Instrumentation

Instrument Error vs Percent Span

Instrument error can be read as a process-unit error, a percent of span, and an equivalent mA error. Learn why span sets the apparent severity and why tolerance must be defined before pass/fail.

TypeEngineering guide — concept explainer

Definition

Instrument error is the difference between what an instrument reads and the true (expected) value. It can be expressed three equivalent ways: as a process-unit error in engineering units, as a percent of the instrument span, and as an equivalent signal error in milliamps. Process error is actual minus expected; percent-of-span error divides that by the span (URV − LRV); and the mA error scales the percent of span onto the 16 mA signal window.

Why it matters

A bare error figure means little until it is tied to the span. Two engineering units of error is trivial on a 0–1000 range and serious on a 0–10 range — the same absolute error is 0.2% of span in one case and 20% in the other. Percent of span is what calibration tolerances, datasheets, and accuracy classes are almost always written against, so converting a process error to percent of span is the step that lets you compare a reading against its specification. Expressing the same error in milliamps then connects it back to what a technician sees on the loop, which is where the check is actually performed.

Formula

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)

Units involved

•expected — the true or reference process value
•actual — the value the instrument reads
•LRV, URV — lower and upper range values defining the range
•span — URV − LRV, the width of the range in engineering units
•% span — the error as a percent of span (the usual basis for tolerance)
•mA error — the error mapped onto the 4–20 mA (16 mA) signal window

Concept diagram

Worked example

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

01span = URV − LRV = 100 − 0 = 100
02process error = actual − expected = 52 − 50 = 2
03% span = (2 / 100) × 100 = 2.0%
04mA error = 16 × (2.0 / 100) = 0.32 mA
05expected mA = 4 + 16 × (50 / 100) = 12.0 mA
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).

Common mistakes

•Quoting an error without the span. "2 units off" is meaningless until divided by the span — it could be 0.2% or 20% depending on the range.
•Confusing percent of span with percent of reading. Percent of span is referenced to the full range; percent of reading is referenced to the current value. They differ at every point except full scale.
•Calling a result pass or fail before a tolerance is defined. The error calculation is just a number; the verdict needs a stated calibration tolerance to compare against.
•Mixing calibration tolerance with process tolerance. How accurately the instrument is allowed to read is not the same as how much process variation the operation can accept.

When to use the calculator

Use the Signal Error Percent calculator to turn an expected/actual pair and the LRV/URV into a process error, a percent-of-span error, and the equivalent and actual mA values in one step. The Instrument Range / Span calculator gives the span and the value↔percent relationship, and the mA to Process Value and Process Value to mA calculators convert between a reading and its signal so you can check the error at the loop.

Signal Error Percent Calculator →Instrument Range / Span Calculator →mA to Process Value Calculator →Process Value to mA Calculator →

FAQ

Why express error as a percent of span at all?

Because span is the reference that makes errors comparable. A fixed absolute error is a different fraction of span on every range, and instrument accuracy specifications and calibration tolerances are written as a percent of span. Converting to percent of span is what 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 100% of span is 16 mA. An error of X% of span is therefore 16 × X / 100 milliamps. A 2% span error is 0.32 mA — the same error seen on the loop current.

Does a small percent-of-span error mean the instrument passes?

Not by itself. Pass or fail depends on the calibration tolerance defined for that instrument and service. The calculator gives the error; you compare it against the site tolerance, which must be established first with the appropriate test equipment and procedure.

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 and should not be used interchangeably.