# Metric typographic units

Typography is an old art. Long before the introduction of the international standard system of units (“metric system”), printing equipment manufacturers all over the world have established a bewildering variety units to measure length, many of which continue to be used today:

• 1 point (Truchet) = 0.188 mm (obsolete today)
• 1 point (Didot) = 0.376 mm = 1/72 of a French royal inch (27.07 mm)
• 1 point (ATA) = 0.3514598 mm = 0.013837 inch
• 1 point (TeX) = 0.3514598035 mm = 1/72.27 inch
• 1 point (Postscript) = 0.3527777778 mm = 1/72 inch
• 1 point (l’Imprimerie nationale, IN) = 0.4 mm
• 1 pica (ATA) = 4.2175176 mm = 12 points (ATA)
• 1 pica (TeX) = 4.217517642 mm = 12 points (TeX)
• 1 pica (Postscript) = 4.233333333 mm = 12 points (Postscript)
• 1 cicero = 4.531 mm = 12 points (Didot)

The printing and publishing software market is at present dominated by manufacturers (Apple, Adobe, Microsoft, Quark, etc.) located in the United States, the last country on the planet that has yet to make significant progress towards the introduction of modern standard units. As a result, the use of standard units is far from well established in digital typography, to the significant annoyance of users all over the world.

The main problems are:

• The dominant unit of length, the Postscript point, has with 25.4/72 = 0.352777... mm a very inconvenient relationship to the most widely used length units (meter and millimeter).
• There exists no well-established practice for denoting a font size. [One example of a somewhat established convention is to specify the length of an “em” in PostScript points. Historically, the “em” was the width of the widest metal type in a font, which was for Roman fonts typically the capital letter “M”. Today, the control points of digital font outlines are stored in terms of coordinates inside a unit square. This square is a vague equivalent of the historic maximum metal type size and its side length has become the modern incarnation of the “em”. As a result, no easily measurable dimension in a text matches the point length that designates a font size]
• Resolutions of output devices are still frequently specified in dpi (dots per inch), which is the reciprocal value of the pixel size multiplied with 25.4 mm.

With the metric system, we have now a well established, consistent, and globally accepted set of length units, ranging from subatomic to cosmological dimensions. The use of archaic ad-hoc special purpose units has become obsolete and should be strongly discouraged.

It is time that the typographic community finally abandons its current unit mess in two ways:

• denote font sizes based on a measurable characteristic length of the printed glyphs

Metric typographic units are already used in Japan and to some degree in Germany and other European countries. However, the market dominance of US-originated typographic software without proper support for metric units at all levels currently hinders the further deployment of metric typographic practice.

The German draft standard DIN 16507-2 suggests that all length measurements in digital typography should be specified in millimeters. It suggests further that dimensions should be multiples of 0.25 mm, or where a finer resolution is required multiples of 0.1 or 0.05 mm.

No more points, picas, ciceros, inches, etc. and all their very inconvenient conversion factors.

Japanese typesetters use the unit Q (quarter) for font sizes, where 1 Q = 0.25 mm, i.e. the same modulus recommended by DIN 16507-2.

This measure nicely coincides with the most common pixel size on traditional computer monitors. For example a typical display area of 320×256 mm, divided into 1280×1024 pixels, makes each pixel 0.25 mm wide.

## Font sizes

### DIN 16507-2

This draft standard defines (among many others) the following two font measures:

Font size (German: Schriftgröße)
This is the baseline distance for which the font was designed. A font should normally be identified and selected by this size, because the intended baseline distance is much more relevant for practical layout work than the actual dimensions of certain characters.
Font height (German: Oberhöhe)
This is the height in mm of letters such as k or H. Typically, the font height is around 72% of the font size, but this is of course at the discretion of the font designer.

If we write say “Helvetica 5.0”, then this means we have a font that was designed for a 5 mm line spacing. It will typically have an H that is 3.6 mm or 10.2 points tall (72% of 5 mm). Calculations become trivial: in a 60 mm high column, we can write exactly 60 mm / 5 mm = 12 lines. The baselines of text become neatly aligned with a millimeter grid, and if millimeters are used to describe both font size and font height, their relationship becomes easier to handle than if different units such as mm and points were used. Layout designers do not have to juggle any more with conversion factors such as 72.27 and 25.4. If you write “Helvetica 5.00/5.25” then this means that you use exactly the same font as above, but with 0.25 mm more baseline skip than it was designed for.

DIN 16507-2 contains a list of preferred metric font sizes, together with the corresponding preferred 72% font heights in mm. The table below shows, in addition to these values from the standard, the corresponding preferred 72% font heights in Postscript points, for easier comparison with the old font sizes. Note: the point sizes of US fonts do not always refer to the k/H height that is defined by DIN as the font height. Some font manufacturers (e.g., Knuth) also refer to the size of taller characters such as “(”, so be careful not to convert incompatible measurements. Instead, try to find out the baseline distance for which a font was originally designed if you want to convert properly to metric sizes.

```    Font Size   Font Height    |   Font Size   Font Height
[mm]      [mm]  [pt]     |     [mm]      [mm]  [pt]
-----------------------------+----------------------------
1.5        1.1   3.1     |      6.0       4.3  12.2
1.75 	 1.3   3.6     |      7.0       5.0  14.3
2.0	 1.4   4.1     |      8.0       5.8  16.3
2.25	 1.6   4.6     |      9.0       6.5  18.4
2.5	 1.8   5.1     |     10.0       7.2  20.4
2.75	 2.0   5.6     |     12.0       8.6  24.5
3.0	 2.2   6.1     |     14.0      10.1  28.6
3.25	 2.3   6.6     |     16.0      11.5  32.7
3.5	 2.5   7.1     |     18.0      13.0  36.7
3.75	 2.7   7.7     |     20.0      14.4  40.8
4.0	 2.9   8.2     |     22.5      16.2  45.9
4.25	 3.1   8.7     |     25.0      18.0  51.0
4.5	 3.2   9.2     |     27.5      19.8  56.1
5.0	 3.6  10.2     |     30.0      21.6  61.2
5.5	 4.0  11.2     |     35.0      25.2  71.4
```

(The above mm values are from the old DIN 16507-2:1984-05 draft. If you implement metric font sizes, please make sure you get the latest version of the actual standard from DIN.)

