# Video encoding: How much does the video file size increase with fps?

Given that the next blockbusters of e.g. Peter Jackson (The Hobbit) and James Cameron (Avatar 2) are going to be shot with a frame rate of 48 fps (or even more) - i.e. more than the usual 24 fps - I was wondering: How much does the file size of the encoded video increase with the fps?

With increasing fps the frame to frame difference becomes smaller and smaller. So I suppose that the file size grows less than linear. Is this true? Is there a rule of thumb? Or does anyone have example file sizes of the same video encoded in 24, 48, 60, and 96 fps (with a modern video codec)?

(Side question: How much does the video file size increase with image sizes beyond Full HD - e.g. from Full HD to 4k?)

• Quick answer to your side question: Directly proportional to number of pixels of a single image. So, if you are going from 1920x1080 to double that, both width and height, then you are quadrupling the bit rate. The main question is much more complex :) – Bora May 14 '11 at 19:45
• File-size will only be affected by the actual frames (container overhead not withstanding), not the frame rate. You could have 24 physical frames per second encoded into the video, but have it report as and/or play at 48fps (the player drops every other frame), while conversely, you could have 48 frames per second play at 24 (the player plays each one for twice as long). The 48@24 will have a larger size than the 24@48 because it has more frames actually encoded into it. – Synetech May 11 '13 at 18:47

The ONLY thing that impacts filesize is bitrate. You can do 1fps or 120fps, and if your bitrate is 1000Mbs, the filesize will be exactly the same. By definition, the bitrate defines the filesize. Feel free to test -- take a video and output it in 10 different dimensions and 10 different fps, and you're going to end up with identical (or negligible difference) filesizes.

This is a simplification, however, if you want to discuss filesize versus quality, then it's a whole different discussion.

• This is a very good point. So for the sake of the discussion can we assume constant quality (not constant bitrate) for all versions? – knweiss May 14 '11 at 22:14

I will try the theoretic approach. I would love to see some real-world examples that would prove or disprove my theory. Good question! If you have any comments or find some flaws, feel free to comment.

For any current encoder (let's take MPEG-4/AVC/h.264 as an example) frame rate does not matter as much as you think. Let's just assume there is no rate control and every picture is encoded with the same base QP (quantization parameter).

You are right with the following: The motion difference (as defined in ITU-R P.910, good read) between two frames of an 48 fps video will be lower than for the same video in 24 fps. This is due to the fact that the frames won't differ as much from each other. Note that the whole temporal motion doesn't increase. In the end, an object moves from point A to B, so its motion vector will be the same length no matter how many frames per second.

As the encoder looks for the difference between two (or more) frames and only encodes the residual values, that means it will have to code less residual per picture. In average, this will be half of the residual. So you're right with that. (We must not forget that only half of the residual does not mean half of the data needed to store it. It depends on the algorithmic coding implemented.)

Then again, you have twice as many pictures per second, which means that – in average – the encoded information doubles again.

To summarize, nothing much changes on that side. The encoder will do its best job to encode all the motion in the video, which in sum is the same (just in smaller steps, if you know what I mean). The only overhead we have to add is the overhead from small residuals that can't be arithmetically coded in an efficient way.

The above only applies to B- or P-pictures, which depend on others. However, we have to insert an intra-coded picture every once in a while which isn't dependent on any other picture. If this rate of intra-coded pictures doesn't increase, we could assume a linear growth in file size, maybe a bit more.

However if you decrease the distance of intra-coded pictures in order to compensate for possible packet-loss or bitstream errors, you will carry more overhead and therefore the increase is more than linear, not much, but probably noticeable.

This really depends on the type of encoding. If you capture the video in RAW format, then yes: more images require more storage in a linear fashion.

If you encode the captured images directly into some compressed format, then it all depends on how that codec works.

In regard to file sizes, that is determined by `bitrate × duration`. So the frame rate is not directly involved. To achieve the same quality like that of the same video encoded at a lower frame rate, you probably will have to raise the bitrate somewhat though. By how much - again - depends on the codec you're using.