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a conventional scale · its standard made of quartz
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Symbol plate SUGAR·01
°Z [α]D
Z in capital, the degree sign closed upnot to be confused with °Bx
Quantity data sheet a companion to the °Bx and °P sheets sheet 1/1 · rev. 2026-09

International Sugar Scale

Unit outside the SI · quantity: sucrose content by the angle of rotation of the plane of polarization

A sugar solution is able to turn the plane of polarization of light, and that turn is proportional to the amount of sucrose dissolved, so it is enough to shine through a tube and see by how many degrees the analyser had to be turned. The discovery belongs to Biot and was made in 1815, and trade seized upon it because optics answers a question no hydrometer answers: how much of the syrup is sucrose in particular, and not dissolved matter in general.

Hence the handsome pairing with the degree Brix, by which the same sample is measured through density. Brix sees everything dissolved — sucrose, invert sugar, salts, colouring matter — whereas polarization answers almost to sucrose alone, and so the difference between the two figures is precisely the admixture the buyer has no wish to pay for. The ratio of those figures is called purity at the works, and it is that, rather than sweetness itself, which sets the price of a consignment.

Notation °Z · pol · [α] at the D line
What they measure sucrose, not dry substance
The normal weight 26.000 g in 100 ml, a 200 mm tube
A hundred degrees equal 34.626° at the sodium line
Specific rotation of sucrose +66.5 deg·ml/(g·dm)
Translations ready / 36
01 · Definition

A hundred degrees of the International Sugar Scale are given to the normal weight: 26.000 grams of pure sucrose dissolved and made up to a hundred millilitres, shone through a tube two hundred millimetres long at twenty degrees Celsius. Such a sample turns the plane of polarization by 34.626 degrees when the yellow sodium line is used, and the whole scale is simply that angle taken for a hundred and divided into a hundred equal parts.

The ability to turn polarization is called optical activity, and it rests on the fact that a molecule of sucrose does not coincide with its own mirror image. The turn is proportional both to concentration and to the length of the path through the solution, and the coefficient of proportionality is called specific rotation; for sucrose it equals plus sixty-six and a half, the plus meaning a turn to the right, clockwise for an observer looking into the beam.

There are exactly as many provisos here as with any conventional scale. Specific rotation depends on wavelength, and that is why the letter D stands in the symbol — the yellow sodium line — although present-day saccharimeters shine with the green mercury line, where a hundred degrees answer to 40.777 degrees of turn. It depends on temperature too, and on the concentration of the sample itself, so the ICUMSA tables set out the corrections separately, and the tube is kept in a thermostat.

A separate subtlety is that the instrument counts not sucrose but the sum of the rotations of everything present in the solution. While the impurities are optically inactive the reading is honest, but let sucrose break down into glucose and fructose and the turn falls and even reverses its sign, because fructose turns to the left more strongly than glucose turns to the right. The phenomenon is called inversion, and upon it a whole method of determining sucrose from the difference of two measurements is built.

Formally α — angle of rotation, deg; l — tube length, dm; c — concentration, g/ml
Specific rotation
[α] at 20 °C and the D line = α / (l · c)
The angle for sucrose
α = 66.5 · l · c
A degree of the scale
°Z = 100 · α / 34.626
Purity of the consignment
P = pol / °Bx · 100 %
1
dimension: the scale itself is dimensionless
26.000
grams in the normal weight, made up to 100 ml
34.626
degrees of rotation — that is exactly one hundred °Z
Interactive · one sample, two instruments

The slider sets how much is dissolved in the sample altogether, and the buttons choose what exactly is dissolved there. The hydrometer and the refractometer count everything alike and give degrees Brix; the polarimeter answers almost to sucrose alone and gives degrees of the sugar scale, so that the gap between the two bars is the non-sugars, for which no one will pay.

dry substance in the sample, % by mass
rotation in a 200 mm tube
degrees of the sugar scale
purity: pol against Brix

Inversion reverses the sign of rotation

While the sucrose is whole, the turn grows to the right along with its amount. Let it break down, however, and instead of one substance there are two, turning in opposite directions: glucose to the right by fifty-three, fructose to the left by ninety-two, so that the sum goes into the minus. It is precisely for this reversal of sign that the phenomenon was named inversion, and on the difference of the rotations before and after it the Clerget method is built.

