs Standard Deviation
• Error Propagation Rules
• Rounding Measurement Results and Uncertainties
• Significant Figures in Uncertainty Reporting

Sources & Further Reading

• JCGM 100:2008, Evaluation of measurement data — Guide to the expression of uncertainty in measurement (GUM), Clauses 2.3.2, 2.3.3, 4.2, 4.3, 5.1, 6.2, 7.2.6.
• NIST Technical Note 1297, Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results.
• ISO/IEC Guide 98-3:2008, Uncertainty of measurement — Part 3: Guide to the expression of uncertainty in measurement.
• ISO/IEC Guide 99:2007, International vocabulary of metrology — Basic and general concepts and associated terms (VIM).
• ASTM E29-22, Standard Practice for Using Significant Digits in Test Data to Determine Conformance with Specifications.

This page is part of our precision-and-rounding reference. Use the significant figures calculator for quick checks, but rely on the rules and citations above for traceable reporting.