Calibration Error

Loop setup

Define the input you apply and the output you measure. Use the ± toggle for compound or below-zero ranges.

Worksheet

Enter the applied input you actually put in and the worksheet computes that row's expected output, then grades the As-Found (before adjustment) and As-Left (after) readings. The point buttons seed the set points; your tolerance caps how far an applied input can stray from its set point, so a reading can't be hidden by fudging the input. Stray past it and the value snaps back to the band edge.

Expected output = your applied input mapped across the ranges, held at the output limits so it never runs past the origin or full scale (marked sat). Error = (measured − expected) ÷ output span × 100. A negative result reads low.

What is as-found vs as-left?

As-found is what the instrument read before you touched it, as-left is what it read after you finished, and only the as-found data tells you whether the process measurements taken since the last calibration can be trusted.

As-found is recorded with the device in its service configuration, before any adjustment, sensor trim, damping change, or re-range; as-left is recorded after the work and proves the device was returned inside tolerance.

The as-found is what carries weight later. A transmitter found reading +0.9% of span high puts every measurement it produced since its last calibration in question, back to that date, and that is the finding a batch investigation, a custody transfer dispute, or an emissions report has to work from. An as-left-only sheet destroys it. ISO/IEC 17025:2017 clause 7.8.4.1 d) requires an accredited calibration certificate to report the results before and after any adjustment or repair, where those are available.

If the as-found is inside tolerance, leave the instrument alone and write as-left = as-found, no adjustment; adjusting an in-tolerance device erases the drift trend that justifies the calibration interval.

How do I calculate calibration error as a percent of span?

Subtract the ideal output from the actual output and divide by the span, so a reading of 12.1 mA where the ideal is 12.00 mA on a 4-20 mA loop is +0.625% of span.

Span is the output span, not the upper range value: on a 4-20 mA loop the span is 16.000 mA, not 20.

Carry the sign through the whole record. Positive is reading high, negative is reading low, and an error column that changes sign across the five points is telling you something a set of absolute values would hide. On a transmitter ranged 0-150 psi, that same +0.625% is +0.9375 psi at the process.

Why is error percent of span and not percent of reading?

Span is a fixed number across the whole test and the reading is not, so percent of span gives one error figure that means the same thing at 4 mA as it does at 20 mA; percent of reading is used where the error genuinely scales with the measurement, mainly flow meters and electrical test instruments.

At the 0% point the measured value is zero, so percent of reading divides by zero and returns nothing usable. Percent of span keeps one denominator, 16.000 mA, at all five points, so 0.100 mA is 0.625% whether it lands at the bottom of the range or the top.

Percent of reading, also written percent of rate, belongs to devices whose error tracks the measurement. Micro Motion ELITE Coriolis meters in the standard option are specified at ±0.10% of rate on liquid and ±0.25% of rate on gas, and a Fluke 87V is ±(0.05% + 1 count) on DC volts.

Percent-of-rate specs carry a floor. The ELITE data sheet states that where flow approaches the low end of the range, accuracy is governed instead by (zero stability ÷ flow rate) × 100%, and that beyond roughly 30:1 turndown the zero stability value may begin to govern, because a fixed zero offset becomes a larger fraction of a shrinking reading.

Why run the calibration up and down instead of just up?

Running both directions is the only way to see hysteresis, which is the difference between the upscale and downscale reading at the same input and cannot appear in a single upward pass.

The five points are 0, 25, 50, 75, and 100% of span, which on a 4-20 mA output is 4.000, 8.000, 12.000, 16.000, and 20.000 mA, taken up and then back down through the same points. Approach each point from one direction only; if you overshoot on the upscale pass and back down onto the point, you have reversed direction and thrown away the hysteresis data for that point.

Hysteresis is usually largest near mid-scale and closes at the endpoints, so a two-point zero-and-span check is a poor way to look for it. If 50% reads 11.980 mA rising and 12.060 mA falling, the separation is 0.080 mA, or 0.50% of span, and the cause is usually mechanical: linkage slop, diaphragm set, packing friction on a positioner.

The 0% point is 4.000 mA of live current, and under NAMUR NE 43 a signal at or below 3.6 mA or at or above 21.0 mA is a fault signal rather than a measurement, with 3.8-20.5 mA as the valid measurement band. The gaps of 3.6-3.8 mA and 20.5-21.0 mA are differentiation zones, which is where a host sets its fault threshold.

How do I tell zero shift from span shift from linearity error?

Read the error column, not the raw milliamps: zero shift is flat across all five points, span shift ramps from zero at 4 mA to its maximum at 20 mA, and linearity error is zero at both ends and largest in the middle.

Each column below is an error profile in percent of span across the same five points, and the shape of the column, not the size of its biggest number, identifies the fault.

Real instruments show a mix. Subtract the 0% error from every point; what remains is span shift plus linearity error, and a remainder that still bows at 50% means the sensor or its conditioning is nonlinear and zero-and-span work will not fix it.

