# Chroma-Subsampling: How to properly calculate the data-rate

I am having a hard time understanding how to calculate the data rate when leveraging chroma-subsampling in e.g. a Y'UV image:

I have the following examples for a calculation:

Image resolution: 352*288 Frequency: 25 fps

For (4:4:4) the example calculation goes as follows:

(352px * 288px) * 3 color channels * 25 fps * 8 bit = 60 825 600 bit/s

So far so good.

But now comes (4:2:0):

(352px*288px) * 1.5 color channels * 25 * 8 = 30 412 800 bit/s

Now, trying to transfer this example to e.g. (4:1:1) I realized I am not sure whether I have a correct understanding how the ratio of 1.5 color channels is being calculated.

My first guess for the calculation was in case of (4:2:0): 2/4*3=1.5 color channels
Likewise for (4:1:1) I would calculate the ratio for the color channels as:

1/4*3=0.75 color channels

But I am simply not sure whether this would be the correct way to go.
As an alternative, I was thinking along following lines:

color channels (4:1:1): 1 Y' + 1/4 UV = 1.25 color channels

Now which would be the correct way of doing this properly?

• @jattr How did you calculate color channels? I am confused where did you get the value 2/4 in (4:2:0) and 1/4(4:1:1) for the color channels? – shubhamagiwal92 Sep 15 '16 at 1:05

Here is a reference to know the difference. I am adding the essential diagram as well: what you realize is that 4:1:1 has full vertical resolution but 1/4 of Horizontal resolution, where as 4:2:0 has half of vertical as well half horizontal resolution.

However, overall, 4:2:0 and 4:1:1 will have the same number of samples and hence the same bit rate.

• 4:2:0 picture is wrong. Chroma values have been put in between valid values. If you place them up one line (half line as shown there) it would be correct. – Nikos Sep 7 '17 at 2:48

The 4:4:4 scheme is confusing. For example Yuv420 video.

The 1st digit specifies the number of 'Y' luminosity values - '4' means full resolution The 2nd digit is the horizontal spacing for U and V (chroma) values - 2 means every alternate horizontal pixel has a colour value. The 3rd digit it the vertical stepping between values, 0 means none are missed to every row had Y,U and V values.

In 4:1:1 both vertical and horizontal directions there is only a U and V value for every 4th pixel.

I found a good explanation in the the wolfcrow-blog

Using chroma sampling numbers to calculate data size

I personally calculate how much information is lost as follows:

Maximum possible quality is 4+4+4 = 12

A full color image is 4:4:4 = 4+4+4 = 12, or 100% of maximum possible quality. From this, you can derive the rest:

• 4:2:2 = 4+2+2 = 8, which is 66.7% of 4:4:4 (12)
• 4:2:0 = 4+2+0 = 6, which is 50% of 4:4:4 (12)
• 4:1:1 = 4+1+1 = 6, which is 50% of 4:4:4 (12)
• 3:1:1 = 3+1+1 = 5, which is 42% of 4:4:4 (12)