# Are there mathematical models behind Google material design metrics?

Google's Material Design guidelines such as Typography - Style - Google design guidelines or Metrics & keylines - Layout - Google design guidelines contains many ad hoc metrics for font sizing, spacing, margins etc.

I wonder if there are any mathematical patterns behind?

For instance, analysis of the proposed font sizes gives the following sequence of ratios (next font size divided by previous):

``````1.166, 1.143,  1.25,  1.2,  1.417,  1.323,  1.244,  2
``````

The ratios here fall (roughly) in the range of `1.14 - 1.42` (with the exception of the last one). This suggests there might be some fundamental value behind, such as the square root of golden ratio `1.27`.

Replacing all those ad hoc ratios by single consistent value would certainly simplify the whole system and make design calculations as well as any implementation much easier.

The same question goes for the layout sizes, the model here being clearly more complicated but not hopelessly impossible.

Are there reasons why the more verbose ad hoc system was preferred and whether using more consistent mathematical model would have had any downside?

• It's likely that the designers thought this ad hoc approach looked better than a fixed ratio across all sizes Commented Apr 25, 2016 at 3:59
• @ZachSaucier Are there evidences that small differences actually matter for the end user? And do they justify the much harder and costlier model? Commented Apr 25, 2016 at 4:28
• It does indeed look like a fixed ratio rounded to the nearest integer. As for why not just use decimal font sizes there are two reasons: 1, people just prefer integers and 2, some fonts are hand optimized (have hints) at certain font sizes and so far all of them are at integer font sizes. Commented Apr 25, 2016 at 4:46
• @slebetman 1: You can easily convert 1.25 into 125% to have integers.;) 2: Google's metrics are in "scaleable pixels" which are not real pixels and are meant to be scaled. I would also stay away from any font looking bad at different scales (if there are any) as it would make any scale change a nightmare. Commented Apr 25, 2016 at 6:01
• Yeah, but point 1 still stands: people prefer integers. I'm not saying the ratio is integer, it's obviously a fixed ratio of roughly 1.2. I'm saying people don't like the font size 14.4 so they just suggest 14. Commented Apr 25, 2016 at 6:30