Free measurement uncertainty budget template
An Excel workbook for a GUM uncertainty budget. List each contributor and pick its distribution. The sheet reduces each one to a standard uncertainty, combines them by root-sum-square, and gives the expanded uncertainty. It works offline and nothing is sent anywhere.
What’s inside the workbook
Instructions
What each column means, how to fill in a row, and how to choose the coverage mode. The limits of the sheet are stated there too.
Budget
A blank budget with 20 contributor rows and a header for the instrument or measurement, measurand, units, preparer and date. Yellow cells are inputs. The rest are formulas, and an empty row stays blank.
Example
An illustrative budget for a 0 to 25 mm outside micrometer checked against a gauge block. It has five contributors: the gauge block certificate, resolution, repeatability, temperature and anvil parallelism.
Each row takes a quoted value, a distribution and a sensitivity coefficient c, and shows the standard uncertainty u_i and its share of the variance. Degrees of freedom are optional. A Check column flags a degrees of freedom entry that is not a number of 1 or more. The method is the one the online uncertainty budget calculator uses.
How to fill in the budget
- 1. Describe the measurement. Fill in the header: the instrument or measurement, the measurand, the units, who prepared the budget and the date.
- 2. Add one row per contributor. Name the source and mark it Type A or Type B. Type A is evaluated from repeated readings. Type B comes from other information, such as a certificate, a specification or the resolution of the instrument.
- 3. Enter the value and pick its distribution. Type the value the way your source gives it: an expanded uncertainty, a ± half-width or a standard deviation. The distribution sets the divisor.
- 4. Set the sensitivity coefficient. c converts the input into the units of the result. It starts at 1. Only its size is used, so its sign does not matter.
- 5. Add degrees of freedom where you have them. For a standard deviation from n readings that is n - 1. Leave the cell blank for a contributor you treat as having infinite degrees of freedom. Anything you do enter must be a number of 1 or more. The sheet flags any other entry, such as a 0, in its row.
- 6. Choose the coverage mode. Use a fixed k, 2 by default, or let the sheet derive k from the effective degrees of freedom at 95%. Then read u_c, k and U in the results block.
The method
The workbook follows the GUM (JCGM 100:2008) and treats the inputs as uncorrelated. Each row is reduced to a standard uncertainty: the quoted value is divided by the divisor of its distribution and multiplied by the size of its sensitivity coefficient:
u_i = (quoted value / divisor) × |c_i|
| Distribution | Divisor | Use it for |
|---|---|---|
| Normal k=2 Divisor 2 | 2 | An expanded uncertainty stated at k = 2, as on a calibration certificate. |
| Normal k=1 Divisor 1 | 1 | A standard deviation, such as a Type A repeatability. |
| Rectangular Divisor √3 | √3 | A ± half-width where any value inside is equally likely, such as resolution. |
| Triangular Divisor √6 | √6 | A ± half-width where values near the center are more likely. |
| U-shaped Divisor √2 | √2 | A ± half-width where the extremes are more likely. |
| Standard Divisor 1 | 1 | A value you have already reduced to a standard uncertainty. |
The rows are combined by root-sum-square into the combined standard uncertainty, u_c = √(Σ u_i²). Each row's share of the variance is u_i² / Σ u_i².
The effective degrees of freedom come from the Welch-Satterthwaite formula (GUM G.4.1), v_eff = u_c⁴ / Σ(u_i⁴ / v_i). Only rows with degrees of freedom enter the sum. A blank cell counts as infinite and adds nothing. When no row has degrees of freedom, v_eff is infinite. An entry that is not a number of 1 or more is flagged in its row. While a row is flagged, v_eff shows a message instead of a number. In the effective degrees of freedom mode, k and U show it too. With a fixed k, k and U still compute.
With a fixed k, the sheet uses the k you enter. In the effective degrees of freedom mode, k is the two-sided 95% Student t value for v_eff, or the normal value 1.960 when v_eff is infinite. The expanded uncertainty is U = k × u_c.
How it compares with the online calculators
The divisors, the use of |c_i| and the root-sum-square combination are the same as in the uncertainty budget calculator. The degrees of freedom step is the same as in the Welch-Satterthwaite calculator, with two differences.
When v_eff is not a whole number, the workbook truncates it to the next lower integer before it looks up t. GUM G.4.1 allows this. The Welch-Satterthwaite calculator interpolates t between table values instead. Truncating means fewer degrees of freedom, so the workbook's k is equal to or slightly larger than the calculator's. At v_eff = 13.5, for example, the workbook uses 13 degrees of freedom and k = 2.160, and the calculator gives about 2.152.
The second difference is what counts as a valid entry. The calculator accepts a number greater than zero, or inf, and leaves any other row out of the whole result. A blank cell is one of those. The workbook reads a blank cell as infinite. Any other entry must be a number of 1 or more. A row that fails is flagged but still counts in u_c, and v_eff shows a message until you fix the entry.
What the workbook does not do
- It does the arithmetic. Choosing the contributors, their distributions, the sensitivity coefficients and the degrees of freedom is your judgement.
- It does not model correlations. Every row is treated as independent of the others.
- It adds the rows as they are, so each u_i must be in the units of the result. Use the sensitivity coefficient to convert.
- It does not validate a budget for accreditation, and it does not replace JCGM 100:2008 or your documented uncertainty procedure.
Keep budgets with the instruments they describe. Axiospec stores a budget for each instrument and uses it for TUR when a calibration states no uncertainty of its own.
Track your instruments freeCommon questions
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What is in the uncertainty budget template?
Three sheets. Instructions explains each column and states the limits. Budget is a blank sheet with 20 contributor rows and live formulas for the divisor, u_i, each row's share of the variance, u_c, the effective degrees of freedom, k and U. Example is the same sheet filled in with an illustrative micrometer budget.
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Is it free? Do I have to enter an email?
It is free and there is no email step. The download button is a plain link to the file. There is no signup and no trial.
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Should I use a fixed k or the effective degrees of freedom?
A fixed k = 2 gives about 95% coverage when the combined distribution is close to normal. Use the effective degrees of freedom mode when a large contributor has few degrees of freedom, such as a standard deviation from a handful of readings. In that case k = 2 can understate U at 95%, and the Student t value accounts for it.
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Why can k differ from the Welch-Satterthwaite calculator?
The workbook truncates a non-integer v_eff to the next lower integer before it looks up t, as GUM G.4.1 allows. The calculator interpolates t instead. Truncating uses fewer degrees of freedom, so the workbook's k can be slightly larger. The difference is largest when v_eff is small.
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Does it handle correlated inputs?
No. Every row is treated as independent, so no correlation terms are added. If your inputs are correlated, the combined standard uncertainty needs the covariance terms in section 5.2 of the GUM, and this sheet does not include them.
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Is the workbook enough for accreditation?
It does the arithmetic. It does not validate the budget. Whether the contributors, distributions and degrees of freedom suit your measurement is your judgement, and an assessor reviews that against your documented procedure.
This template applies the GUM arithmetic to the values you enter. It does not choose your contributors and does not model correlations. It does not replace JCGM 100:2008, ISO/IEC 17025 or your documented uncertainty procedure. Check a budget against that procedure before you rely on it.
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Keep the budget with the record
Axiospec keeps every calibration, uncertainty budget, and certificate in one tamper-evident ledger built for ISO/IEC 17025, with per-instrument uncertainty budgets and test uncertainty ratios.
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