The shape of the relationship
Because the sun protection factor is defined as a ratio of doses, the proportion of erythemally effective radiation reaching skin under test conditions is one divided by the factor. The relationship is a reciprocal, and reciprocals behave in a way that the human eye reading a shelf does not.
At the low end, each step matters a great deal. Moving from a factor of 2 to a factor of 4 takes the fraction from one half to one quarter, and one quarter of the original dose is a large change. At the high end, each step matters much less in absolute terms. Moving from 30 to 50 takes the fraction from one thirtieth to one fiftieth. Both are small; the difference between them is smaller still.
This is not an argument for a lower factor. It is an argument for reading the numeral correctly, because a scale that rises linearly on a pack describes an effect that flattens.
| Labelled factor | Fraction of erythemally effective radiation reaching skin | Step down from the previous row |
|---|---|---|
| 6 | One sixth | Reference point |
| 15 | One fifteenth | Large |
| 30 | One thirtieth | Smaller |
| 50 | One fiftieth | Smaller again |
| 50+ | Less than one fiftieth | Not distinguished further on the label |
Fractions are arithmetic consequences of the definition of the factor, holding under the conditions of the test method. They are not measurements of performance in use.
Doing it as fractions rather than percentages
We set this out in fractions deliberately. Percentages are where sun protection writing tends to go wrong, because a percentage compresses the interesting part of the scale into a range so narrow that everything above a factor of 15 looks identical, and a reader concludes either that the differences are trivial or that they are being hidden.
Fractions keep the structure visible. One fifteenth, one thirtieth and one fiftieth are visibly different quantities, and the ratios between them are easy to see: the fraction getting through at 50 is three fifths of the fraction getting through at 30, and about one third of the fraction getting through at 15.
Those are the correct comparisons, and they are the ones almost never made. A retail listing that shows the factor rising from 15 to 30 to 50 invites the reader to interpolate a straight line. The line is not straight.
Where the misrepresentation happens
Three patterns account for most of it, and all three are about presentation rather than about the numbers themselves.
The doubling implication. Wording that presents a higher factor as delivering proportionally more protection, or as being twice as good, is describing the numeral rather than the effect. The United Kingdom advertising codes require that claims are not misleading and that they can be substantiated, and a proportionality that does not exist cannot be substantiated.
The comparative without a baseline. Wording that presents a step up the scale as a step up in safety, without stating that both figures already sit at a high level of attenuation under test conditions, leaves the reader with an impression of a much larger gap than exists.
The number as permission. The most consequential pattern is not a claim at all. It is the implicit suggestion, carried by prominence and by the size of the numeral on the front of a pack, that a higher figure changes what a person can do. Public health guidance in the United Kingdom is consistent on this point: sun protection products sit alongside shade and clothing rather than replacing them, and the figure does not change that ordering.
The variable that matters more than the numeral
There is a second reason to be careful with the sequence 15, 30, 50 on a shelf. The figure printed on each of those products was measured at the same fixed application quantity. If the quantity applied in real use is lower than the test quantity, then the protection delivered falls, and it falls for every product on the shelf.
The mechanism is set out in detail in the application quantity the number assumes. The short version is that attenuation through an absorbing film does not vary in step with the thickness of the film, so applying half as much does not deliver half the protection. It delivers less than half, and the shortfall is larger for higher factors than for lower ones.
That is why a discussion of whether 30 or 50 is better, conducted without reference to how much is applied, is answering a smaller question than the one being asked.
What the shelf does to the arithmetic
Retail presentation compounds the misreading in a way that no single claim does. Products are usually arranged so that the factor is the most prominent element, ordered from low to high, with the numerals close together and the conditions nowhere in sight. That arrangement invites a straightforward inference: the numbers are on a scale, higher on the scale is further along it, so the distance between 30 and 50 is comparable to the distance between 10 and 30.
It is not. In terms of the fraction of erythemally effective radiation reaching skin, the step from 10 to 30 is far larger than the step from 30 to 50. A shelf that presents them as evenly spaced options is presenting a linear scale for a reciprocal quantity, and the reader who assumes even spacing is reasoning correctly from a display that is misleading them.
Nothing in the labelling rules governs shelf layout, and it would be strange if they did. What the rules do govern is the wording used around the display: shelf edge copy, promotional wording, category headings and retail listings are all advertising, and all subject to the requirement not to mislead. Wording that presents a step up the numeral as a proportionate step up in protection is the point at which a display problem becomes a claims problem.
Why labels stop at 50 plus
The flattening of the curve is one of the reasons labelling convention stops at 50 plus rather than continuing upwards. A figure of 100 on a pack would be twice the numeral of 50 and would correspond to one hundredth rather than one fiftieth of the erythemally effective dose under test conditions. The absolute difference is small, the measurement uncertainty at that end of the scale is proportionally larger, and the communication risk is considerable, because a numeral that doubles reads as a benefit that doubles.
The reasoning behind the cap, and the four protection categories that sit behind the figures, are covered in protection categories and why labels stop at 50.
What a fair presentation looks like
A presentation that does not mislead does three things. It states the factor without implying proportionality. It states the conditions under which the factor was measured, or at least does not obscure them. And it does not let the numeral do work that the measurement cannot support, such as implying a duration, a level of safety or a change in what a person can do.
This is not a demanding standard. It is close to what the common criteria for cosmetic claims already require: that a claim is truthful, supported by evidence, and expressed in a way that allows a reader to make an informed decision. A claim that relies on a reader misreading a reciprocal as a straight line does not meet that.
What to take from this
The number rises linearly and the effect does not. Read the factor as the reciprocal it is, compare fractions rather than numerals, and treat any presentation that implies proportional benefit as a presentation problem rather than a fact about the product.