# Fun with Power BI and Color Math

I recently published my color contrast report in the Power BI Data Stories Gallery. It allows you to enter two hex color values and then see the color contrast ratio and get advice on how the two colors should be used together in an accessible manner.

I could go on for paragraphs about making sure your report designs are accessible and useful for your intended audience. But this post focuses on how I made this report.

## The Calculations

Color contrast (as calculated in the WCAG 2.1 success criteria) is dependent on luminance. Luminance is the relative brightness of any point in a color space, normalized to 0 for darkest black and 1 for lightest white. In order to calculate color contrast you must first get the luminance of each color.

As an example, I have colors #F3F2F1 and #007E97. In this hex notation, often explained as #RRGGBB, the first two digits represent red, the second two digits are green, and the last two digits are blue. Each two digits is a value that represents the decimal numbers 0 to 255 in hexadecimal notation. The same red, green, and blue values can be represented in decimal notation as integers, and this is what is used to calculate luminance. #F3F2F1 is RGB(243, 242, 241), and #007E97 is RGB(0,126,151).

On a side note, there are places in Power BI where we can change the transparency of the color which is referred to as RGBA (where A represents opacity/transparency). But whenever you copy a hex color value out of the color palette in Power BI, you will just see the 6 digits without the A because the A is stored separately in the UI. When you set colors using DAX formulas, you can specify the A value.

The sRGB color space is non-linear. It compensates for humans’ non-linear perception of light and color. If images are not gamma-encoded, they assign too many bits or too much bandwidth to highlights that humans can’t distinguish, and too few bits to shadows to which humans are sensitive and would require more bits to maintain the same visual quality. To calculate luminance we have to linearize the color values.

For each color component (R,G,and B), we first divide our integer value by 255 to get a decimal value between 0 and 1. Then we apply the linearization formula:

• if R sRGB <= 0.04045 then R = R sRGB /12.92 else R = ((R sRGB +0.055)/1.055) ^ 2.4
• if G sRGB <= 0.04045 then G = G sRGB /12.92 else G = ((G sRGB +0.055)/1.055) ^ 2.4
• if B sRGB <= 0.04045 then B = B sRGB /12.92 else B = ((B sRGB +0.055)/1.055) ^ 2.4

Note: You will find sources online that that incorrectly use the number 0.03928 in the linearization formula instead of .04045. My understanding is that this is incorrect for sRGB.

Then we plug those values in to calculate luminance:

L = 0.2126 * R + 0.7152 * G + 0.0722 * B

The luminance of #F3F2F1 is .8891. The luminance of #007E97 is .1716.

The final calculation is color contrast:

(L1 + 0.05) / (L2 + 0.05), where

• L1 is the relative luminance of the lighter of the foreground or background colors, and
• L2 is the relative luminance of the darker of the foreground or background colors.

The color contrast between #F3F2F1 and #007E97 is 4.24, and we usually write this as 4.24:1. You can check my math here.

## The Dataset

The source data for the report is generated entirely in Power Query. It starts with a simple list of the integers 0 through 255. I placed this in a query called Values.

``````let
Source = List.Numbers(0,256),
#"Converted to Table" = Table.FromList(Source, Splitter.SplitByNothing(), null, null, ExtraValues.Error),
#"Changed Type" = Table.TransformColumnTypes(#"Converted to Table",{{"Column1", Int64.Type}})
in
#"Changed Type"``````

My linearization function is called ColorConvert.

``````(colornum as number) =>
let
Source = if colornum < .04045 then colornum/12.92 else  Number.Power(((colornum+0.055)/1.055),2.4)
in
Source``````

