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Ratios of flags

Last modified: 2014-02-16 by rob raeside

Keywords: ratio of flags | flag ratios | naval ensign | off-centered | scandinavian cross | golden section |

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Summary of Ratios of Flags

My "holy book" (Whitney Smith, Flags Through the Ages and Across the World) quotes for the United States' flags a 10:19 ratio, really closer to the 1:2 traditional ratio of the British flags, from which the "Star Spangled Banner" comes.

In fact there are three main "threads" in the world of flags: British flags have a 1:2 ratio (United Kingdom, Australia, Bahamas, Canada, Ireland and with the little correction of 10:19 United States and of course Liberia); French flags have a 2:3 ratio (France, Italy, Cameroon, Ivory Coast, Algeria, Spain and the most of Latin-American flags); German flags have a 3:5 ratio; Moreover some nations have unusual ratios, as Denmark (28:37) or Belgium (13:15).

Alessio Bragadini

The British ensigns (including the Union Jack) ratio varied with the standard breadth of the textile industry, but always retaining a length of 18: Year Ratio of Length to Breadth 1687-17xx 11:18 17xx-1837 10:18 (5:9) 1837-present 9:18 (1:2) On the other hand, I'm not sure how strict this regulations would be followed in civilian rebellions taking place in faraway Australia, nor how fast they were enforced throughout the empire... I don't know at what point after 1837 the proportions were actually regulated. Possibly not until the reorganisation of Squadron colours in 1864.

David Prothero, 03 June 1999

The Golden Section

Many flags, picture frames, book covers, etc., are proportioned in accordance with what artists and mathematicians call "the golden section." This relationship exists when the length and width of a rectangle are divided into extreme and mean ratio, or when the parts follow (or approximate) the formula:

L² = W (L + W) Another way to look at it is if the length and width roughly equal 62 and 38 percent of their sum respectively.

Lou Stewart, 1998 January 30

If you solve the equation Lou Stewart gave analytically,

L * L = W * ( L + W ) you'll find a solution:

L = alpha * W where:

alpha = (1 + sqrt(5))/2 = 1.618… [sqrt being the square root] Mathematically, there's another solution to this equation, namely

alpha = -0.618… but I don't think we're looking for a flag with a negative length.

So, the ratio is 1.618…:1. This ratio was already known to the Greeks, and the Acropolis reflects this ratio in many ways (correct me if I'm wrong).

Filip Van Laenan, 1998 January 30

Let's try it this way:

the first format to think of is 1:1 (A:B), then we put the B as a new A, and A+B as a new B. So next we'll get 1:2, and next 2:3 and 3:5 and 5:8 and 8:13 and 13:21 and 21:34 and 34:55 and 55:89 and so on... We'll get closer and closer to 1.618 or something like that, the golden section. It has been used a lot in art and Kepler spoke of 'divina proportio'. It is mostly a proportion that 'looks nice'. Many mathematicians and physicists have written about it.

Ole Andersen, 1998 January 30

1.1618… is phi the golden ratio and is, like pi, irrational. However, if we look at the Fibonacci series we'll see that the difference between each number gets closer and closer to the ratio first over then under. The series is 1 1 2 3 5 8 13 21 ... where each number is the sum of the previous two. You will also note that the numbers are not far from many flag ratios 5:8 8:13 13:21 etc.

Rich Hansen, 1998 January 30

A more interesting approach uses the Golden Ratio's connection to the Fibonacci sequence: 1, 1, 2, 3, 5, 8, 13,…, in which each new member of the sequence is the sum of the preceding two. Then, you can generate successive (and closer) approximations to the Golden Ratio as 1/1, 2/1, 3/2, 5/3, 8/5, 13/8,... where the numerator is just the member of the sequence that is one ahead of the denominator. (The two... approximations above are derived from this method, just a bit further along in the sequence). An awful lot has been written about the Golden Ratio (also called 'The Divine Proportion'). It crops up in nature: shapes of shells, arrangements of sunflower seeds; in architecture (the most aesthetic shapes are ones having proportions equal to the Golden Ratio), and flags! It was known to the Ancient Greeks (look at a picture of the Parthenon), and probably earlier. Interesting it should show up in flag design too! anonymous, 1999 February 03 1999 February 03

At least one flag used the "golden proportions" as an integral part of its design: Saarland

Dave Martucci, 1998 January 30

No. There wasn't such flag manufactured in Saarland. I don't know where the document which mentioned this was to be found, but all the projects of laws of 1947 mentioned a flag with the proportions 1 x 1,5, not 1 x 1,61803398875. If such flag was proposed in Saarland, this was really absurd and ridiculous: how can you draw precisely such a flag, and above all how can you manufacture such a flag: it is impossible and not practical! If the flag existed it was only a proposition, not a real flag.

Pascal Vagnat, 1999 February 05

New Brunswick's isn't a national flag, but its 5:8 ratio is the closest approximation you can get to the golden ratio with one-digit numbers. The designer probably considered this when choosing the ratio. Any other flags with this ratio were probably designed with the golden ratio in mind.

Dean Tiegs, 1999 February 05

Artists Bruno Tuukkanen and Eero Snellman had the Golden Ratio in their mind when they designed the Finnish flag. Ratio 11:18 = 0.6111… which differs very little from 0.6180…

Ossi Raivio, 1999 February 06

Chuvash Republic - the designer of this flag artist Mr. E. Jurjev has specially made ratio of width and lengths of a flag as golden ratio.

Mikhail Revnivtsev, 12 August 2005

Vertical Proportions of Flags

The proportions of vertical stripes on French naval flag are 30:33:37, to enable good visual effect of flag when flying. Portugal, too, obviously, has an off-centered pattern and I suppose the Scandinavian cross flags have the same reason for the vertical bar shifted right.



Željko Heimer, 23 September 23 1995

Bangladesh, North Korea, Nauru, Turkey and the Japanese Ensign all shift their designs to the hoist. Whitney Smith's book mentions that Bangladesh does this so that the flag will look proper while flying. There is no reason given for the others and in the case of Nauru especially I suspect that the star is toward the hoist for some other reason.

Nathan Augustine, 27 September 1995

Why keep the right proportions?