Page margins in principle and practice

Imagine a book with no page margins. The text runs right to the edge of the paper. You’ll have to crack the spine to gain access to characters in the gutter. To access the text at the bottom, you have to move your thumbs our of the way. If the book is a little old, the characters on the outside may be worn off entirely. No header or footer is present, so navigation is a task. To make a note on something you find, you’ll have to write it between the lines. We haven’t even mentioned the fact that the book looks horrible, or has forced the publisher through hoops to produce the book in full bleed.

The margin, then, is an essential element of all paged media. It solves all the horrors above: spinal injuries are greatly reduced; the closed book when dropped has its content protected by a chunk of wood; you can hold it comfortably; page numbers and section titles guide you around; you have space for marginalian comments; the composition is pleasing; and ‘printing on the edge’ is no longer an issue (you can’t do it with your home printer).

Competing rationales

So margins are a Good Thing. In implementing them, though, we’ll have to be more specific: how big should the four margins (top, bottom, inside, outside) be, given the size of the book?

This simple question doesn’t have a simple answer. The big reason for this is competing rationales; for each design consideration there is a different optimum:

Goal	Ideal margin appearance
Save the book’s spine	Give precedence to the inside margin, especially in fat books.
Blank space for holding the book	Precedence to the bottom and outside margins.
Wear does not affect book content	Precedence equally to all but the inside margin, which doesn’t wear.
Navigation is easy	Precedence to the top and bottom margins.
Ample space for reader’s notes	Precedence to outside margin.
Pleasing composition	Printed area vertices lie on page “ley lines”; geometrical ratios.
Don’t require print bleed	At least 5mm on all margins.

So different goals are pushing in different, sometimes opposite, directions. Some goals are independent of the page area; some are not. Some are independent of page ratio, others not. Some are dependent on book length, others not, and so on.

Canons of page construction

Let’s begin with the most complex of the design goals: pleasing composition. Wikipedia calls these considerations the canons of page construction. The geometrical means of constructing an ideal page seem surprisingly long-standing and agreed upon. Surprisingly, though, I couldn’t find implemented algorithms online, so over at github I’m hosting a small library I’ve written for this article.

The first principle is that some ratios are better than others. These ratios should be applied both to the page and to the printable area. The less ratios in the composition, the letter. They are:

• 2 : 3
• 1 : φ (the golden ratio)
• 1 : √2 (the ratio governing A3, A4, A5 paper, etc.)

The second principle is that the rectangle defining the printable area should have vertices that lie on what I would call “ley lines”. If you have a two-page spread in front of you, these lines are those you can draw between five vertices: the four corners of the book plus the top of the gutter.

A third principle, not always applied, is that the print width should be the same as the page height.

A few different methods exist over at Wikipedia, aiming for the above goals. Most actually boil down to the same result: the Van de Graaf canon.  This is the most general algorithm, and the two other main methods obtain the same result when the page ratio is 2 : 3.  I’ll let you judge for yourself whether the results are pleasing. In order of decreasing page height, these are outputs from my above script:

The Van de Graaf Canon at 1:φ page ratio

The Van de Graaf Canon at 2:3 page ratio

The Van de Graaf Canon at 1: √2 page ratio

The Van de Graaf Canon at 1:1 page ratio

The Van de Graaf Canon at 2:3 page ratio

Let’s say you agree with me that the above are beautiful.  Note that, looking at the right-hand page:

• the printed area is the same shape as the page area
• the top left and bottom right vertices of the printed area lie on the diagonal of the right-hand page
• the top right vertex of the print area lies on the diagonal of the two-page spread
• the gutter margins together are the same width as an outer margin

Meditation on the Van de Graaf

I would guess that your first thought after looking at these (other than that they’re attractive), is that they are so liberal in their use of space.  I would secondly guess that your thinking that derives from experience: have you ever seen a bottom margin as big as that on the 1:φ ratio?  Why not?  The answer lies firstly in the competing rationales above, and secondly in more rationales, aiming to reduce margins to nothing, that I now list here:

• Spend less on paper. Paper margins and profit margins aren’t friends.
• Save trees. Publishers and consumers alike are conscious of the environment.
• Save space and weight. Less margin means paying for less shelf space at the bookshop.  Volume and weight could be halved, which reduces transportation costs for the publisher and consumer (you’re travelling with your Comprehensive Travel Guide to Asia; decide between buying the Van de Graaf edition, or buying a zero-margin copy letting you squeeze another pastel-coloured holiday novel in your suitcase).

