Balance and scale calibration: eccentricity, repeatability and minimum weight

Putting a test weight on a balance and reading the display tests one point, in one place, once. A calibration that means something tests the things that actually go wrong: the reading changing when the load moves across the pan, the scatter between repeated weighings, and whether the instrument can resolve the smallest quantity anyone intends to put on it.

The four tests

Of these, eccentricity is the one most often skipped and the one whose absence is most obvious in use. Nobody places a flask exactly in the centre of the pan every time, and on a balance with a worn or misadjusted corner the error from placement can exceed everything else.

Minimum weight: the number that decides what you may weigh

A balance's smallest usable weighing is not set by its readability. It is set by the repeatability near zero, because that scatter is a fixed absolute quantity while the thing you are weighing is not. Weigh 10 mg on a balance with a standard deviation of 0.05 mg and the relative uncertainty is enormous; weigh 10 g on the same balance and it vanishes.

The usual construction is to take the standard deviation of a repeatability test at or near zero load, expand it, and divide by the relative tolerance the process requires. A widely used convention in pharmaceutical work is a 0.10 % relative requirement, which combined with a k = 3 expansion gives a minimum weight of 3 s divided by 0.001 — that is, 3000 times the standard deviation. USP <41> sets the requirement on repeatability in these terms, and the resulting minimum weight is the figure that should be written on the balance itself.

The balance does not become inaccurate below the minimum weight. What happens is that the relative uncertainty grows past the point where the result supports the claim being made from it. This matters most for small standards, small API quantities and anything where the weighed amount is the basis of a concentration.

Calibration is not verification

These get conflated constantly, and they answer different questions. Calibration measures the instrument's error and its uncertainty, and reports them. Verification — legal metrology, under OIML R 76 and the national regimes built on it — asks whether the instrument conforms to the requirements of its accuracy class for trade use, and returns a pass or a fail.

An instrument can pass verification comfortably and still be the wrong instrument for your smallest weighing, because the accuracy class is expressed in scale intervals and your requirement is expressed in the relative uncertainty your process needs. Verification is not a substitute for knowing your minimum weight.

Environment and installation

• A draught shield that is actually closed. An analytical balance in a moving air stream is measuring the air.
• A bench that does not transmit vibration; a dedicated weighing table if the readability warrants it.
• Temperature stability, and the sample at the balance's temperature. A cold flask in a warm room drives convection currents and drifts upwards for minutes.
• Level, checked at the balance's own indicator, not by eye.
• Static: dry powders and glass in dry air generate charge that behaves like a phantom mass and is maddening to diagnose.
• The same position it will be used in — a balance moved after calibration should have at least its level and zero rechecked.

The weights themselves

Test weights carry their own class and their own calibration. OIML R 111 defines the classes from E1 down through M3, each with its own maximum permissible error, and the weight used must be good enough that its uncertainty does not dominate the calibration it is supporting. A weight used to calibrate a balance to a tight specification is itself an instrument with a certificate, an interval and a handling regime — bare fingers on an E-class weight are a measurable problem, not an etiquette one.