Figuring Out Numerals

  • Type Tips
Type Tips, Typography Basics | Yves Peters | September 25, 2011

A support request made me realize that we don’t really have an all-encompassing post to forward to users requesting information about figures. Figuring It Out: OSF, LF, and TF Explained, the very handy overview FontFont Marketing Director Ivo Gabrowitsch published here on The FontFeed is already three years old. How the different figures can be accessed is only briefly touched upon in my overview of basic OpenType features OpenType in Adobe Creative Suite – The Raiders of The Lost Glyphs Pt. 1. Still, there are gaps that warrant compiling and updating the information from these two posts. I want to make this as comprehensive as possible, so don’t hesitate to point out any aspect that may be missing.

Back in the days when the character sets of digital fonts were still limited to 256 glyphs, there was only room for one numeral set per font. The most common were tabular lining figures, and one had to use separate fonts – Expert sets and / or Small Caps & Oldstyle Figures fonts – to have access to proportional oldstyle figures. However since the advent of OpenType and the implementation of Unicode, professional fonts now include up to six sets of numerals, and sometimes even more.


Vertical measurements in the anatomy of a typeface.
Typeface: Tiina Professional

Because the different types of numerals are defined by their dimensions, I would like to start with a brief refresher course. The illustration above shows the vertical measurements in the anatomy of a typeface, which will be used in all the illustrations in this post. The baseline is the imaginary line upon which the letters in a font appear to rest. Please take note that ascenders often extend above the cap height, and small caps are typically a little larger than the x-height.

For a complete overview of terminology related to digital type, please refer to the Typographer’s Glossary.

Overview of the different figure styles


In professional OpenType fonts both lining figures (top row) and the oldstyle figures (bottom row) are available in tabular versions (left column) and proportional versions (right column).
Typeface: Tiina Professional

The two basic styles of numerals are the lining figures (top row) and the oldstyle figures (bottom row).
Lining figures rest on the baseline and all have the same height, usually as high as the capital letters. Numbers in selected text are switched automatically to their lining forms when applying the All Caps feature.
Oldstyle figures – sometimes called hanging figures – have different heights. Their “body” corresponds to the x-height of the lowercase letters (0,1,2), with certain numbers descending below the baseline (3,4,5,7,9), and others extending above the x-height (6,8). The design of oldstyle figures sometimes differs from their lining counterparts.

In professional OpenType fonts both lining and oldstyle figures are available in tabular versions (left column) and proportional versions (right column).
Tabular figures share identical character widths, as shown by the red divider lines in the left column. Because they all take up the exact same amount of space, numerals in subsequent lines of numbers neatly line up in vertical columns. This is especially useful for tables, thus “tabular” figures. To compensate for its narrow shape, sometimes foot serifs are added to the figure 1 (see illustration below).
Proportional figures are spaced according to their design; the spacing of the red divider lines varies. For instance, the space taken up by the figure 1 is narrow, and less wide than the space taken up by number 6. The design of proportional figures sometimes differs from their tabular counterparts.


The difference in spacing and design between proportional figures (left column) and tabular figures (right column).
Typeface: FF Sero

Beyond these two basic styles, each spaced in two different ways, there are two additional styles of smaller figures, primarily for use in mathematical and scientific applications.


Numerators and denominators (left) have a different vertical position than subscript and superscript figures (right).
Typeface: Tiina Professional

Although they may look identical, superscript & subscript figures (right) have a different vertical position than numerators & denominators (left). Because they are designed to be used in mathematics amongst others, these figure styles are usually tabular.
Superscript & subscript figures are centred against respectively the top of the lining figures (the cap height) and the baseline.
Numerators & denominators are vertically positioned in relation to the solidus. The top of the numerator aligns with the top of the lining figures (the cap height), while the denominator rests on the baseline.


Small caps figures are lining figures exactly as tall as the small caps in a typeface.
Typeface: Tiina Professional

Small caps figures, the last figure style, are lining figures exactly as tall as the small caps in a typeface (a little taller than the x-height).

The figure style you choose ought to be appropriate for the type of setting, with readability in mind. But which style is best for which purpose?

Tabular Lining Figures

Tabular lining figures line up neatly both horizontally and in vertical columns.
Typeface: Panno Text

Tabular lining figures are as tall as the capitals and have fixed widths. This makes them line up neatly both horizontally and in vertical columns. They are ideal for any tabular numeral material, ranging from simple number work and ordered lists over forms and prices in menus to complex financial tables in business reports – any situation where alignment is crucial.

