[css-values] Radians considered useless without π

[Crissov]

rad has been a valid angular unit since they have existed in CSS, but it never has been useful or widely used. A major reason for this, despite popular familiarity with degrees, is most probably that values in radians tend to be long floats with a single digit before the decimal marker and hence make authors feel unable to express definite values that won’t be rounded in an unexpected way. (Many intuitively expect decimal rounding, although it’s usually hexadecimal/binary.) This is due to a lack of the constant π in CSS.

Although a turn unit has already been defined, which equals 2π, I’d like to suggest another unit for radians muliplied by π: either pirad or just pi. It’s okay to defer it to the next level, although I believe it should already have been included in Level 2.

Length units may benefit from other irrational multipliers, e.g. √2, but there’s no obvious identifier comprised of only ASCII letters for them (unless you wanted 1sqrttwomm). We do have precedents for unit prefixes with dp…, ms and kHz (and if there was m, also mm and cm).

[tabatkins]

2pirad is just 1turn, right? I'm not sure that's worth including.

[Crissov]

Yes, like I said 1turn equals 2π and hence 1pirad = 0.5turn = 180deg = 200grad. Although halving or doubling may seem like really simple steps, they’re really about as complex as multiplication or division by 180 or 200 conceptually.

The idea and benefit of pirad is to be mixed with rad transparently, although it’s rare having to deal with an even radian value without π or 0 being a factor. It’s also simpler to relate to sources external to stylesheets where you may use the π symbol.

[prlbr]

2pirad is just 1turn, right? I'm not sure that's worth including.

Seems like τ-rebels can celebrate a victory then. :) Given that schools all over the world still teach that a unit circle’s circumference is 2π, including pirad would actually seem sensible though, if the idea in CSS was to start from where the people are. I bet something times π rad is used by magnitudes more often than, say, grad.

Personally, I’m fine with turn though. τ for the win.

[Crissov]

Yeah, if the proposal was to add an alias taurad or tau for turn I’d probably agree that it was overkill.

[tabatkins]

No, multiplication by 2 is substantially different than by 180 or 200. The size of numbers matters when doing mental math.

turn is already something we probably wouldn't add today; it's only in because somebody slid it in years ago and we all sorta implemented it. Just use tau radians (or pi diams) like math should have been. ^_^

[Crissov]

Do you have data for usage of rad (and turn), including frequent values?

[Crissov]

• In an ideal world,
  • all math would be using τ and hence CSS would be using tau (instead of turn and rad).
• In the real world,
  • professional math is using π together with (often implied) ‘rad’, while CSS is using explicit rad without π and, rarely, turn instead of tau, τ or 2π,
  • colloquial math is using ° and hence CSS is using deg (in addition to turn and rad).
• In @tabatkins’ conclusion, actual people should assume ideal math and apply it to actual CSS,
  i.e. τ = 1turn = 2π ≈ 6.283rad.
• In my conclusion, actual people should assume actual math and be able to apply it to actual CSS,
  i.e. π = 1pi (or 1pirad) = ½τ = 0.5turn ≈ 3.141rad, just like 1° = 1deg.