Transmitter Total Probable Error Calculator
Combine every error source of a transmitter loop into the total probable error (root sum of squares), in % of span and in engineering units. Errors given in % of URL are converted to % of span automatically.
Download
- Calculator sheet with a worked example
- How to Use sheet with steps
- 33 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.
Error sources (enter values from the data sheet for your conditions)
| Error source | Value (±) | Basis | In % of span | Squared | In units |
|---|---|---|---|---|---|
| Reference accuracy | 0.065 | % span | 0.065 | 0.00422 | 0.065 |
| Ambient temperature effect (URL part) | 0.025 | % URL | 0.062 | 0.00391 | 0.062 |
| Ambient temperature effect (span part) | 0.125 | % span | 0.125 | 0.01562 | 0.125 |
| Static pressure effect | 0.100 | % URL | 0.250 | 0.06250 | 0.250 |
| Long term stability | 0.125 | % URL | 0.312 | 0.09766 | 0.312 |
| Power supply effect | 0.005 | % span | 0.005 | 0.00003 | 0.005 |
| DCS analog input card | 0.100 | % span | 0.100 | 0.01000 | 0.100 |
About this Calculator
The reference accuracy on a data sheet is only part of the story. In the field, ambient temperature, static pressure, long term drift and the DCS input card all add error. Combining them properly shows whether a transmitter really meets the loop requirement, and why a smaller span (more turndown) makes things worse.
Basis: Root sum square combination of independent errors, as used in manufacturer total performance calculations.
How to use
- Enter the transmitter URL and the calibrated span in the same unit.
- List each error source with its value and whether it is in % of span, % of URL or engineering units.
- Scale temperature and static pressure effects to your actual conditions before entering them.
- Read the total probable error (RSS) and compare it with the accuracy the loop needs.
Formulas used
- % URL values × URL ÷ span give % of span.
- TPE = √(Σ error²) in % of span.
- The simple sum shows the absolute worst case.
Related tools
Frequently Asked Questions
What is total probable error?
The combined error of all independent sources, calculated as the square root of the sum of their squares (RSS).
Why is % of URL worse at low span?
A fixed error in % of URL becomes a larger % of span when the transmitter is turned down to a small span.
Should I use RSS or simple sum?
RSS for independent random errors (normal practice); the simple sum is a conservative worst case.
Learn more on the blog
Instrumentation calibration and troubleshooting guide
A practical guide on instrumentationblog.in that explains the engineering behind this workbook.
Read Full Article