Avoid using tabular lining figures in mixed case or lowercase setting as they stand out too much and distract the reader, or in uppercase display setting or headlines as the fixed widths produce irregular spacing.

Proportional Oldstyle Figures


The shapes and spacing of proportional oldstyle figures makes them perfectly harmonise with the surrounding text, preventing the numbers from standing out too much and distracting the reader. In this illustration superscript figures were used for the footnote indications.
Typeface: FF Spinoza

The “body” of proportional oldstyle figures corresponds with the x-height of the lowercase, with the upwards and downwards extenders mimicking the ascenders and descenders of the lowercase letters respectively. The proportional spacing gives the numbers an even colour which matches the text colour. These two characteristics makes proportional oldstyle figures perfectly harmonise with the surrounding text, preventing the numbers from standing out too much and distracting the reader. They are ideal for use in body copy in magazines, newspapers, books, and more generally for any type of running text in mixed case setting.

Avoid using proportional oldstyle figures in uppercase setting as they look too small, or in tables as the numbers won’t align horizontally nor line up in vertical columns.

Proportional Lining Figures


Proportional lining figures are to be used in uppercase setting, for example in headlines.
Body copy from Scott Creney’s terrific Nirvana’s Nevermind, 20 Years Later on Collapse Board.
Typeface: ARS Maquette

Proportional lining figures are also as tall as the capitals, but the proportional spacing produces an even colour which matches the text colour. They are ideal for use in uppercase display setting and headlines, as well as in abbreviations that mix capitals and numerals, like model numbers and so on.

Avoid using proportional lining figures in mixed case or lowercase setting as they stand out too much and distract the reader, or in tables as the numbers won’t line up in vertical columns.

Tabular Oldstyle Figures


Because they are monospaced, tabular oldstyle figures are ideal for setting phone and fax numbers on stationery, page numbers in tables of contents, and so on.
Typeface: FF Tundra

Tabular oldstyle figures also mimic the x-height, ascenders and descenders of the lowercase letters, but their fixed widths make them line up neatly in vertical columns. They are ideal for phone numbers on business cards and letterheads, numbered lists and tables of contents in books and catalogues, and in any situation where tabular material needs a little more refinement, a little more class.

Avoid using tabular oldstyle figures in uppercase setting as they look too small, or in running text as the fixed widths produce irregular spacing.

Small Cap Figures


Comparing oldstyle figures for mixed case setting, lining figures for all caps setting, and small cap figures for small caps setting.
Typeface: Fayon

Small cap figures are less common, yet are very useful in sophisticated typography and even indispensable in specific cases. Because they are exactly as tall as the small caps – which typically are a little taller than the x-height – numbers will nicely blend in in text set in small caps. Any numbers in selected text will be automatically converted to their small cap forms when applying the Small Caps or All Small Caps OpenType features.

If small cap figures are missing, always use oldstyle figures instead. Avoid using lining figures as they are too tall, which makes them stand out too much and distract the reader.

Superscript & Subscript


Examples of superscript and subscript: from left to right the formula for glucose, the atomic isotope uranium, and y raised to the fourth power.
Typeface: Fayon

Superscript and subscript are smaller in size and centred on respectively the cap line and the baseline. Perhaps the most familiar example of subscript figures is in chemical formulas, but they can also be used in other scientific settings and mathematics, as do superscript figures. Superscript figures are commonly used to indicate numbered footnotes.

Numerator & Denominator


Examples of numerators and denominators in fractions in a mathematical equation.
Typeface: Fayon

Numerators and denominators are a special kind of superscript and subscript figures. They are sized and positioned to be used in fractions. The top of the numerators align with the top of the solidus –  which corresponds with the cap height and the top of the lining figures –, while the denominators align with the bottom of the solidus which rests on the baseline. Applying the Numerator / Denominator OpenType feature on numbers separated by a slash will not only automatically convert the figure(s) before the slash into numerators and the figure(s) after the slash into denominators, but also the slash into a solidus.

How to access the specific figure sets

As the different figure sets are built-in as OpenType features, certain (older) operating systems and applications that don’t support these features will only be able to access the default figures. These default figures differ from foundry to foundry, from type designer to type designer. Some stick to the tabular lining figures that were the original default in the early PostScript days, others prefer the typographically sound proportional oldstyle variants. But you’re stuck with their choice.


The OpenType window in Adobe Illustrator CS4.


The OpenType fold-out menu in the Character window in Adobe InDesign CS4.

In OpenType fonts the different figure sets can be accessed in different ways.

