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Instrumentation

Signal Error Percent Calculator

Instrument error is the gap between what an instrument reads and the true value. This calculator takes an expected and an actual process value plus the lower and upper range values, and reports the error in three equivalent forms: process units, percent of span, and equivalent milliamps — along with the expected and actual mA signals. It is a linear signal-error calculation, not a calibration pass/fail verdict; the tolerance must be defined separately.

TypeInteractive engineering calculator

Calculator

Results
Span100
Process error (actual − expected)2
Error as % of span2%
Equivalent mA error0.32 mA
Expected mA12 mA
Actual mA12.32 mA

Pass/fail depends on the site calibration tolerance, which must be defined separately. This is a signal-error calculation, not a calibration verdict.

Formulas

Span
span = URV − LRV
Process error
error = actual − expected
Percent of span error
% span = (error / span) × 100
Equivalent mA error
mA error = 16 × (% span / 100)
Signal at a value
mA = 4 + 16 × ((value − LRV) / span)

Diagram

Signal error: % span = (actual − expected) / span × 100LRV · 4 mAURV · 20 mAexpected50% · 12 mAactual52% · 12.32 mAerror = 2% span = 0.32 mA

Worked example

An instrument ranged 0–100 reads 52 when the true value is 50. What is the error in process units, percent of span, and milliamps?

  1. 01span = 100 − 0 = 100
  2. 02process error = 52 − 50 = 2
  3. 03% span = (2 / 100) × 100 = 2.0%
  4. 04mA error = 16 × (2.0 / 100) = 0.32 mA
  5. 05expected mA = 4 + 16 × (50 / 100) = 12.0 mA
  6. 06actual mA = 4 + 16 × (52 / 100) = 12.32 mA
Result

A 2-unit error on a 0–100 span is 2.0% of span, equal to 0.32 mA (12.0 mA expected vs 12.32 mA actual).

FAQ

Why express error as a percent of span?
Because span makes errors comparable. The same absolute error is a different fraction of span on every range, and accuracy specifications and calibration tolerances are written as a percent of span. Converting to percent of span lets you check a reading against its specification.
How does percent of span become a milliamp error?
The 4–20 mA signal puts the whole span across 16 mA, so an error of X% of span equals 16 × X / 100 milliamps. A 2% span error is 0.32 mA.
Does a small error mean the instrument passes calibration?
Not on its own. Pass or fail depends on the calibration tolerance defined for that instrument and service. This calculator gives the error; you compare it against the site tolerance, which must be established first.
What is the difference between calibration tolerance and process tolerance?
Calibration tolerance is how far the instrument may read from true and still be accepted as calibrated. Process tolerance is how much real process variation the operation can accept. They answer different questions.

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