Pressure Gauge Calibration Error and Uncertainty Calculator
Enter each calibration point's reference pressure, ascending and descending mean readings, uncertainty intervals and reference standard uncertainty. The calculator returns the mean reading, error, hysteresis, standard and expanded uncertainty and error span for every point. The results are calibration estimates, not a conformity or accuracy class verdict.
How to use the calculator
- Choose bar or MPa. Every pressure input and every result uses that unit, and switching converts them all with 1 MPa = 10 bar.
- For each calibration point, enter the reference pressure p and the ascending and descending mean readings a and d.
- Enter the full-width intervals: the larger repeatability interval b, the resolution interval r and the zero error interval z.
- Enter the reference standard's expanded uncertainty Uref with its coverage factor kref, and the coverage factor k you want for the reported expanded uncertainty.
- Add a point for every pressure you calibrated, or remove points you do not need. At least one point is always kept.
- Results update as you type. Any input that is missing or out of range is flagged next to the field.
Method
Each point is evaluated on its own with the model in EURAMET cg-17, version 01 (2007), pp. 16–17 and 20–23, equations 19–21 and 25, Table 3 and Table E1. All intervals are full-width rectangular intervals, so an interval of width w contributes w² / 12 to the variance.
mean = (a + d) / 2
error = mean − p
h = d − a (signed hysteresis)
u = √( (Uref / kref)² + (r² + b² + z² + h²) / 12 )
U = k · u
error span = |error| + U
Worked example from Table E1
At the 100 bar point of Table E1: p = 100.057 bar, a = 99.983 bar, d = 100.001 bar, b = 0.035 bar, r = 0.001 bar, z = 0 bar, Uref = 0.00820456 bar, kref = 2 and k = 2. The mean is 99.992 bar, the error is −0.065 bar and h = 0.018 bar. The standard uncertainty is u = 0.0120828543 bar, so U = 2 × 0.0120828543 = 0.0241657086 bar and the error span is 0.065 + 0.0241657086 = 0.0891657086 bar. In that example the reference uncertainty follows Uref = 0.0002 + 0.00008 · p in bar.
Frequently asked questions
What does the error span represent?
The error span is the absolute value of the error plus the expanded uncertainty U. It is a calibration estimate of how far the indication may differ from the reference pressure at that point. It is not a conformity decision or an accuracy class verdict.
Why do I enter the repeatability interval myself?
The repeatability contribution comes from the spread between repeated measurement series. Table E1 of EURAMET cg-17 does not publish all the individual observations, so you enter the larger full-width repeatability interval b directly for each point.
Why is hysteresis part of the uncertainty?
The guide treats the difference between the descending and ascending mean readings as a full-width rectangular interval. The signed hysteresis h = d − a enters the uncertainty as h² / 12, so its sign does not change the uncertainty.
How are the full-width intervals converted to standard uncertainties?
Each interval is treated as a rectangular distribution of full width w, which gives a variance of w² / 12. The reference standard contributes its expanded uncertainty divided by its coverage factor.
Does switching between bar and MPa change the coverage factors?
No. Switching units converts every pressure input and result using 1 MPa = 10 bar. The coverage factors kref and k are dimensionless and stay exactly as entered.
Can the reference pressure be zero or the readings negative?
Yes. The reference pressure may be zero and the ascending and descending readings may be signed. Only the intervals, the reference expanded uncertainty and the coverage factors have sign restrictions.
This calculator reports calibration estimates from the stated uncertainty model only. It does not apply an accuracy class, a maximum permissible error or any conformity rule, and it does not replace your laboratory's documented calibration procedure or the judgement of a qualified metrologist.