Calculate measurement uncertainty using repeatability and instrument inputs. Compare coverage, confidence, and component effects quickly. Download clean reports, inspect formulas, and validate results faster.
| Input | Example Value | Meaning |
|---|---|---|
| Repeated Measurements | 10.12, 10.09, 10.11, 10.10, 10.13 | Observed values used for repeatability. |
| Instrument Resolution | 0.01 mm | Least count of the instrument. |
| Calibration Expanded Uncertainty | 0.02 mm | Certificate uncertainty before division by k. |
| Calibration Coverage Factor | 2 | Used to convert expanded to standard uncertainty. |
| Reference Standard Uncertainty | 0.005 mm | Standard uncertainty from the reference. |
| Environmental Uncertainty | 0.004 mm | Effect of temperature or surroundings. |
| Operator Uncertainty | 0.003 mm | Reading and handling variation. |
| Drift Uncertainty | 0.002 mm | Instrument change between checks. |
Mean: Mean = Sum of measurements ÷ Number of measurements.
Sample standard deviation: s = √[Σ(x − x̄)² ÷ (n − 1)].
Type A standard uncertainty: uA = s ÷ √n.
Resolution standard uncertainty: ures = Resolution ÷ √12. This assumes a rectangular distribution from rounding.
Calibration standard uncertainty: ucal = Calibration expanded uncertainty ÷ Calibration coverage factor.
Combined standard uncertainty: uc = √(uA² + ures² + ucal² + uref² + uenv² + uop² + udrift²).
Effective degrees of freedom: veff = uc4 ÷ [uA4 ÷ (n − 1)] when Type A contributes.
Expanded uncertainty: U = k × uc, where k is chosen from the selected confidence level and effective degrees of freedom.
Reported result: Mean ± Expanded uncertainty at the chosen confidence level.
Measurement uncertainty shows how much doubt remains around a result. A measured value alone can look precise, but it may hide instrument limitations, calibration effects, drift, operator influence, and environmental changes. Reporting uncertainty makes the result more trustworthy because it shows the likely range around the measured value.
Type A uncertainty comes from repeated observations. It reflects repeatability and random variation. Type B uncertainty comes from other sources such as resolution, certificates, reference standards, experience, previous data, or technical knowledge. A sound estimate normally combines both categories. This calculator supports both so you can build a fuller uncertainty budget.
Each standard uncertainty component is converted into a common form and combined with the root sum of squares method. That gives the combined standard uncertainty. To report a wider interval with stated confidence, the combined value is multiplied by a coverage factor. The result is called expanded uncertainty. Many reports present the final result as measured value plus or minus the expanded uncertainty.
This calculator gives you the mean, sample deviation, Type A component, major Type B components, combined standard uncertainty, coverage factor, expanded uncertainty, and a simple uncertainty interval. The chart helps identify which component dominates the budget. The CSV and PDF options make it easy to save records, share calculations, or document a method review.
Measurement uncertainty is the quantified doubt around a measured result. It describes a reasonable range where the true value is expected to lie.
Type A uncertainty comes from repeated observations and statistical analysis. It is often calculated from the sample standard deviation and the number of measurements.
Type B uncertainty comes from non-statistical sources, such as calibration certificates, instrument resolution, reference standards, experience, specifications, or environmental influence.
This assumes rounding creates a rectangular distribution over one scale division. The standard uncertainty of a rectangular distribution equals the half-width divided by square root of three.
Calibration certificates often report expanded uncertainty. Dividing by the coverage factor converts that expanded value into standard uncertainty for combination with other inputs.
It is the root sum of squares of all standard uncertainty components. It represents the overall standard uncertainty before applying a coverage factor.
Expanded uncertainty equals the combined standard uncertainty multiplied by a coverage factor. It gives a wider reporting interval at a chosen confidence level.
No. It is a practical calculator for estimation and review. Formal methods may require distribution choices, sensitivity coefficients, correlations, and procedure-specific rules.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.