The Window Mat Golden Ratio Explained

Below are advice and information on the Golden Ratio of window mats. While we have tried to be as accurate as possible, no liability is assumed for any errors herein. It is the responsibility of users to ensure the correctness of all information. For help with orders, please visit our Store Help and FAQS page, or use our Contact page.

This is a question often asked by Customers during a picture framing consultation. A simple way to answer this is to refer to the window matting illustration below. Most people do not find the left window mat ( Ratio of 1.34 ),  or right window mat ( Ratio of 2.95), as the most pleasing one. The majority seem to choose the middle window mat ( Ratio of 1.64 ). And the reason why this is so is because  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.

The Calculator below computes several, useful geometric functions and their results, as well as generating the Golden Ratio border widths of a window mat (or window mount).  All inputs and outputs are in centimetres only. The most useful result, this being the actual width of the window mat's sides, is the last one in the results' rows.

  Enter the image's width and height   

Calculator Results Table

  The perimeter (sum of 4 sides) of the image (without the window mat) is:

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

  The perimeter of the image, with a mat cut by the Golden Ratio, is:

  The total area of the framed image with a Golden Ratio window mat is:

  The difference between the image's area and the area with the mat is:

  ∴ the width of the Golden Ratio window mat right around the image is:

Please note that the contents of and formulas in this page are theoretical in nature and that we assume no 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, accuracy, usefulness or timeliness.  No additional or further development, data, documentation, information, or support are available, planned or envisaged.