# How Long Would it Take to Print Out YouTube?

Hint: a really, really long time.

Introduction

My goal for this post was to calculate approximately how long it would take to print out every video on the massively popular online video-sharing site, YouTube. I thought this might be something fun to try and work out. What I didn’t know was that it would lead me down a rabbit hole of data, calculations, and trillions of dollars of printer ink (see below). I got this idea from this video, where someone suggests printing every frame of video on their company servers to create a physical backup. I then began thinking about how long it would take someone to print out all the videos on YouTube, whether it was possible1, and whether it was practical2. This was a surprisingly fun project to work on, and the results were quite interesting.

How much is there to print?

I’m assuming that we’re going to print every frame of video on a separate sheet of paper, in full color, on a desktop printer. To print every video on YouTube, we need to know how many frames there will be to print3. Let’s start by determining how many videos are on YouTube4. It was hard to find actual data on this, but we can roughly approximate it based on available data. There are two things we need to know to determine how many videos are on YouTube: how long each video is and how much video content is on YouTube.

It is surprisingly hard to find the average length of a YouTube video, but we can estimate it by taking a sample of the lengths of a few videos. For this project, I decided to take the lengths of the first 20 videos from the YouTube Trending page and average them. Here are the lengths in minutes and seconds for each video:

1. 6:08
2. 13:54
3. 31:04
4. 4:13
5. 3:38
6. 5:07
7. 3:23
8. 3:24
9. 7:09
10. 3:33
11. 3:14
12. 6:52
13. 1:06
14. 7:43
15. 6:30
16. 2:11
17. 4:45
18. 4:25
19. 2:31
20. 2:34

We can convert all these lengths into seconds by multiplying the number of minutes by 60 and adding the seconds. For example, 6:08 is 6 minutes and 8 seconds. 6 minutes times 60 seconds in a minute is 360 seconds, so the video is 368 seconds long. After calculating the length of each video in seconds, these are the updated video lengths5:

1. 368
2. 834
3. 1864
4. 253
5. 218
6. 307
7. 203
8. 204
9. 429
10. 213
11. 194
12. 412
13. 66
14. 283
15. 390
16. 131
17. 285
18. 265
19. 151
20. 154

Let’s Use Some Math

To calculate roughly how much video was uploaded each year, I decided to create a function that represents how quickly new content is added to YouTube from what year it is. According to data published on Forbes, by 2013, 100 hours of video were being uploaded to YouTube each minute. I couldn’t find much more up-to-date data on the content uploaded to YouTube. To find the exact trend, I estimated the data points from this graph and used Microsoft Excel to plot them. I then calculated a polynomial regression trendline using Excel, with a degree 2 polynomial10 The graph looked like this:

The thicker blue line (behind the orange line) is the data that we already have – the video upload rates for YouTube from 2005 to 2013. The thinner orange line is a polynomial regression approximation of the data, created by Excel. After the blue line ends, you can see where the estimated values (from 2014 to 2018) are. The polynomial regression matches the data quite well, but I chose not to use it because of the way quadratic functions behave – their y value decreases and then increases again at their vertex, while our data is better represented by an exponential function11.

This is the first exponential equation I tried12. This fit the data that we already had quite well, but had far too sharp an increase, and showed that over 2,000 hours per minute of video were being uploaded by 2018, when the actual figure is closer to 300. An exponential curve fits the steepness of YouTube’s growth better than any other equation that I’ve tried.

To improve the accuracy of the curve, I added the one more recent data point we have – about 300 hours of video uploaded per minute13 in (or close to) 2018, and generated another trendline. Unfortunately, the actual line of best fit misses our 300 hours per minute of video uploaded by a quite substantial margin14, so I created a new equation from scratch. I focused the most on having it fit the first few data points and the latest data point, and came up with y = 1.37x 15.

Using the exponential trendline, we can recalculate the values for every year from 2005 to 201816. To find out how much video is uploaded to YouTube, we can find the average value of our video-uploading curve17. This gives us the following values for how much video is uploaded each minute in each year that YouTube has been available:

 Years Since 2000 Approximate Hours of Video Uploaded Each Minute 5 4.826172446 6 6.611856251 7 9.058243063 8 12.409793 9 17.00141641 10 23.29194048 11 31.90995845 12 43.71664308 13 59.89180102 14 82.05176739 15 112.4109213 16 154.0029622 17 210.9840582 18 289.0481598

Now what?

