What you are working out
Use the symbols you name below. + - * / ^ ( ) and
sqrt ln log exp sin cos tan abs, plus pi and e.
What you measured
| Quantity | Value | u | ∂f/∂x | Contribution | Share |
|---|
Everything above is computed in this page. It makes no network requests at all, which you can check in your dev tools. Nothing you type leaves the tab.
What the spec on your meter actually means
A digital multimeter's accuracy is written as a percentage of the reading plus a number of counts, because it has two separate error sources: one that scales with the signal, and one fixed to the last digit of the display. A count is worth whatever the last digit is worth on the range you are using. On a 6.000 V range, one count is 0.001 V.
So a Fluke 115 reading 5.000 V on that range, at ±(0.5% + 2), is off by
at most 0.5% × 5.000 + 2 × 0.001 = 0.027 V.
From a bound to a standard uncertainty
That 0.027 V is a bounded error under the conditions in the manufacturer's specification; it is not itself a standard deviation. When only the bounds are known and a rectangular distribution is appropriate, the standard uncertainty is 0.027 / √3 = 0.0156 V. This tool applies the selected distribution and shows the conversion in the budget.
If a calibration certificate explicitly reports expanded uncertainty with
k = 2, select that option. Other coverage factors are not currently supported.
Where the number in the answer comes from
Each quantity gets a standard uncertainty u. A supported expression
gives each one a sensitivity ∂f/∂x, worked out numerically. For independent inputs, the
combined uncertainty is the root of the summed squares of ∂f/∂x × u.
The expanded uncertainty is that multiplied by a coverage factor. With repeated readings in the mix the factor comes from Student's t at 95% for the effective degrees of freedom (Welch–Satterthwaite), so five readings give a wider interval than fifty. With no repeats it settles at 1.96.
The budget table is the useful part. It sorts your inputs by how much of the total variance each one owns, so you can see whether buying a better meter would help or whether one sloppy measurement is carrying the whole error.
What it does not do
- It does not check your units. Values and uncertainties have to be in the same unit as each other; the unit box is a label that gets printed with the answer.
- It assumes the inputs are independent and omits covariance terms. Correlation can make the combined uncertainty higher or lower.
- It has no instrument database. Type the numbers from your own manual, because a spec depends on range, function, temperature and time since calibration.
- It will not tell you your result is wrong. It tells you how precise it is, which is a different thing.
Offline
Download index.html and core.js into the same folder and
the tool works without a connection. There is no server to send anything to, no analytics, and no
storage.