Again: The font size refers to the baseline distance for which the font was designed, and is used to generally identify the font. The font height is the actual height of characters such as H or k. The font height is typically 72% of the font size as a preferred value, but this is of course left to the discretion of the font designer. One writes “Courier 6.0” to get the Courier font designed for 6 mm baseline distance (where the height of an H is typically 4.3 mm or 12.2 pt), and one writes “Courier 6.0/9.0” to get the same font but to use it with 50% more space between the lines.

### Other proposals

Authors such as (Ó Brógáin, 1983) argue instead that font sizes should be based on the x-height. This clearly has a number of advantages:
• The x-height can easily be measured directly in a sample printout and is not an invisible dimension found only in font data.
• Whether two fonts appear to have the same height is primarily determined by whether their x-heights match.
• The concept of x-height is also present in Greek and Cyrillic typography. Hebrew, Arabic and Devanagari glyphs can be aligned quite nicely with a Roman x-height, too.
• Recommended baseline distances are often related to the x-height (2 seems to be a very common factor), therefore using the x-height as a reference dimension will in practice often also lead to round measurements for the baseline distance.

Possible disadvantages of using the x-height as the reference dimension for denoting a font height might:

• In some applications (e.g., traffic and warning signs in some countries), text is commonly written uppercase only, or consists only of digits, so there are no visible lowercase letters as a measurement reference. However, the fonts used in these applications usually also include lowercase characters, therefore the x-height is always well-defined (except for some numeric-only displays such as 7-segment LEDs).
• Chinese characters are more easily aligned with the H-height of Roman characters. However, as East Asian fonts typically also contain Roman lowercase characters, the x-height is also well-defined here, too.

Draft proposals for an international standard on font sizes drawn up in the late 1970s were based on the height of capital letters and did not find international agreement.

Both x-height and the size of capital letters are attributes stored in existing font files, therefore scaling font sizes such that the x-height or H-height matches a specified length in millimeters is easy to implement on top of existing font-management mechanisms.

An idea that might at least be worth considering is to define a series of preferred sizes for fonts. Unlike the values given in DIN 16507-2, this could be a geometric series in which the quotient of neighboring sizes approximates a root of the square root of two. The international standard paper sizes were designed to be magnified and reduced by factors of sqrt(2) or sqrt(sqrt(2)), and for example standard technical drawing pen sizes follow the same progression. Such a series of standard font sizes could either be designated in a millimeter length and made available via pull-down menus, or it could be designated by an index number, as is already done for ISO paper sizes.

## Metric device resolutions

Instead of giving a reciprocal pixel size in dpi, it would be much more convenient to specify the pixel size directly in micrometers, as it is also common practice in the semiconductor industry.

The following table shows a few commonly used typesetting resolutions in both µm and dpi:

 µm dpi 10 20 21.2 40 42.3 80 84.7 100 250 254 2540 1270 1200 635 600 317 300 254 102 100

So far, phototypesetters have traditionally used metric resolutions (with 10 µm = 2540 dpi being most common one), while laser and inkjet office printers currently still mostly have inch-based resolutions.

## Metric modes in layout software

While US-originated typographic software frequently does allow to switch into some sort of metric mode, these metric modes usually have lots of loose ends and were obviously never used in daily work by their developers. Add-on metric modes often suffer from bizarre rounding bugs (you enter 210 mm and always get ugly 209.902777 mm displayed, alignments on metric grids do not work out, startup defaults are often fixed to US units, etc.), and the metric support stops at critical details like the font or pixel size, such that in the end metric users still have to constantly convert between millimeters, points, inches, and 1/inches. US developers should realize that over 95% of the world population grew up using the metric system and that it is therefore prudent to design a system today from the very lowest level up purely in metric units. Conversion to archaic units like the inch and the various points should only be an add-on feature in the user interface on top of an underlying purely metric architecture, and not the other way round.

One font handling system design that got things right is the W3C’s CSS2 specification. Here, a DIN 16507-2 font description of the form “Helvetica 4.0/4.5” can directly be written as

```  P { font: 4mm/4.5mm "Helvetica" }
```

Also the ISO 9541 font file format uses millimeters to denote font design sizes (see ISO/IEC 9541-1:1991, section 8.6.17).

## Literature

The titles of some relevant DIN, BSI and ISO standards are

• DIN 16507-1, Ausgabe: 1998-09, Drucktechnik – Schriftgrößen, Maße und Begriffe - Teil 1: Bleisatz und verwandte Techniken
• DIN 16507-2, Ausgabe: 1999-05, Drucktechnik – Schriftgrößen – Teil 2: Digitaler Satz und verwandte Techniken
• BS 4786:1972, Specification for metric typographic measurement (withdrawn)
• ISO/IEC 9541-1:1991, Information technology — Font information interchange — Part 1: Architecture.

Unfortunately, the DIN standards on metric typography seems to be available at the moment only in German. I hope that a standardization group such as ISO/TC130 will eventually set up a very similar international guideline for the use of metric font sizes.

Further literature:

I wish to thank Karlsson Kent and Jörg Knappen for providing valuable information for this text. Comments and suggestions for improvement are always welcome!

You might also be interested in the International Standard Paper Sizes Web page.