Adjust zero first, then span, then re-check zero. The span adjustment pivots the output about the lower range value on most instruments, and the two interact enough that one pass rarely holds.

How tight should the calibration tolerance be?

Set it from what the process actually needs, and never set it tighter than the instrument's published accuracy under the conditions it will actually see.

A tolerance of ±0.25% of span on a 4-20 mA loop is ±0.040 mA, or ±0.375 psi on a transmitter ranged 0-150 psi; write it in both forms on the record so nobody has to re-derive it.

The manufacturer's number is a floor, and the wrong number is usually the one quoted. A Rosemount 3051C in Ranges 2-5 carries a reference accuracy of ±0.065% of span, and that figure covers spans down to 10:1 turndown. For spans narrower than that, the data sheet gives accuracy = ±[0.015 + 0.005 × (URL/Span)]% of span, so a 20:1 turndown works out to ±0.115% of span. The same data sheet's Total Performance figure, which is the combined reference accuracy, ambient temperature effect, and static pressure effect, is ±0.15% of span for ±50 °F (28 °C) temperature changes, up to 1000 psi line pressure, from 1:1 to 5:1 rangedown.

A field tolerance of ±0.10% of span on that transmitter is tighter than its own Total Performance figure and will generate failures that are not failures.

How accurate does my calibrator have to be compared to the transmitter?

The common guidance is 4:1, meaning the reference standard should be at least four times better than the tolerance you are judging the device against.

MIL-STD-45662A (1 August 1988) stated it as the collective uncertainty of the measurement standards not exceeding 25% of the acceptable tolerance for each characteristic being calibrated, unless otherwise specified. The same wording carried into ANSI/NCSL Z540-1-1994 clause 10.2(b). ANSI/NCSL Z540.3-2006 clause 5.3(b) changed the target: the probability of false accept shall not exceed 2% and shall be documented, with a test uncertainty ratio of 4:1 or better where that probability is not practicable to estimate.

The Z540.3 Handbook defines TUR as the span of the tolerance divided by twice the 95% expanded uncertainty of the calibration process, not against a catalog accuracy spec. A ratio built from data sheet figures is a test accuracy ratio, and it is the optimistic version.

Worked as a TAR: a Fluke 754 measuring 12 mA on its 30.000 mA range is specified at 0.01% of reading + 5 µA for one year, which is 0.0012 + 0.005 = 0.0062 mA. Against a ±0.040 mA tolerance, 0.040 ÷ 0.0062 = 6.45:1 and the test supports the decision. Against a ±0.008 mA tolerance, 0.008 ÷ 0.0062 = 1.29:1 and it does not.

What has to be on a calibration record?

Enough that someone who was not there can reconstruct the test and defend it: the device, the standard used and its own calibration status, the tolerance applied, and both data sets in full.

The minimum content:

• Tag number, manufacturer, model, serial number, and the configured range with units
• Date performed, and who performed it
• Reference standard manufacturer, model, serial number, and the due date on its own certificate
• The tolerance applied, stated in percent of span and in engineering units
• As-found: all five points, both directions, in the units actually read
• As-left: all five points, or an explicit no-adjustment statement
• Pass or fail against the tolerance, plus ambient temperature and process conditions where the device is sensitive to them

The standard's serial number and due date matter more than they look. If that calibrator is later found out of tolerance, every calibration performed with it is suspect back to its last good certificate, and without the serial number you cannot tell which records those are.

When do I need an accredited calibration lab instead of a field calibration?

Send it out when the result has to stand up to someone outside your organization, when the required accuracy is beyond what a field standard can support at 4:1, or when the item being calibrated is your own reference standard.

Field calibration with a traceable calibrator is not accredited calibration, and the record should say which one it is; accreditation is to ISO/IEC 17025:2017, granted by a body such as A2LA, ANAB, or NVLAP, and it applies only within the laboratory's published scope.

That scope lists the parameters, the ranges, and the laboratory's Calibration and Measurement Capability, which is the smallest expanded uncertainty, at roughly 95% confidence with a coverage factor of k = 2, that it reports for that measurement. Under ILAC P14 the reported expanded uncertainty cannot be smaller than the CMC.

Clause 7.8.4.1 requires an accredited calibration certificate to state the measurement uncertainty, the conditions that influenced the result, and how the measurement is metrologically traceable; if it states pass or fail, clause 7.8.6.1 requires the laboratory to document and apply the decision rule behind that statement, accounting for the level of risk. Custody transfer, fiscal metering, regulated emissions and pharmaceutical records, disputed measurements, and the calibration of working standards are all cases where that paperwork is the point, and producing it is someone else's laboratory.

Still not reading right?

If the numbers here do not match what the loop is doing, the problem is usually the installation, the ranging, or the process itself rather than the device. Describe the symptom and a specialist answers by email, at no charge.