# What's the relationship between the L value of HSL and fractional paint mixing?

My question is simple - I want to know if there's a linear relationship between adjustments made to an HSL value's L amount and the corresponding adjustments achieved by taking a paint of that colour and mixing it with white (or black).

For example, say I have an HSL red: `0, 50, 50`, and a paint which is exactly this red. If I took the paint and mixed it 1/1 with white (for the sake of argument, assume I do this extremely accurately), would the resulting colour match HSL `0, 50, 75`?

• For anyone who is interested, I use sketch to design abstract paintings. Oct 12, 2019 at 20:06

Well perhaps. It depends entirely wether you are doing phisically correct blending or not. HSL is just a polar cordinate RGB with the same gamut as said RGB and same nonlinearity of said RGB.

If you would normal mix paint in a bucket then the answer is clearly no. As that would require your monitor to be linear and lose ability to show 8bit per channel images without banding.

• Edited to add the assumption that I mix perfectly Oct 12, 2019 at 20:25
• @ToniLeigh what does that mean? If you would mix real paint then the answer is no. If you mix digitally it depends on what kinds of assumption the maker of the mixing engine made, as in do they try to mimic paint, how light mix in a camera or what is that they try to simulate. Or do they just take the easy way out and treat the numbers as linear (which is commonly done, but hard to justify). So we can not do things perfectly unless the specifics are narrowed down considerably. Oct 12, 2019 at 20:54
• So are you saying that the HSL representation in software like Sketch is not linear? i.e. the difference in lightness between `0` and `1` is not the same as between `50` and `51`? Oct 12, 2019 at 20:58
• @ToniLeigh thats right. RGB and thus HSL has no scientific basis. If you want to even have some semblance of color calculation accuracy use Lab or HCL. Oct 12, 2019 at 20:59
• How much do these discrepancies matter to the unaided eye? For example, if the two colours were side by side, could a person discern the difference? Oct 12, 2019 at 21:05

Your number example is right in certain case: You work entirely in RGB color system, not with physical paints and "mix 1:1 red and white" means you watch the red color through 50% transparent white.

In that case your HSL(0,50,50) is equal with RGB(191,64,64). When that's seen through a half-transparent layer of white RGB(255,255,255), the resulted color is RGB(223,160,160). Each number is got as average.

If we convert it back to HSL, we get HSL(0,50,75) as you assumed. The lightness (=L) is the average of the largest and smallest RGB number divided by 255. In this case L=((223+160)/2)/255 = 0,75 = 75 %

Someone could shout "it cannot be as saturated as the original after inserting white!!!!" This is natural for Photohop users, because there the saturation would be smaller. But Photoshop uses HSB (also known as HSV) where the saturation has totally different meaning.

You can find conversion formulas here https://www.rapidtables.com/convert/color/rgb-to-hsl.html

With a little elementary math you get the next general formula for the new HSL lightness after mixing with white:

L2 = P+(1-P)L1

L1 is the lightness of the original color, P is the opacity of the white in scale 0...1. In your example case L2 = 0,5+(1-0,5)0,5 = 0,75 as proposed.

Do NOT expect as simple formula for cases where neither of the mixed colors is white nor other grayshade.

Can this be used with real paints? Answer: I cannot see how it could work. HSL assumes RGB screen, paint has no red, green nor blue leds, it reflects ambient light. Paint manufacturers have published paint mixing tables and curves which are valid only for their listed paints. The listed mixing results are shown as printed cards or as curves or numbers in some non-screen dependent color system like CIELAB.

I haven't seen any usable general math formulas for the color of mixed paints. I guess it's caused by the complexity of the interaction possibilities between paint material molecules in the mixed paint itself and the resulted new interaction possibilities between light and paint.

• I also haven't seen any "usable general math formulas for the color of mixed paints", but I've seen some attempts. This RYB color wheel is quite fun. The logic behind is described in this paper. Oct 14, 2019 at 16:48