![]() A given C sheet size should be the geometric mean between its corresponding A and B sizes. That is, √(841*594)=707mm.Ĭ series sheets are meant for envelopes for A sheets, that is, a C4 envelope should be able to hold an A4 sheet without having to fold anything. For example, B1’s height will be the geometric mean between the heights of A0 and A1. You can also verify these values as geometric means. ![]() The height of the previous size is now halved. We can now work our way down the remaining A sizes.Īs illustrated earlier, the width of the previous size becomes the height of the next size. If we halve an A1, we get an A2, and so on. Other A sheet sizesĪt this point it should be pretty obvious: if we cut an A0 in half, we get an A1. If you multiply these however, you will get 999,949 which isn’t exactly 1m 2 - this is due to the rounding necessary for instruments involved in the manufacturing and measuring process. The answer - an A0 sheet is 0.841m wide and 1.189m tall.Īs defined by the standard it’s 841mm x 1189mm. That gives us the convenient formula x*y=1, and we can start substituting x as 1/y and y as 1/x in the above ratio. The A0 size has an additional property, which is: Within each series, the 0 size is the starting point, which is why we’ll start at size A0, as the B and C series definitions depend on it. The ratio of height to width of a standard sheet of paper is √2, or 1.414… Calculate the size of an A0 sheet Or in simplest terms, the ratio x÷y = √2. Move the x and y across the equal sign, and we get: And remember that the ratio must be maintained. Given a sheet with x height and y width, the next size down results in a ‘new’ sheet with y height and x/2 width. Using the above image as reference, we can now calculate the ratio of an A0 paper. Maintain ratio while folding Calculate the ratio That new height and width should have the same ratio as the original piece of paper. It is cut width-wise, and one half is discarded. To illustrate this principle, in the image below, we take a sheet of paper with height x and width y. Once we have that ratio, we can also figure out the actual sheet sizes for the different series. Using just this statement we can figure out the required aspect ratio. When a sheet is cut in half (by width), the aspect ratio should be maintained The single underlying premise for any standard paper size is extremely simple: They are quite intuitive and easy to work with and are based on good mathematical foundations. The well known A, B, C series paper sizes may seem arbitrary at first glance, but they are actually based on some simple basic principles which make it easy to calculate and understand. Standard paper sizes are an elegant example of simple maths Mendhak / Code Standard paper sizes are an elegant example of simple maths
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