Measurement Uncertainty Budget Calculator
Build an uncertainty budget for a calibration. Each source is converted to a standard uncertainty using its distribution, then combined and expanded with your coverage factor. The test uncertainty ratio is calculated too.
Download
- Calculator sheet with a worked example
- How to Use sheet with steps
- 34 built in formulas, no macros
- Yellow input cells, grey results
- Calculation sign off block
- Excel, Google Sheets and LibreOffice
Worked Example
These are the results of the example already filled in the workbook. Replace the yellow cells with your own data.
Uncertainty contributions
| Source | Value (±) | Distribution | Divisor | Sensitivity ci | Standard uncertainty | u² |
|---|---|---|---|---|---|---|
| Reference standard calibration certificate | 0.00400 | Normal (k=2) | 2.000 | 1 | 0.00200 | 4.00 × 10⁻⁶ |
| Reference standard drift since calibration | 0.00200 | Rectangular | 1.732 | 1 | 0.00115 | 1.33 × 10⁻⁶ |
| Resolution of instrument under test (half digit) | 0.00050 | Rectangular | 1.732 | 1 | 0.00029 | 8.33 × 10⁻⁸ |
| Repeatability (standard deviation of readings) | 0.00150 | Normal (k=1) | 1.000 | 1 | 0.00150 | 2.25 × 10⁻⁶ |
| Temperature effect on reference | 0.00100 | Rectangular | 1.732 | 1 | 0.00058 | 3.33 × 10⁻⁷ |
| Head correction (height difference) | 0.00050 | Rectangular | 1.732 | 1 | 0.00029 | 8.33 × 10⁻⁸ |
About this Calculator
ISO/IEC 17025 laboratories must state measurement uncertainty on calibration certificates, and in house labs increasingly do the same. An uncertainty budget makes every contribution visible, so you can see which one dominates and where better equipment would actually help.
Basis: JCGM 100:2008 (GUM): standard uncertainty from distribution divisors, root sum of squares combination, expanded uncertainty U = k × uc.
How to use
- Enter the measurand, unit, coverage factor and the tolerance of the instrument you are calibrating.
- List every source of uncertainty with its half width (±) and distribution.
- Enter a sensitivity coefficient if the source is in a different unit; leave blank for 1.
- Read the combined and expanded uncertainty, and check the TUR.
Formulas used
- u = value ÷ divisor × sensitivity.
- uc = √(Σ u²), U = k × uc.
- TUR = tolerance ÷ U.
Related tools
Frequently Asked Questions
What is an uncertainty budget?
A table of every uncertainty source in a measurement, converted to standard uncertainties and combined into the total uncertainty.
Why divide by √3 for resolution?
Resolution is a rectangular distribution: any value within ± half a digit is equally likely, and its standard deviation is the half width ÷ √3.
What TUR is acceptable?
4:1 is a common target. Below that, use guard banding or a better reference.
Learn more on the blog
Calibration traceability
A practical guide on instrumentationblog.in that explains the engineering behind this workbook.
Read Full Article