The first one is to activate the corresponding OpenType features in the OpenType window in Adobe Illustrator, or in the OpenType fold-out menu in the Character window in Adobe InDesign. For the four basic styles – lining and oldstyle figures, both in tabular and proportional variants – this can be done by applying the desired style to whole blocks of text, because it doesn’t influence the appearance of any of the other characters. There is no need to select individual numbers and apply the styles to them separately. An even better approach is to include the appropriate figure styles in style sheets, also known as the Paragraph Styles and Character Styles in Adobe InDesign and Illustrator.

As they could affect other characters it is not a good idea to apply the Superscript / Subscript and Numerator / Denominator OpenType features to whole blocks of text or style sheets on a paragraph level, only on a character level. Remember to never use the Superscript and Subscript functions in the Character window, as these produce artificially scaled and repositioned figures. See OpenType in Adobe Creative Suite – The Raiders of The Lost Glyphs Pt. 1 for more information.

Small cap figures are a special case. Because they are specifically designed to only be used with small caps, they should always be applied in context, together with the surrounding text or incorporated in a style sheet.


The Character window with fold-out menu in Adobe Illustrator CS4.


The Character window with fold-out menu in Adobe InDesign CS4.

A different way to influence the appearance of the figures is by applying letter-oriented OpenType features to text. Selecting All Caps will override the formatting of any numbers and convert them to their lining variants. The tabular or proportional qualities of the figures are respected. Similarly, applying Small Caps or All Small Caps will override the formatting of any numbers and convert them to their small cap variants.


Selecting alternate glyphs for the numeral five in the Glyphs window.
Typeface: Fayon

The final option to select different figures sets is through the Glyphs window. Any glyph with alternates has a little fly-out arrow at the bottom right; clicking the glyph area and holding down the mouse button reveals alternates present in a one-to-one substitution feature. Thus clicking a figure will offer all the alternate forms for selection. As this needs to be done one figure at the time, this is a time-consuming procedure and thus not advisable.

Why tabular figures sometimes won’t line up in vertical columns

Applications like Adobe InDesign, Illustrator and Photoshop allow you to override the spacing and kerning of fonts. The default setting Metrics (Auto in Adobe Illustrator) in the Character menu uses the spacing and kerning as specified by the type designer or font engineer. This makes tabular figures all occupy the exact same width, as they are intended to do.

Another setting called Optical analyses the actual shapes of the characters and modifies the kerning accordingly, overriding both the spacing and the built-in kerning tables of the fonts in the process. Although Optical kerning is advertised to improve the setting of headlines and display type, the result can be quite arbitrary at times. The mathematical analysis of character shapes seldom measures up to the judgement of a trained eye. However it can be useful when combining letters of different fonts, or when the built-in kerning of the font is to be desired.


When tabular figures don’t line up in vertical columns, check if Kerning is set to Metrics (Auto in Adobe Illustrator) and not Optical.

Optical kerning will prevent tabular figures from lining up in vertical columns, as both spacing and (lack of) kerning are ignored, and the figures are spaced according to their character shapes. Always make sure to check if Kerning is set to Metrics (Auto in Adobe Illustrator). When in doubt and as a measure of last resort, set kerning to 0 for tabular figures.

Header image: Woodtype numerals by Youri Penders, DING Creative Studio

Tags: , ,

22 Comments:

  1. By far the best piece I’ve read on this topic, Yves.

    Posted by John Boardley on Sep. 25, 2011
  2. Other related things that might be worth mentioning:

    - Slashing the zero is another OpenType feature that is sometimes available. It might be useful to give advice on when that would be appropriate.

    - You see “three-quarter figures” here and there, too (e.g. H&FJ’s “short-lining figures” in Verlag).

    - The monoline style of oldstyle zero is a glyph that throws many people off when they take a closer look at figures.

    Posted by Craig Eliason on Sep. 25, 2011
  3. Thanks John, really appreciate this. : )

    Posted by Yves Peters on Sep. 25, 2011
  4. Good suggestions, Craig.

    I was hesitating to include the slashed zero/dotted zero as it is so specific for coding, so not really “mainstream” typography.

    Three-quarter figures are no OpenType feature, are they?

    Adding the monoline oldstyle zero might indeed be an idea.

    Posted by Yves Peters on Sep. 25, 2011
  5. No, not a separate OT feature as far as I know. In my example of Verlag, the default “short-lining figures” are triggered the same way you’d usually select oldstyle figures (sensibly, since you’d use them in the same situations you described using oldstyle figures above).

