The Picture Frame Mat Golden Ratio is an elusive, but very pleasing aesthetic feature, not infrequently mentioned or inquired by Customers during a picture framing consultation. An effective way to visually introduce and understand the Picture Frame Mat Golden Ratio concept is to refer to the three window matting examples illustrated below. Most Customers do not find the left window mat ( Ratio of 1.34 ), or right window mat ( Ratio of 2.95), as the nicest, or most pleasing ones. The majority seem to prefer and choose the middle window mat, which has the felicitous Ratio of 1.64 .

We might then ask, why is this so? The implicit reason of this is that the middle window mat ratio is the closest one to the Golden Ratio of 1.618. This ratio ( also known as the Golden Section, Golden Mean, Golden Number, Divine Proportion, Divine section, etc.,) has been known since antiquity. The Greek sculptor and mathematician Phidias (500 BC to 432 BC) is thought to have first recognized its value and used it in the design the sculptures for the Parthenon. Nevertheless and for the simpler purpose of this extract, we will simply say that the Golden Ratio is represented by the Greek letter Phi (Φ) and has a value of 1.618. It follows then, that the most pleasing window matting proportions will be those when the window mat is designed to have an area roughly being 1.6 times to that of the art, or image, being framed. To this end, the Window Mat Golden Ratio Calculator below can be used to calculate this ratio.

The Calculator below computes several useful geometric results. It also generates the Golden Ratio border widths of a window mat (or window mount). All inputs and outputs are in centimetres. Perhaps the most useful result, is the last one, the Golden Ratio, and also the actual width of the window mat’s sides.

Enter the image’s width cms and height (cms)

Golden Ratio Calculator Results Table

The perimeter of the image (without the window mat) is cms :

The surface area of the image (without the window) mat is cm2 :

The difference between the image’s area and the matted area is cm2 :

The matted image perimeter, with mat cut as shown below, is cms :

The total area of the matted image with the window mat is cm2 :

The Golden Ratio window mat width all around the image is cms :

PLEASE NOTE: All statements, contents and formulas herein are untested, unproven and theoretical in nature. We neither proffer nor assume responsibility or liability for any errors, inaccuracies or omissions. The information contained herein is published on an “as is” basis with no guarantees of completeness, or accuracy. There is no need to contact us inquiring as to additional or further development, updates, data, documentation, information, or support as none are available nor planned or envisaged for the future.

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