If we want to print out all of YouTube, we will need 1 sheet of paper for each frame in each video. If we assume24 that half of the videos on YouTube use a 24 frames per second video codec, and the other half use 60 frames per second, we have an average framerate of 42 FPS. After multiplying this by our roughly 1,878,839,820,000 seconds of video on YouTube, we can calculate that there are about 78,911,272,440,00025 frames of video on YouTube26, and therefore that you would need to print out 78,911,272,440,000 frames27. To find out how long this would take to print, we first need to know how long printers take to print a single page. I couldn’t find much information on this, so we’ll need to make some more assumptions28. Let’s assume that printing one frame takes, on average, 8 seconds. In this case, printing all the frames on YouTube 6.3129018 × 1014 seconds29 (if you only had one printer). This is about 20 million years, or 120 times as much time has passed since Earth’s last glacial period30.

How much paper would I need?

Since there are 78,911,272,440,000 frames to print, you would need 78,911,272,440,000 sheets of paper. Let’s assume we are using standard printer paper with a thickness of about 0.1 millimeters. To print all of the frames, you would need a stack of paper 5 million miles tall31, or enough to go to the Moon from Earth and back again nearly 10 times32. The volume of this stack would be about 0.5 cubic kilometers33, which is about the total volume of water in Sydney Harbour, or the total volume of all the humans alive today35. Finally, the stack would weigh about 4×109 metric tons, as much as all humans would weigh together36 or as much as all the trash produced by the United States in one year37. Then again, you could never actually print all of YouTube out because new video content is being added all the time.

Could you keep up? How many printers would you need? What would it cost?

Pixels

How many pixels are on YouTube? Every frame that makes up every video on YouTube consists of many millions or billions of individual pixels. To find out just how many, we need to know how many frames are in the video and what the length of the video is. We’ll assume an average resolution somewhere between 640 × 480 (standard definition), 1280 × 720 (high definition), and 1920 × 1080 (full high definition). If we average the number of horizontal and vertical pixels from each resolution, we get an average resolution of 1280 × 760. To find the total number of pixels, we can multiply the horizontal and vertical resolutions together56, and find that each video frame contains 972,800 pixels. This means that the average 361.2 second-long YouTube video, which has 15170.4 frames, would have roughly 14,757,765,120 pixels, more than twice the number of people alive today57. For all 78,911,272,440,000 frames, this would be about 76,764,885,829,632,000,000, or 76 quintillion 764 quadrillion 885 trillion 829 billion 632 million, total pixels. If each pixel was a kilogram, this would weigh roughly as much as all the biomass on Earth right now58.

How Much Data is This?

If we were treating the YouTube video database as a series of images, we could simply multiply the number of total frames by the average amount of digital storage space that one 1280 × 760 image takes up. However, due to interframe compression and interpolation, some of this storage space usage can be eliminated by combining similar parts of consecutive frames59, 60. So let’s instead look at the average file size of a video, to get a more accurate measurement. I selected a random video file from my hard drive, which was 52 seconds long. It had a 59.94 frames per second framerate, and a 1920 × 1080 resolution. The total file size was 150,873,130 bytes, or around 143 megabytes61. If we divide this by the video length, we get a bitrate of about 2.901 megabytes per second62. To compare this to our hypothetical 1280 × 760, 42 FPS video63, we need to account for the change in both framerate and video resolution. First, we’ll look at the resolution. If we divide our 1920 horizontal resolution for our sample video by our 1280 horizontal resolution for our average video, to find that the horizontal resolution is 1.5 times larger. We can then do the same thing for the vertical resolution (1080 / 760), and find that the sample video has a roughly 1.421 times larger vertical resolution64. We can then scale our bitrate to our average video by dividing by both of these, and get a 1.361 megabytes per second bitrate. However, we also need to factor in the framerate. If we divide 59.94 (our sample video framerate) by 42 (or average video framerate), we get a ratio of 1.42765. This gives us a final bitrate of roughly 0.9537 megabytes, or 953.7 kilobytes. Now back to our original quantity for all the video on YouTube – 1,878,839,820,000 seconds. After multiplying these 2 figures together, we find that there is about66 1.7918 exabytes of video content on YouTube67. This is about as much data as all the words that have ever been spoken68. It’s a lot.

Is this practical?

No69. Not at all. But it would be a lot of fun. Anyway, the point is – YouTube is really big. See you next weekend in the next post.