Data-gathering

I’ve got about as far as I can with theory.  I decided at this point to take some measurements of some books on my shelf.  (The data from my twenty samples is in an OO spreadsheet in the about git repo.)  Here’s some summary findings:

• Books, and the printable area, are taller and thinner than Jan Tischichold’s use of the 2:3 ratio.  The average is 2:3.1 for page size, and 2:3.3 for printable area — hovering around 1:φ but not hitting it.
• The printable area was invariably taller and thinner than the page area, compared to the constant ration of the Van de Graaf.
• Publishers can’t decide between bigger outside margins (space for comments, &c.) and bigger inside margins (saving cracked spines).  On average, the ratio of inside to outside was 1:1, but few or not hit that deliberately.

The Typography of Discworld

I found many page constructions that were unappealing, niggardly, and un-functional.  However, I did come across a few that were not.  One neat one is in the Corgi editions of Terry Pratchett’s Discworld books.  The construction is as follows.

Draw the diagonals of the full-page spread.  Next draw the ‘V’-shape as in the Van de Graaf, but upside-down.  Mark the verticals at the intersections (thus dividing the spread into three equal slices, as in the Van de Graaf).  Draw diagonals from the intersections to the bottom of the vertical on the opposite page.  The new intersections are the inside bottom of the printable areas.  Draw two more diagonals, from the top of the verticals to the outside bottom corners of the same page.  From the two known printable area vertices, draw horizontally; the intersection at the new diagonal is the outside bottom of the printable area.  Finally, draw vertically until you hit the ‘V’; this marks the top of the printable area.  Look at it:

Geometrically constructing the page of a Corgi Discworld book (my image)

Constructing the Van de Graaf canon on the same page spread

The Discworld canon certainly looks similar in geometric spirit, but they are dissimilar in other ways.  The Discworld gives you more page area (66% compared to 44%).  It throws most of the outside margin away, disregarding the aesthetic principle that the gutter width should be the same as one outside margin.  Take a look at it on the same page ratios I used earlier:

The Discworld canon at 1:φ ratio

The Discworld canon at 2:3

Discworld canon at 1:√2

Discworld canon at 1:1

Discworld canon at 3:2

Word processors, and designing a single-page canon

How do today’s word processors implement page margins? The first thing to note is that, by default, all pages are symmetrical: there’s no such thing as left and right pages. Considering that its output will most likely be unbound A4 from a home printer, this makes sense.

Specifically, the following margins are set by default (My figures for Word are based on Google; I don’t have access to an installation myself):

Word processor	Top margin	Bottom margin	Inside margin	Outside margin
Microsoft Word	1″	1″	1.25″	1.25″
OpenOffice Writer	20mm	20mm	20mm	20mm

How were these figures decided upon?  My guess is that foremost they’re fetishes for an individual measurement system: Word the imperial, Writer the metric.  Neither seems to be a good basis for a sensible default.  For example, when working with an A4 page, in which the long side is an irrational figure (210mm × √2), we would expect irrational figures for the margins, too.  Word’s decision to go for larger side margins than end margins is especially odd; my survey above put side margins at 60% of end margins.

First attempt at a single-page canon

The reason that word processors don’t have agreed sensible margins is that, seemingly, no canon has been designed for pages that are not part of a two-page spread.  So, why not use our principles from above to create one?  Let’s proceed:

1. We this time only work with four starting vertices: the four corners of a rectangle.
2. There are only two ‘ley lines’: the diagonals from one corner to its opposing corner.
3. We can (and so will) place the printable area’s vertices on these leylines.
4. The less ratios, the better: let’s use the page ratio for the printable area ratio.  (So far is equivalent to a scaling-down of the page rectangle on its centre.  We just need one principle to fix the scale…)
5. The printable height is equal to the page width.

We end up with the following:

The naïve single-page canon

The naïve single-page canon at 2:3

Lovely!  We’ve just bettered the two biggest word processing packages!  Or have we …

Naïve single-page canon at 1:2. Only 25% of the page used.

Naïve single-page canon at 1:1. 100% of the page used!

Naïve single-page canon at 3:2. A full 225% of the page used!

A successful single-page canon: the Double-Circle

Working on a 2:3-ratio sheet, I disregarded the other possibilities.  The naïve canon above varies the printable area wildly with the page ratio, and it won’t do.  We need one that produces sensible results for all page shapes: tall, square, and fat.  I’ve developed one that does so, and I call it the Double-Circle Canon.  Here it is:

Double-Circle canon at 2:3

And, as before, let’s see it in action:

The Double-Circle canon at 1:φ

The Double-Circle canon at 2:3

The Double-Circle canon at 1:√2

The Double-Circle canon at 1:1

The Double-Circle canon at 3:2

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