Data compression ratio

Definition

Data compression ratio is defined as the ratio between the uncompressed size and compressed size:

${\displaystyle \mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{R}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}=\frac{\mathrm{U}\mathrm{n}\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{d}\mathrm{S}\mathrm{i}\mathrm{z}\mathrm{e}}{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{d}\mathrm{S}\mathrm{i}\mathrm{z}\mathrm{e}}}$

Compression Ratio = Uncompressed Size/Compressed Size

Thus, a representation that compresses a file's storage size from 10 MB to 2 MB has a compression ratio of 10/2 = 5, often notated as an explicit ratio, 5:1 (read "five" to "one"), or as an implicit ratio, 5/1. This formulation applies equally for compression, where the uncompressed size is that of the original; and for decompression, where the uncompressed size is that of the reproduction.

Sometimes the space saving is given instead, which is defined as the reduction in size relative to the uncompressed size:

${\displaystyle \mathrm{S}\mathrm{p}\mathrm{a}\mathrm{c}\mathrm{e}\mathrm{S}\mathrm{a}\mathrm{v}\mathrm{i}\mathrm{n}\mathrm{g}=1-\frac{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{d}\mathrm{S}\mathrm{i}\mathrm{z}\mathrm{e}}{\mathrm{U}\mathrm{n}\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{d}\mathrm{S}\mathrm{i}\mathrm{z}\mathrm{e}}}$

Space Saving = 1 - Compressed Size/Uncompressed Size

Thus, a representation that compresses the storage size of a file from 10 MB to 2 MB yields a space saving of 1 - 2/10 = 0.8, often notated as a percentage, 80%.

For signals of indefinite size, such as streaming audio and video, the compression ratio is defined in terms of uncompressed and compressed data rates instead of data sizes:

${\displaystyle \mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}\mathrm{R}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}=\frac{\mathrm{U}\mathrm{n}\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{d}\mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a}\mathrm{R}\mathrm{a}\mathrm{t}\mathrm{e}}{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{d}\mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a}\mathrm{R}\mathrm{a}\mathrm{t}\mathrm{e}}}$

Compression Ratio = Uncompressed Data Rate/Compressed Data Rate

and instead of space saving, one speaks of data-rate saving, which is defined as the data-rate reduction relative to the uncompressed data rate:

${\displaystyle \mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a}\mathrm{R}\mathrm{a}\mathrm{t}\mathrm{e}\mathrm{S}\mathrm{a}\mathrm{v}\mathrm{i}\mathrm{n}\mathrm{g}=1-\frac{\mathrm{C}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{d}\mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a}\mathrm{R}\mathrm{a}\mathrm{t}\mathrm{e}}{\mathrm{U}\mathrm{n}\mathrm{c}\mathrm{o}\mathrm{m}\mathrm{p}\mathrm{r}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{e}\mathrm{d}\mathrm{D}\mathrm{a}\mathrm{t}\mathrm{a}\mathrm{R}\mathrm{a}\mathrm{t}\mathrm{e}}}$

Date Rate Saving = 1 - Compressed Data Rate/Uncompressed Data Rate

For example, uncompressed songs in CD format have a data rate of 16 bits/channel x 2 channels x 44.1 kHz ≅ 1.4 Mbit/s, whereas AAC files on an iPod are typically compressed to 128 kbit/s, yielding a compression ratio of 10.9, for a data-rate saving of 0.91, or 91%.

When the uncompressed data rate is known, the compression ratio can be inferred from the compressed data rate.