1. Yes.
2. No.
3. This ended up being a slightly more complicated process than I had at first imagined, due in no small part to the frustratingly limited amount of data available, but it was an interesting project nevertheless. The only data I could find from YouTube was from their press page, which mostly contained audience and reach statistics, but not content.
4. Not strictly necessary for determining how many frames of video there are, but still good to know.
5. Assuming I didn’t make any mistakes.
6. Source: https://www.wolframalpha.com/input/?i=Average+368+834+1864+253+218+307+203+204+429+213+194+412+66+283+390+131+285+265+151+154
8. WOW. Every time I see this statistic it amazes me, no matter what.
9. The figures on this vary – I have read that anywhere from 100 to 500 hours of video are uploaded to YouTube each minute, but I find it is best to use a more moderate figure when the publicly available data is this inconsistent or unreliable.
11. To be completely honest, I definitely could have used a quadratic function for this, and it might even have worked better than the exponential function that I decided to go with, but a 3-term equation seemed somewhat like overkill for this project, in addition to the reasons that I already discussed.
12. Excel formats exponential trendlines with a logarithmic formula, where e is the mathematical constant that acts as the base of a natural logarithm.
13. I realize that this figure is rounded and probably not extremely accurate, but it’s close enough for the purposes of this post.
14. At least ~50 hours or so.
15. A very rough approximation; again, more than accurate enough for the purposes of this post.
16. I’m recalculating the values from 2005 to 2013 that we already have as well, so that they fit our model better. Whether this is a good idea or not, I’m not sure.
17. I won’t be bothering with calculus to find the average value of the curve; for this application, taking averaging 10 or so points is fine for this purpose.
18. 75.51 hours • 60 minutes • 60 seconds = 271,836 seconds
19. 271,836 seconds / 60 seconds = 4530.6 seconds
21. Source: https://www.wolframalpha.com/input/?i=Seconds+between+February+14,+2005+and+April+7,+2018
22. [Very roughly]
23. Source: https://www.wolframalpha.com/input/?i=414,700,000+*+4530.6
24. I am making a lot of assumptions here.
25. Or 7.891 × 1013 or 78 trillion 911 billion 272 million 440 thousand.
26. Again, WOW.
27. Good luck with that.
28. Of course, this also depends on the type of printer you are using, how many colors are in the frame/image, how much of the page is used, what ink you are using, etc.
29. Again, good luck with that.
30. Source: https://www.wolframalpha.com/input/?i=78,911,272,440,000+*+8+seconds+in+years
31. Source: https://www.wolframalpha.com/input/?i=Thickness+of+a+sheet+of+paper+*+78,911,272,440,000
32. Source: https://www.wolframalpha.com/input/?i=5+million+miles+%2F+Distance+from+the+Earth+to+the+Moon
33. Source: https://www.wolframalpha.com/input/?i=8.5+inches+*+11+inches+*+Thickness+of+a+sheet+of+paper+in+inches+*+78,911,272,440,000
34. Source: https://www.wolframalpha.com/input/?i=0.5+cubic+kilometers], 34In other words, about as much as one giant human smoothie. Yuck.
35. A slightly less gruesome scenario than the aforementioned “human smoothie.”
36. Source: https://www.wolframalpha.com/input/?i=Weight+of+a+sheet+of+paper+*+78,911,272,440,000
37. 300 hours * 60 minutes * 60 seconds / 60 seconds = 18,000
38. In US dollars, at about \$60.00 per inkjet printer.
39. As I am writing this. Source: https://www.wolframalpha.com/input/?i=US+states+with+population+of+about+6,048,000
40. This is downright generous for a desktop printer printing in full color, running 24/7.
41. A considerable amount, at the current and totally ridiculous ink cartridge prices.
42. Note how this is about as much as the printer itself.
43. This would also add some time to the total printing time, but this would be inconsistent and hard to measure, so I’m going to leave it out of my calculations.
44. 6,048,000 printers * 2.628 × 106 seconds in a month / 8 seconds per frame = 1,986,768,000,000
45. If we divide the approximate total number of frames on YouTube (78,911,272,440,000) by this, we get a figure of ~39 months to print out all of YouTube, with enough printers to keep up with all the new content constantly being added to YouTube.
46. 1,986,768,000,000 frames per month / 440 frames per cartridge * \$55.89 per cartridge = \$252.4 billion
47. This is using the estimated cartage yield of ~440 pages, which we might not (read: “will not”) actually get when printing every page in full color.
48. Compared to this amount, the costs of the printers themselves, the paper, and the electricity required to run them seems downright negligible.
49. Believe it or not, the first time I did these calculations, I forgot to account for paper. And that paper was even a thing that you need to print stuff.
50. Although why anyone would ever want to, I am not sure.
51. Source: http://energyusecalculator.com/electricity_printer.htm
52. \$0.000001416 dollars per hour / 60 minutes / 60 seconds
53. And assuming that I did everything right.
54. This isn’t counting having to pay people to do this for you. After explaining why they should – “If the internet ever explodes, this would be the safest way to store humanity’s information and collective knowledge!”
55. I’m going to ignore video compression for now.
56. Source: https://www.wolframalpha.com/input/?i=15170.4+*+972,800
57. Source: https://www.wolframalpha.com/input/?i=78,911,272,440,000+kilograms