02 · Conversion

Enter what the instrument showed

Within the optics the conversions are exact, since a degree of the scale is simply an angle divided by a constant number. The approximation begins where one passes from optics to mass: the concentration is obtained from the angle in grams per millilitre, while per cent by mass call for the density of the solution, which is taken from tables.

The length of the tube can be changed in the fine settings of the sheet: the standard one is two hundred millimetres, but for dark syrups a hundred is taken, and for very weak solutions four hundred.

A quartz control plate is what actually keeps this scale. Sucrose will not serve as a standard, since it is hygroscopic, goes cloudy and slowly inverts of itself, whereas quartz turns light by virtue of its own structure and does so unchangingly for years, so a saccharimeter is verified not with sugar but with a plate certified in degrees of the same scale.

Conversion table
ValueNote
Grade by polarization
Rotation
Comparable to

03 · Orders of magnitude
specific rotation: to the left and to the right

specific rotation, deg·ml/(g·dm)
To the left of zero are the substances that turn the plane of polarization to the left, to the right those that turn it to the right, and zero itself means either an optically inactive substance or a mixture of the two mirror forms in equal parts. This quantity has no orders of magnitude in the usual sense: it is signed, and the sign in it matters more than the size.
04 · Measuring instruments

What sugar is measured with

saccharimeter · polarimeter · refractometer · chromatograph
The saccharimeter with a quartz wedge

The instrument is cunningly built: instead of measuring the angle directly it cancels the turn of the solution by an opposing turn of a quartz wedge, which is moved until the field becomes uniform. The scale is then graduated at once in degrees of the sugar scale, so the operator need neither reckon nor consult tables.

The Landolt polarimeter

The chemist's universal instrument, whose scale is honestly graduated in angular degrees and whose source is a sodium lamp with that very D line. With it the rotation of any optically active substance is measured, not sugar alone, and that is why all the tabulated values of specific rotation were obtained on precisely this instrument.

The refractometer and the pycnometer

The instruments of the neighbouring scale: one catches the refraction of the beam at the face of a prism, the other simply weighs a known volume, and both give degrees Brix, that is, the sum of everything dissolved. Without them polarization remains a figure without a denominator, because the purity of a consignment is reckoned as the ratio of one reading to the other.

The liquid chromatograph

The only instrument that counts each sugar separately: the sample is separated on a column and separate peaks of sucrose, glucose and fructose are obtained. In disputed consignments and in laboratory arbitration it is this that is believed, while polarization remains in trade because it gives an answer within a minute and calls for neither reagents nor a column.

05 · Writing rules

The sign of rotation matters more than its size

The degree of the scale is written closed up with a capital Latin letter, and the value is set off by a space. With specific rotation the sign is obligatory, since without it one does not know which way the plane turns, and the symbol carries the wavelength and the temperature: the letter D answers for the yellow sodium line, and the superscript for twenty degrees Celsius. Degrees of the sugar scale must not be equated to degrees Brix even for a pure solution: the figures may coincide, but what they measure is different.

Correct
96.25 °Z
pol 99.8 %
+66.5 deg·ml/(g·dm)
purity 96.3 %
Incorrect
96.25° Z
specific rotation 66.5
96 °Z = 96 °Bx
sugar 96 %

The second notation has dropped the sign, and without it the quantity loses half its meaning: sucrose and fructose differ not so much in figure as in direction. The third sets an equals sign between polarization and density, whereas a coincidence of figures is possible only for pure sucrose and proves nothing. The fourth speaks of «sugar» in general, although the polarimeter sees sucrose alone, and invert sugar it counts with the opposite sign and therefore subtracts.