My main query is called color 1. This is where all the calculations through luminance are done.

``````let
//Get values 0 - 255
Source = Values,
//Call that column R for Red
#"R Dec" = Table.RenameColumns(Source,{{"Column1", "R Dec"}}),
//Crossjoin to Values to get Green values 0 - 255
#"G Dec" = Table.AddColumn(#"R Dec", "Custom", each Values),
#"Expanded G Dec" = Table.ExpandTableColumn(#"G Dec", "Custom", {"Column1"}, {"G Dec"}),
//Crossjoin to Values to get Blue values 0 - 255
#"B Dec" = Table.AddColumn(#"Expanded G Dec", "B", each Values),
#"Expanded B Dec" = Table.ExpandTableColumn(#"B Dec", "B", {"Column1"}, {"B Dec"}),
//Get hexidecimal values for R,G,B
#"R Hex" = Table.AddColumn(#"Expanded B Dec", "R Hex", each Text.End("00" & Number.ToText([R Dec], "x"),2)),
#"G Hex" = Table.AddColumn(#"R Hex", "G Hex", each Text.End("00" & Number.ToText([G Dec], "x"),2)),
#"B Hex" = Table.AddColumn(#"G Hex", "B Hex", each Text.End("00" & Number.ToText([B Dec], "x"),2)),
//Concatenate to get full 6-digit Hex color value
#"Changed Hex Type" = Table.TransformColumnTypes(#"B Hex",{{"R Hex", type text}, {"G Hex", type text}, {"B Hex", type text}}),
#"Full Hex" = Table.AddColumn(#"Changed Hex Type", "Hex", each [R Hex] & [G Hex] & [B Hex]),
//Convert integers to decimals and linearize
#"R Lin" = Table.AddColumn(#"Full Hex", "R Lin", each ColorConvert(([R Dec]/255))),
#"G Lin" = Table.AddColumn(#"R Lin", "G Lin", each ColorConvert(([G Dec]/255))),
#"B Lin" = Table.AddColumn(#"G Lin", "B Lin", each ColorConvert(([B Dec]/255))),
//Calculate luminance with the linearized values
#"Luminance" = Table.AddColumn(#"B Lin", "Luminance", each 0.2126 * [R Lin] + 0.7152 * [G Lin] + 0.0722 * [B Lin]),
#"Changed Luminance Type" = Table.TransformColumnTypes(#"Luminance",{{"Luminance", type number}}),
//Create a column for hexidecimal value with the hash/pound at the beginning
#"Hex Dup" = Table.DuplicateColumn(#"Changed Luminance Type", "Hex", "Hex With Hash"),
#"Hex with Hash" = Table.TransformColumns(#"Hex Dup", {{"Hex With Hash", each "#" & _, type text}}),
//Remove Hex and linearized RGB columns to keep model under 1 GB limit for Pro license
#"Removed Columns" = Table.RemoveColumns(#"Hex with Hash",{"R Hex", "G Hex", "B Hex", "R Lin", "G Lin", "B Lin", "Hex"}),
//Rename Hex with Hash to Hex
#"Renamed Columns" = Table.RenameColumns(#"Removed Columns",{{"Hex With Hash", "Hex"}})
in
#"Renamed Columns"``````

In order to allow users to choose two colors, I made a reference query to Color 1 called Color 2.

``````let
Source = #"Color 1"
in
Source``````

If you are interested in these Power Query scripts, you can get them from this Gist.

## DAX Calculations

The color contrast calculation is a DAX measure because it is dynamically calculated based upon the colors selected in the report.

``````Color Contrast =
If( Max('Color 1'[Luminance]) > MAX('Color 2'[Luminance]),
Divide((Max('Color 1'[Luminance]) + 0.05) , (Max('Color 2'[Luminance]) + 0.05)),
Divide((Max('Color 2'[Luminance]) + 0.05) , (Max('Color 1'[Luminance]) + 0.05))
)``````

The advice given based upon the color contrast ratio is also a DAX measure.

``````Advice =
IF (
[Color Contrast] < 3,
"Not enough contrast for text or non-text content, use only for decorative items",
IF (
[Color Contrast] < 4.5,
"Appropriate for large text at least 18pt, bold text at least 14 pt, or non-text content",
IF (
'Color 1'[Color Contrast] >= 4.5,
"Appropriate for any size text and any non-text content"
)
)
)
``````

The example charts showing the two colors as foreground and background are SVG measures.

``````Chart 1 =
VAR Bkgrnd =
MAX ( 'Color 1'[Hex] )
VAR Frgrnd =
MAX ( 'Color 2'[Hex] )
VAR chart = "data:image/svg+xml;utf8,<svg xmlns='http://www.w3.org/2000/svg' width='100' height='100' viewBox='0 0 24 24' style='background-color:" & Bkgrnd & "'><path fill= '" & Frgrnd & "' d='M7 19h-6v-11h6v11zm8-18h-6v18h6v-18zm8 11h-6v7h6v-7zm1 9h-24v2h24v-2z'/></svg>"
RETURN
chart
``````
``````Chart 2 =
VAR Bkgrnd =
MAX ( 'Color 2'[Hex] )
VAR Frgrnd =
MAX ( 'Color 1'[Hex] )
VAR chart = "data:image/svg+xml;utf8,<svg xmlns='http://www.w3.org/2000/svg' width='100' height='100' viewBox='0 0 24 24' style='background-color:" & Bkgrnd & "'><path fill= '" & Frgrnd & "' d='M7 19h-6v-11h6v11zm8-18h-6v18h6v-18zm8 11h-6v7h6v-7zm1 9h-24v2h24v-2z'/></svg>"
RETURN
chart
``````

The check or x mark to indicate whether the colors can be used together in a graph or in text is created using Unicode characters.

``````UseInGraph =
IF ( [Color Contrast] < 3, "✗", "✔" )
``````
``````UseInText =
IF ( [Color Contrast] < 4.5, "✗", "✔" )
``````

The RGB value shown for each color in the report is a DAX measure because storing it in the model made the model size larger than 1 GB, which would have prohibited me from deploying the report and publishing it to the web.

``````RGB1 =
VAR R =
SELECTEDVALUE ( 'Color 1'[R Dec] )
VAR G =
SELECTEDVALUE ( 'Color 1'[G Dec] )
VAR B =
SELECTEDVALUE ( 'Color 1'[B Dec] )
RETURN
R & "," & G & "," & B
``````

## Check Out the Report

This post was an enjoyable combination of color, Power BI, and a bit of math. It was fun to make the report since it brought together my interests in accessibility and Power BI model optimization. At the least I’m hoping this gives you some exposure to how accessibility guidelines are applied to reports. If you are like me, you’ll find the color math fascinating and go down that rabbit hole.

Take a few seconds, pick some colors, and give the report a try.