Wastewater Academy™ (a WSI offering) is the online training arm of Wastewater Solutions, Inc.Visit our consulting site: ActivatedSludge.com
Wastewater Academy emblemWastewater Academy™

Instrument Accuracy and Calibration Check

An accuracy spec means very different things depending on whether it is a percent of span, of reading, or of the sensor upper limit. The first tool shows the real error band at the reading you care about. The second records a 5-point check (0, 25, 50, 75 and 100% of range) and grades the as-found and as-left results against your tolerance.

Accuracy: % of Span vs % of Reading

Formula

% of span:     Error = Accuracy % / 100 x (URV - LRV)
% of reading:  Error = Accuracy % / 100 x Reading
% of URL:      Error = Accuracy % / 100 x Upper range limit
Error as % of reading = Error / Reading x 100
Inputs used
  • Lower range value (LRV) (EU)
  • Upper range value (URV) (EU)
  • Reading of interest (EU)
  • Stated accuracy (plus or minus) (%)
  • Accuracy is stated as
  • Upper range limit (URL) of the sensor (only for % of URL) (EU)

Worked example (fictional plant data)

  1. Pressure transmitter 0 to 150 psi, accuracy 0.25% of span, reading 30 psi
  2. Error = 0.0025 x 150 = 0.375 psi
  3. Band = 30 ± 0.375 = 29.625 to 30.375 psi
  4. As % of reading = 0.375 / 30 x 100 = 1.250%

5-Point Calibration Check (As-Found and As-Left)

Formula

Expected (mA) = 4 + 16 x Point % / 100
Expected (EU) = LRV + Point % / 100 x (URV - LRV)
Error, % of span = (Reading - Expected) / Span x 100   (span = 16 mA, or URV - LRV)
Pass when |Error| ≤ Tolerance at every point
Inputs used
  • Lower range value (LRV) (EU)
  • Upper range value (URV) (EU)
  • Tolerance (plus or minus) (% of span)
  • Readings recorded as
  • As-found reading at 0% input
  • As-found reading at 25% input
  • As-found reading at 50% input
  • As-found reading at 75% input
  • As-found reading at 100% input
  • As-left reading at 0% input (optional)
  • As-left reading at 25% input (optional)
  • As-left reading at 50% input (optional)
  • As-left reading at 75% input (optional)
  • As-left reading at 100% input (optional)

Worked example (fictional plant data)

  1. 0 to 150 psi transmitter, tolerance 0.5% of span, readings in mA at 0, 25, 50, 75 and 100% of range
  2. As-found error at 100% = (20.15 - 20.00) / 16 x 100 = 0.938% of span, the largest of the five
  3. As-found result: FAIL, because 0.938% is more than the 0.5% tolerance
  4. As-left largest error = (8.01 - 8.00) / 16 x 100 = 0.063% of span, so as-left PASS

Cautions

  • Your reference (calibrator, dead weight tester, test gauge) should be several times more accurate than the tolerance you are checking; 4 to 1 is a common target.
  • Record as-found readings before adjusting anything. As-found data tells you whether past readings were good.
  • Let the transmitter and reference settle at each point. Check up and down the range if hysteresis matters.
  • Tolerances come from your calibration procedure, permit or QA plan, not from this page.

References

  • ISA-51.1, Process Instrumentation Terminology (span, accuracy and error definitions).
  • ISO/IEC 17025 and your plant QA plan for reference standard traceability.

Results are estimates for operator and technician use. Equations follow the references above; always check against the instrument manual, your calibration procedure and plant data.

This calculator also appears on ActivatedSludge.com, our consulting site. Results are for training and operator use; always follow your plant’s procedures.