# How to measure combined clothing and sunscreen?

As I understand it, you can't combine multiple suncreens to combine their SPF values. This makes sense as they all work on the same concepts and your skin can't simply "hold more" because it's two different brands.

But how do you measure combined sunscreen and clothing? Or for that matter, combined layers of clothing?

My instinct is that you would multiply them:

Clothing:   UPF 3, passes 33% of UV.  C=0.33
Sunscreen:  SPF 5, passes 20% of UV.  S=0.20
Total = C * S = 0.066, or SPF 15


Can anyone confirm this?

Bonus question: What about tan + sunscreen? Would they add, multiply, or just be the maximum of the two? I'm guessing it's not the last because black skin with a natural SPF of around 13 still benefits significantly from an SPF 15 sunscreen.

• Where I live, SPF 5 would be considered makeup.
– user5330
Mar 14 '18 at 21:06
• It's just an example! :-) Like frictionless pulleys, massless strings, and infinitely long superconductors. (Lab on Wednesday so pick up yours in the basement of the physics building before you go home today.) Mar 16 '18 at 19:23

Purely theoretical (in practice sunscreen isn't as strong as it says on the bottle to begin with) you multiply it.

If 1/3rd of the UV photons make it through the first layer, and of those that made it through 1/5th get through the second layer as well, then 1/15th of the original photons made it through both layers, and 3*5=15.

It's the same for tan, that's melanin, which is a pigment that's great at absorbing light. That's why it looks dark. Any light that gets absorbed does not get through to the living layer of the skin where it can be harmful, because it would need to be not absorbed to do that, so the same idea as for clothing and sunblock applies. So with three layers of protection the total factor would then be 3*5*13(=15*13=10*13+5*13=130+65)=195.

Furthermore it does not matter for the protection factor whether the protecting layer reflects light away, which makes it look light or white or in special cases like a mirror, or absorbs it, which makes it look dark or black. As long as the photons don't arrive at the layer below it. (Although I guess you could make a case for several reflecting layers above each other being less effective then several absorbing layers, because they could re-reflect reflected photons back down, but that's taking this theory further than its practical purpose.)

In practice: adjust the numbers for sunscreen down a little, do what usually works for you and get out of the sun when you're getting burned.

• I am just guessing, but I would assume that the effectiveness of sunscreen does vary by wavelength. E.g. if it is effective almost 100% over 90% of wavelengths, and almost ineffective over the rest, it has factor 10. If then the second screen (shirt, melanin, ...) has the same characteristics, it depends whether the covered wavelengths overlap. If they do, it has still 10, if they don't, it is virtually perfect. Mar 13 '18 at 16:31
• That could certainly be a part of it. But it doesn't have to be. The behavior of molecules and sub-molecular particles can often be approximated by the collision model. An object that seems solid to us, like a thread in a shirt is not solid on the scale of a photon. There's atomic nuclei in there and electrons and a lot of free space between. For a shirt with an SPF of 3 the photon needs to have a chance of 1 in 3 to hit something solid enough to absorb or reflect it. SPF does not by the standard mean "reflects 100% of 1/3 of the wavelengths". Mar 13 '18 at 16:39
• However, there are loads of colored substances, so different percentages for different wavelengths are definitely a thing. They're just not a thing you have any chance of calculating by yourself for a random shirt. (Also, this may be the wrong stack exchange for an in debt discussion of particle physics, and as a biochemist kind of person I may not be the best at this subatomic particle physics stuff.) In general, I'm guessing most sunscreen materials do a bit more against near UV than far UV, while the latter is more dangerous. Mar 13 '18 at 16:39
• My example is very simplified and obviously unrealistic. It's just there to illustrate my point about an effect, that may (doesn't need to) have an effect and skew the simple multiplication. Mar 13 '18 at 16:42

The fine answer of @Monster is correct for UVB rays, but the point raised by @imsodin is pertinent.

The following information and quotes are taken from the Skin Cancer Foundation, UVA and UVB.

When talking about sun protection, there are two broad ranges of ultraviolet (UV) light: UVA and UVB. UVA rays have a wavelength between 320 and 400 nanometers, and UVB rays a wavelength between 290 and 320 nanometers.

UVA rays "are 30 to 50 times more prevalent than UVB rays" and go through clouds and glass. UVA rays cause aging of the skin (wrinkles) and relatively recent evidence implicates UVA rays in skin cancer.

UVB rays are the cause of sunburn. Glass stops most UVB rays. The SPF factor applies to the UVB rays.

Since both UVA and UVB are harmful, you need protection from both kinds of rays. To make sure you're getting effective UVA as well as UVB coverage, look for a sunscreen with an SPF of 15 or higher, plus some combination of the following UVA-screening ingredients: stabilized a avobenzone, ecamsule (a.k.a. MexorylTM), oxybenzone, titanium dioxide, and zinc oxide. You may see the phrases multi spectrum, broad spectrum or UVA/UVB protection on sunscreen labels, and these all indicate that some UVA protection is provided. However, because there is no consensus on how much protection these terms indicate, such phrases may not be entirely meaningful. (emphasis added).

Thus, you cannot calculate the combined protection from multiple protective layers for UVA rays the way you can for UVB rays.