    Posted by Craig Eliason on Sep. 25, 2011
  6. I’ll add those, but then I have to add hybrid figures as well. Give me a moment.

    Posted by Yves Peters on Sep. 25, 2011
  7. Great article, Yves! This is something I’ve had on my list for a long time …

    One remark: Just as you show it, SC figures best fit “All Small Caps” setting, so I think the right way to access them in InDesign is via “OpenType > All Small Caps” rather than just “Small Caps”.

    Posted by Christoph on Sep. 26, 2011
  8. I don’t agree. Even if there’s the odd full-sized capital in a small caps setting I wouldn’t use lining figures, only small cap figures, or oldstyle figures if small cap versions are not present in the typeface. Is there a convention for this?

    Posted by Yves Peters on Sep. 26, 2011
  9. I don’t know any covention. But still, my opinion is:
    Mixed case letters (even if UC/sc) – mixed case numerals.
    Same with sc-punctuation, btw.

    Posted by Christoph on Sep. 26, 2011
  10. OK, I can agree to that, as long as lining figures are not used. But then it’s not logical that the Small Caps OpenType feature automatically converts any numbers to their small cap variants. This should be limited to only the All Small Caps feature.

    Posted by Yves Peters on Sep. 26, 2011
  11. very detailled and elaborate, yet succinct summary. thank you!

    Posted by Jo on Sep. 26, 2011
  12. Wonderful post. I think it will make a great education resource. One question regarding the sentence, “However it can be useful when combining letters of different fonts, or when the built-in kerning of the font is to be desired.” Does the “it” refer to Optical kerning? If so, doesn’t the Metrics option keep the built-in kerning for the font?

    Posted by Carina on Sep. 26, 2011
  13. “It” indeed refers to Optical kerning. Two adjacent characters from two different fonts will not kern properly, because the built-in kerning tables from one font will not apply to the other one. If for example you have a initial “T” at the start of a paragraph that is in a different font than the rest of the text, then the first letter after that initial won’t kern and there will be a big gap.

    Posted by Yves Peters on Sep. 26, 2011
  14. Just for the record, I am already working on a follow-up post which will include:
    • Hybrid Figures
    • ¾ Figures
    • Slashed/Dotted Zero
    • Monoline Oldstyle Zero
    Anything missing?

    Posted by Yves Peters on Sep. 26, 2011
  15. >> This should be limited to only the All Small Caps feature.

    That’s what we’re doing at FontFont.
    But the question of implementation is even trickier: If you choose Proportional Oldstyle and switch on All Small Caps, they’ll stay unchanged. The proportional Small Caps figures are only applied when Proportional Lining + All Small Caps are activated …

    Posted by Christoph on Sep. 27, 2011
  16. > Anything missing?

    Maybe include font families that have consistent figure widths across styles (weight duplexing)?
    If you want to complicate things further, you could explain Roman numerals!

    Posted by Florian on Sep. 27, 2011
  17. @Yves
    Excellent post.

    @Florian
    Compatible figures through weights (“duplexing”) is indeed an excellent topic as very handy for annual reports. Not all typefaces feature such things.

    I should add that some typefaces (as ours typofonderie.com) include compatible widths between figures, maths and some punctuation such .,;: + space, also useful for tabs.

    Posted by Jean F Porchez on Sep. 28, 2011
  18. > Avoid using proportional tabular lining figures in mixed case…
    An error? Very informative otherwise.

    Posted by Keyaar on Sep. 28, 2011
  19. Oops! Cut’n'paste snafu. Thanks for catching that, Keyaar! :-)

    Posted by Yves Peters on Sep. 28, 2011
  20. Nice, Yves.
    This was due for a fresh explanation.

    rich

    Posted by Richard Fink on Oct. 5, 2011
  21. This is very nice, Yves.

    I have one question about super/subscript and numerator/denominator numerals: why (or when) do they need to be tabular? I cannot come up with any usage where the alignment of these numerals are crucial. It makes some sense if the fractions are monospaced (also it would make much more sense if they are of the same width of the standard tabular numerals), but I don’t think the individual numbers need to be like that.

    It might be necessary for a mathematics font, but that’s a totally different story.

    Posted by Toshi Omagari on Nov. 16, 2011
  22. Very helpful. But Is there no way to set the figure style from Photoshop?

    Posted by Matt on Jan. 7, 2013

Post a comment:

  •  

The FontFeed

The FontFeed is a daily dispatch of recommended fonts, typography techniques, and inspirational examples of digital type at work in the real world. Eat up.

Archives

Subscribe

The FontFeed RSS The FontFeed Comments RSS