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= 3 ( 40665857401448 + 2001055256793 2 + 144 17 ( 10411242561157458401 − 2208656823577139226 2 ) ) 164926945077845 {\displaystyle ={\frac {3\left(40665857401448+2001055256793{\sqrt {2}}+144{\sqrt {17\left(10411242561157458401-2208656823577139226{\sqrt {2}}\right)}}\right)}{164926945077845}}}

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The following table shows the aspect ratio (height to width ratio) of national flags and subnational flags used by countries and dependencies. Variant flags such as ensigns are listed in the "Alternative flags" column if they have different proportions from the national flag. Territories without an official flag distinct from that of their controlling country are excluded.

For comparison, the ratios are also given as a decimal number, which is the flag width divided by its height (e.g. a 2:3 flag has a decimal ratio of ⁠3/2⁠ = 1.5). Flags with irrational ratios have only a decimal approximation, and have the exact form given in the "Notes" column (which also includes additional information such as similar flags, recent flag changes, etc.).

The ratios most commonly used are 2:3, used by 88 of 195 sovereign states, such as Algeria and Pakistan, followed by 1:2, used by 55 sovereign states, such as Canada and Nigeria, followed by 3:5, used by 17 sovereign states, such as Germany and Bangladesh. Most dependencies and former colonies use the same proportions as their mother countries: all British Overseas Territories use 1:2 ratios, while the flags of most former and current Dutch and French areas have 2:3 proportions.

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