Total Probable Error Calculator
Transmitter datasheets list several independent error sources. Combine them by the root sum square (RSS) method to estimate the total probable error in your installation, and compare it with the worst case sum.
- TPE = √(e₁² + e₂² + … + e₆²) = ± 0.1712 %
- Worst case = e₁ + e₂ + … + e₆ = ± 0.375 %
Error budget
| Source | Error | In EU | Share of total |
|---|---|---|---|
| Reference accuracy | ± 0.065 % | ± 0.065 | 14.4 % |
| Temperature effect | ± 0.1 % | ± 0.1 | 34.1 % |
| Static pressure effect | ± 0.05 % | ± 0.05 | 8.5 % |
| Stability | ± 0.1 % | ± 0.1 | 34.1 % |
| Power supply and other | ± 0.01 % | ± 0.01 | 0.3 % |
| Input card or DCS | ± 0.05 % | ± 0.05 | 8.5 % |
Total Probable Error Formula
Independent random errors rarely all reach their maximum at the same time. The root sum square method combines them statistically:
Convert every effect to the same basis, usually percent of calibrated span, before combining. Temperature effects are often quoted per 28 °C or per 10 K, so scale them to your actual ambient swing first.
Worked example
With the default values the TPE is √(0.065² + 0.1² + 0.05² + 0.1² + 0.01² + 0.05²) = ± 0.17 % of span, compared with a worst case sum of ± 0.375 %.
Frequently Asked Questions
Why use root sum square instead of adding errors?
Adding all errors assumes every one is at its limit in the same direction at the same moment, which is very unlikely. RSS gives a realistic estimate for independent errors.
How does turndown affect total probable error?
Many specifications are given as a percent of upper range limit. If you calibrate a smaller span, convert them to percent of your span, which makes them larger.
Is total probable error the same as uncertainty?
It is a simplified uncertainty estimate. A formal uncertainty budget to the GUM also considers the distribution and coverage factor of each term.
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