Skip to main content
Search IntMath

Is she beautiful? The new Golden Ratio

By Murray Bourne, 16 Feb 2010

Canadian and US researchers found there were certain facial proportions that made some women more beautiful than others.

In the SMH article Shania Twain more beautiful than Angelina Jolie? we read the researchers manipulated the photos of certain women using Photoshop so the facial proportions were changed. Then warm-blooded males were asked to choose the photos that were most appealing. It turns out the "ideal" value (the one found to be more beautiful) for the following facial ratio was 36%:


Another key ratio affecting our perception of beauty is the following:


An ideal value for this ratio is 46%.

Apparently, the canadian singer Shania Twain has pretty much the perfect face. Let's check out her proportions. In this image, the eye to mouth distance is 72px, marking 36% of the facial height (200px).

shania twain

While the distance from her hairline to the bottom of her chin is quite easy to determine, and the center of the eyes is also quite clear, there is some uncertainty about the "mouth". In the above photo, she is smiling. Even with the mouth closed, it's not that exact where the "mouth" is.

Next, we look at the ratio of the distance betwen the eyes to facial width. The ratio 72:156 is equivalent to 46%, as claimed in the research.

shania twain

Once again, there is some ambiguity. What do we take as the "side" of the face? The article says the face width is the distance "between the inner edges of the ears". But it is rather subjective deciding quite where that comes.

A New Golden Ratio?

It is generally believed we are attracted to people whose physical features are symmetrical (a mirror image down the center) and in proportion. That proportion often turns out to be connected with the "Golden Ratio" (Φ = 1.618033...)

The above research claims to be a "new Golden Ratio" for determining beauty.

Comparison with Stephen Marquardt's Research

Stephen Marquardt has conducted similar studies to find the "beautiful" face. He has created a mask which can be placed over different faces to determine whether they fit the classic notions of beauty (at least from a mathematical point of view). The mask is based on the Golden Ratio (or more specifically, the "golden decagon".

Let's use his mask and measure the same ratios as used by the canadian/US researchers.


For the mouth-eyes to facial height ratio, we get 148:390 = 37.95%. This is greater than 36%, and possibly significant.

Now we look at the other ratio, eye distance to face width.


The ratio 138:279 = 49.5%. Once again, this is larger than the more recent research above, but it's not clear where the "inner edge of the ear" is for the Marquardt mask.


While the above is interesting mathematically, I wouldn't take it too seriously...

You may also be interested in: The Math Behind the Beauty.

[Image sources: Shania Twain, Marquardt mask]

See the 18 Comments below.

18 Comments on “Is she beautiful? The new Golden Ratio”

  1. hailegwergs says:

    hi dear your principle is i admire. but this golden ratio
    is this for only white peoples or for both black and white
    peoples of the world?
    thanks for your assistant(help me).

  2. Murray says:

    Hi Hailegwergs. The above article is based on experiments with white faces, but the proportions of Marquardt's mask apply for all races - and that's what makes it interesting.

  3. Katy says:

    I have to agree, she is pretty beautiful 🙂

  4. Junior says:

    i'm sure Shania is very beautiful!!! I love her face, her body too rss. Remember she is not just a pretty face rss.

  5. chysanthi says:

    hello! all these are very interesting but i'm a little bit comfused. Is any mathimatical operation tha could be applied to the face of anyone??? I mean a mathimatical operation like 2x2=4 or somethig like that? I need an examble in order to apply te golden ratio at anyone's face!!! thank you! (bb from Greece!!!)

  6. Murray says:

    Hello Chysanthi. This link may help:

  7. Emma says:

    Is it possible to find a place on the internet where you can test the mask on your own face?

  8. Murray says:

    Hi Emma. This is one of the enhancements I want to make to this page - when I have time!

  9. mariam says:

    how can you try this on your family

  10. Murray says:

    Hi Mariam. Hopefully coming soon on the Math of Beauty page.

  11. billyjean smith says:

    i would like to know how to mesure it in simple terms please if you could help me

  12. Joy saxena says:

    Its very beautiful system. I m tring most to get my ratio bt i m unable. I want to able.

  13. Miguel says:

    Hi, simmetry is also important, it is when the right side of the face is very similar to the left side. There maybe very small differences on each of us... and very, very small, on her, :). I agree that Eilleen aka Shania is such a very pretty woman.

  14. Gary says:

    The Canadian/US study was flawed in its conclusion that beauty can be reduced to simplistic measures and that the golden ratio of 1.618 is not a factor in beauty. See the page referenced in this comment, which reveals a dozen "old" golden ratios in the ideal facial model selected in their study and how their new ratios are incomplete.

  15. Murray says:

    @Gary: Your site was down when I tried to access the link.

  16. Gary Meisner says:

    Unusual for my site to be down. Please try again at Thanks!

  17. Murray says:

    @Gary - It seems fine now!

  18. ►Philosophy: “Beauty, according to Plato” / Mythology: “Some Greek Myths, based on Beauty”⭐ .- | La Audacia de Aquiles says:

    […] […]

Leave a comment

Comment Preview

HTML: You can use simple tags like <b>, <a href="...">, etc.

To enter math, you can can either:

  1. Use simple calculator-like input in the following format (surround your math in backticks, or qq on tablet or phone):
    `a^2 = sqrt(b^2 + c^2)`
    (See more on ASCIIMath syntax); or
  2. Use simple LaTeX in the following format. Surround your math with \( and \).
    \( \int g dx = \sqrt{\frac{a}{b}} \)
    (This is standard simple LaTeX.)

NOTE: You can mix both types of math entry in your comment.


Tips, tricks, lessons, and tutoring to help reduce test anxiety and move to the top of the class.