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Percent of full scale fixes the error band in absolute units across the entire span, which makes it generous at the top and punishing at the bottom. Percent of reading scales the band with the number on the display, so it stays proportionate wherever you are. On an instrument spanning 0 to 1000 ppm, an accuracy of 5 percent of full scale is plus or minus 50 ppm whether the display shows 900 or 20, and at 20 ppm that band is two and a half times the reading itself. The same 5 percent written as percent of reading is plus or minus 1 ppm at that point. Most consumer gas and air listings publish neither form.
Two accuracy statements that mean different things at the same reading
A full scale statement is referenced to the top of the span. Take the span, multiply by the percentage, and you have one absolute band that applies everywhere. It exists because the physical error sources it describes are themselves fixed in absolute terms: electronic noise, a zero offset, a departure from a straight line between the calibration points. None of those shrink when the concentration you are looking at shrinks, so expressing them as a fraction of the span is the truthful thing to do.
A reading statement is referenced to the measured value. Multiply the displayed number by the percentage and the band grows and shrinks with it. This form describes a gain error, where the instrument’s sensitivity is slightly wrong, so the mistake is proportional to the signal passing through it. Real instruments have both kinds of error, which is why serious specifications combine them: a percentage of reading for the gain term plus a fixed number of counts of the least significant digit for everything that does not scale.
The practical consequence is that the same percentage, written two ways, describes two different instruments. Neither notation is a marketing trick in itself. Reading a full scale figure as though it behaved proportionately is what produces the trap.
Working the arithmetic at the bottom of a span
Here is the whole problem in one table, for a 0 to 1000 ppm instrument with an accuracy of 5 percent stated each way.
| Reading | Band at 5 percent of full scale | Band at 5 percent of reading | Full scale band as a share of the reading |
|---|---|---|---|
| 900 ppm | plus or minus 50 ppm | plus or minus 45 ppm | About 6 percent |
| 500 ppm | plus or minus 50 ppm | plus or minus 25 ppm | 10 percent |
| 200 ppm | plus or minus 50 ppm | plus or minus 10 ppm | 25 percent |
| 100 ppm | plus or minus 50 ppm | plus or minus 5 ppm | 50 percent |
| 50 ppm | plus or minus 50 ppm | plus or minus 2.5 ppm | 100 percent |
| 20 ppm | plus or minus 50 ppm | plus or minus 1 ppm | 250 percent |
Look at the last row. A full scale specified instrument displaying 20 ppm has an error band that reaches from well below zero to 70 ppm, which means the display cannot distinguish a real trace of gas from clean air. Nothing is broken and the manufacturer has promised nothing it is failing to deliver. The specification simply does not support a decision at that concentration, and that is the information the arithmetic gives you.
Where the two specifications cross over
The two forms are equal at exactly one point, the top of the span, where the reading and the full scale value are the same number. Below that the reading form is always tighter, and the ratio between them is just the span divided by the reading. At half scale the full scale band is twice as wide, at a tenth of scale it is ten times as wide, at a fiftieth it is fifty times as wide. The divergence is not gradual, it accelerates as the reading falls, which is why the gap feels so much larger in practice than the shared percentage suggests.
That geometry explains a counterintuitive piece of instrument selection. Given two monitors with the same percentage of full scale figure, the one with the narrower span is the more accurate instrument at every concentration both can read. A wide span looks like capability on a listing and acts like a penalty at the readings people actually care about, which tend to sit in the lowest tenth of the range.
Combined specifications behave like a hybrid. In the middle of the span the percentage of reading term dominates and the band scales. Near zero the fixed count term takes over and the band stops shrinking, so the behaviour collapses back to an absolute floor. The floor is referenced to the resolution rather than to the span, which is usually far better than a full scale statement, but it is still a floor and still worth computing before trusting a small number.
