Definitions

# Quality factor (video compression)

The quality factor (qf) of encoded video streams (a.k.a. frame quality) is the amount of bits for each pixel in a given video.

## Calculation

The quality factor can be calculated by the formula:

$Q_f = frac\left\{1000 cdot b\right\}\left\{v cdot h cdot f\right\}$

where $Q_f$ is the quality factor, $b$ is the bit rate (expressed in kbit/s), $v$ is the vertical resolution of the frame, $h$ is the horizontal resolution of the frame, and $f$ is the frame rate (expressed in frames per second).

As an example, consider a 90 minutes video with a resolution of 640x360 pixels and a frame rate of 23.976 frames per second (frame/s) to be encoded. The video is supposed to fit onto a 700 MiB CD. If you reserve 100 MiB for the audio stream, this will leave you with 600 MiB for the video stream, which equals a video bandwidth of

$b = frac \left\{600 cdot 1024 cdot 1024 cdot 8\right\} \left\{90 cdot 60\right\} = 932,067.\left(5\right) bit/s = 932.067\left(5\right) kbit/s$

At a frame rate of 23.976 frame/s the quality factor equals

$Q_f = frac \left\{1000 cdot 932.067\left(5\right)\right\} \left\{ 640 cdot 360 cdot 23.976 \right\} = 0.1687$ bits per pixel.

Accordingly you can use the formula to calculate the bit rate needed to produce an encode of a given $Q_f$.

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