06 · Neighbouring units

The nearest kin is the degree Brix, by which the same sample is read through density, and the degree Plato, built the same way but for brewer's wort. Both scales answer the question «how much is dissolved altogether», while the sugar scale answers the question «how much of it is sucrose», and that is why at the works they are always kept together.

°Z
optics
sucrose alone
°Bx
density
all dry substance
P
ratio
purity of the consignment
Non-sugars
non-sugars = °Bx − pol
The Clerget method
S = (P direct − P invert) / (142.66 − 0.5 · t) · 100
Invert sugar
[α] of invert = (52.7 + (−92.4)) / 2 = −19.9

Of the Simetrium data sheets nearby stand degree Brix and degree Plato, the hydrometer scales °Bé / °Tw / °API, where the same density is read the oilman's way, alcoholic strength, where the sugar goes after fermentation, and density in kg/m³ as the common ground of all these scales.

07 · Historical section

From a turn of light to the price of a consignment

archive · 1815 → 1988
1815 · Paris
Biot notices the rotation

Jean-Baptiste Biot found that the plane of polarization is turned not only by crystals but by solutions as well, and that the size of the turn grows with concentration. There was no chemical explanation at the time, but it became clear at once that optics can look inside a substance without destroying the sample, and that proved more important than the theory itself.

the rotation grows with concentration
1842 · Berlin
Ventzke makes a scale

Karl Ventzke thought of graduating the instrument not in angular degrees but directly in per cent of sugar, taking for a hundred the turn from a definite weight. From then on the operator needed neither to reckon nor to know any optics: he read a figure that could be copied into a bill of lading, and the sugar works got its first real measuring instrument.

a hundred for the normal weight
1846 · Clerget
Inversion as a method

Clerget grasped that the change of sign upon the breakdown of sucrose is not a hindrance but a tool: if the sample is measured before inversion and after, the difference of the rotations depends on sucrose alone, while everything else in the solution cancels out. The double polarization method made the reading trustworthy at a stroke, even for cloudy factory syrups.

the difference of two polarizations
1988 · ICUMSA
One scale for everyone

National scales had differed in the third digit for centuries, and the International Commission for Uniform Methods of Sugar Analysis brought them to one, tying the hundred to the normal weight and to the green mercury line. Since then the exchange contract for raw sugar is written in these degrees, and a premium for a tenth of a degree means the same thing in London and in São Paulo.

546.2271 nm · 40.777°
A quartz control plate: the standard of the scale, containing no sugar at all
Metrological note

The sugar scale is kept by quartz, not by sugar

One would think the standard of such a scale ought to be sucrose itself, yet for that part it will not serve at all: sucrose draws water out of the air, goes cloudy from the least impurity and breaks down of its own accord, while a solution of it lives a matter of days. Quartz, on the other hand, turns the plane of polarization by virtue of its own structure, does so unchangingly for years and calls for neither a weighing nor a flask, and therefore saccharimeters are verified with a quartz plate certified in degrees of the same scale.

It turns out that a quantity named after sugar and devised for the sugar trade is tied to a mineral, to a wavelength and to the geometry of a tube, while the sugar itself appears in that chain only at the end, when the instrument looks at the sample. Such an arrangement is what makes it a conventional scale rather than a constant of nature: what is reproduced here is not sugar but agreement between instruments, and so ICUMSA rewrites not nature but a protocol.

The analyser is turned to a dark field: that angle is the reading
Catalogue · units of measurement

A data sheet for every quantity

Seven SI base units, twenty-two derived ones with names of their own, and the non-SI quantities that neither science nor daily life does without. Each gets its own sheet: definition, conversion, instruments, writing rules, history. In 36 languages.

7
base
22
derived
36
languages

Concentration and the optics of a solution

the scales of the open data sheet are highlighted

SI base units

the metre and the mole are highlighted

Methods and trade

standards and wavelengths
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