What gas and air listings actually publish about accuracy
| Instrument | Span stated | Resolution stated | Accuracy statement |
|---|---|---|---|
| ZYKYCX hydrogen gas detector | 0 to 1000 ppm | 0.1 ppm | Not stated in the listing bullets |
| HENRUN portable particle counter | Not stated in the listing bullets | Particles down to 0.3 microns | Not stated in the listing bullets |
| GANGSUQD fixed oxygen detector | Not stated in the listing bullets | Not stated in the listing bullets | Not stated in the listing bullets |
| Srliya insulation and loop tester | 0 to 440 V phase voltage, 45 to 65 Hz | Not stated in the listing bullets | Not stated in the listing bullets |
The first row is the pattern to learn from. The ZYKYCX hydrogen monitor publishes an electrochemical sensor, a 0 to 1000 ppm span, a 0.1 ppm resolution, a response time of half a second and visual, audible and vibrating alarms with adjustable thresholds. It describes itself as high accuracy and publishes no accuracy figure, so the span and the resolution are all a buyer has. Run the full scale arithmetic on that span and a 5 percent figure would be plus or minus 50 ppm, which would make the 0.1 ppm resolution a property of the screen alone.
The HENRUN particle counter states that it measures particles down to 0.3 microns with preset measurement modes and automatic logging, naming cleanrooms, hospital ventilation and post renovation interiors as its intended settings, and it publishes no count span and no accuracy. The GANGSUQD fixed oxygen detector lists a catalytic sensor type, an audible alarm with an LED display and a die cast aluminium housing, and no measurement figures of any kind. Even the Srliya loop and residual current tester, which does publish spans including a 0 to 440 V phase voltage range, a frequency range from direct current through 45 to 65 Hz and test current multipliers of half, one and five times, stops short of an error band.
Instruments sold against a formal installation test standard behave differently, because the standard obliges the result to be reported with its uncertainty. The photovoltaic installation tester review is a useful contrast for how much more a specification sheet contains when a standard is driving it.
Turning a published accuracy figure into a usable error band
Four steps turn a specification into something you can act on. Find the span, since a full scale figure is meaningless without it. Identify the reference the percentage uses, full scale or reading, and note any fixed count term added to it. Compute the absolute band at the concentration you actually work at rather than at the top of the range. Then compare that band with the threshold your decision depends on, whether that is an alarm level, an exposure limit or a leak or no leak call.
If the band straddles the threshold, the instrument cannot support the decision and no amount of staring at the display changes that. If no accuracy is published at all, the honest classification is indicator rather than measuring instrument: useful for presence, for trend and for pointing you at a location, not for a number you will write down. That is a perfectly reasonable thing to own, and it is the right way to read most of the handheld gas sniffers. Where a figure has to stand up, the instrument classes that publish one are set out in what a combustible gas detector is, what a multi gas detector is and the hydrogen sulphide detector guide.
Frequently Asked Questions
Which accuracy statement is more honest?
Neither is dishonest, they describe different error structures. Percent of full scale is the natural expression for an instrument whose dominant errors are zero offset, noise and linearity, because those are fixed in absolute units. Percent of reading suits instruments whose dominant error is a gain term that grows with the signal. Trouble starts when a buyer reads one as though it were the other.
What does a specification like plus or minus 3 percent of reading plus 5 digits mean?
It is a combined statement. The percentage applies to the displayed value, and the digits term adds a fixed number of counts of the least significant digit on top. In the middle of the span the percentage dominates and the specification behaves proportionately. At the bottom the digits term dominates and the specification behaves like a fixed absolute band, which is the same arithmetic problem as a full scale statement in a different costume.
Does a wider span make an instrument worse at low readings?
Under a full scale specification, yes, directly. The absolute band is a fixed fraction of the span, so doubling the span doubles the band at every reading including the smallest. That is why a narrow range instrument chosen to suit the concentrations you care about often beats a wide range one with a more impressive sounding number.
If a listing publishes resolution but no accuracy, what can I conclude?
Only that the display can show small increments. Resolution is a property of the counting arrangement behind the display and carries no guarantee about closeness to the true value. An unaccompanied resolution figure is best read as a statement about the screen rather than about the measurement.
How does response time interact with accuracy?
A published accuracy applies to a settled reading. If the sensor needs a given interval to reach its final value and you read it sooner, the error you see includes an unsettled component that no accuracy specification covers. Fast response figures matter most where concentrations change quickly, and they are a separate axis from the error band.
Why do so many air quality listings publish no accuracy at all?
Because publishing a figure creates an obligation and omitting it does not. Instruments sold against a formal test standard are far more likely to state an uncertainty, since the standard requires it to be reported with the result. Consumer monitors are usually sold on features, and accuracy ends up as an adjective rather than a number.