# Why 'h' for Planck's constant? **URL:** \ **Category:** Factual Questions\ **Created:** [May 26, 2010, 12:18am UTC](https://boards.straightdope.com/t/why-h-for-plancks-constant/540768 "2010-05-26T00:18:52Z")\ **Posts on this page:** 20\ **Page:** 1
**Author:** ![Pacomalino](https://avatars.discourse-cdn.com/v4/letter/p/db5fbb/32.png) [@Pacomalino](https://boards.straightdope.com/u/Pacomalino)\ **Post date:** [May 26, 2010, 12:18am UTC](https://boards.straightdope.com/t/why-h-for-plancks-constant/540768/1 "2010-05-26T00:18:52Z")
I’ve wondered for a long time why Planck’s constant is called, ‘h’. I know, as a physics guy, Planck is going to be all into the math. Clever reasoning in letter selection for a constant is probably not something Planck would focus on. He studied with Helmholtz, and Hermes is a speedy god, but it just doesn’t seem like Planck would waste his time with this sort of planning for his constant’s name. I don’t know German. Maybe a german word starting with ‘h’ is behind this? Could it be just a random letter he chose? Thanks for your consideration. ---
**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\ **Post date:** [May 26, 2010, 2:56am UTC](https://boards.straightdope.com/t/why-h-for-plancks-constant/540768/2 "2010-05-26T02:56:33Z")
Here’s my guess, backed up with absolutely no citations. Planck needed a symbol for a constant of proportionality, but _k_ was taken by Boltzmann’s constant (German: “konstant”). _h_ is nearby, distinct, and unused (contrast _i_ and _l_). I doubt it came from any particular word. Indeed, there was no good physical interpretation of _h_ when it was first written down. ---
**Author:** ![DHMO](https://avatars.discourse-cdn.com/v4/letter/d/ecc23a/32.png) [@DHMO](https://boards.straightdope.com/u/DHMO)\ **Post date:** [May 26, 2010, 4:46am UTC](https://boards.straightdope.com/t/why-h-for-plancks-constant/540768/3 "2010-05-26T04:46:07Z")
From the Wiki page for Planck’s constant, > **[Planck constant](https://en.wikipedia.org/wiki/Planck_constant)** > > The Planck constant, or Planck's constant, denoted by > > > > h > > > {\\displaystyle h} > > , is a fundamental physical constant of foundational importance in quantum mechanics: a photon's energy is equal to its frequency multiplied by the Planck constant, and a particle's momentum is equal to the wavenumber of the associated matter wave (the reciprocal of its wavelength) multiplied by the Planck constant. > The constant was postulated by Max Planck in 1900 as a proportion... it would be reasonable to conjecture that “h” represents the “harmonic oscillator”. > [@](#): > > Planck hypothesized that the equations of motion for light are a set of [harmonic oscillators](http://en.wikipedia.org/wiki/Harmonic_oscillator), one for each possible frequency. He examined how the [entropy](http://en.wikipedia.org/wiki/Entropy) of the oscillators varied with the temperature of the body, trying to match Wien’s law, and was able to derive an approximate mathematical function for black-body spectrum… > [@](#): > > …the “energy element” must be proportional to the frequency of the oscillator, the first version of what is now termed “Planck’s relation”: > E = hv > > [http://upload.wikimedia.org/math/9/5/9/9594901b51008ac92c2709a69122a120.png](http://upload.wikimedia.org/math/9/5/9/9594901b51008ac92c2709a69122a120.png) ---
**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\ **Post date:** [May 26, 2010, 1:00pm UTC](https://boards.straightdope.com/t/why-h-for-plancks-constant/540768/4 "2010-05-26T13:00:38Z")
[This paper](http://arxiv.org/pdf/physics/0402064) claims that Planck used _h_ for the German word _Hilfsgrösse_. My German is nicht sie gut, but as far as I can tell this means “auxiliary quantity”. ---
**Author:** ![Pasta](https://avatars.discourse-cdn.com/v4/letter/p/ecccb3/32.png) [@Pasta](https://boards.straightdope.com/u/Pasta)\ **Post date:** [May 26, 2010, 6:40pm UTC](https://boards.straightdope.com/t/why-h-for-plancks-constant/540768/5 "2010-05-26T18:40:50Z")
> [@](#): > > This paper claims that Planck used _h_ for the German word _Hilfsgrösse_. My German is nicht sie gut, but as far as I can tell this means “auxiliary quantity”. Good find. It would be interesting to see if anyone can find an independent mention of this etymology. The citation given in that unrefereed document doesn’t warm the heart with confidence: > [@the paper](#): > > I owe this remark to M. F. Ranada (Zaragoza). Who? A quote from Planck himself (or perhaps one of Planck’s contemporaries) might be required on this one (at least for me to believe it)… ---
**Author:** ![EinsteinsHund](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/einsteinshund/32/8400_2.png) [@EinsteinsHund](https://boards.straightdope.com/u/EinsteinsHund)\ **Post date:** [May 26, 2010, 6:55pm UTC](https://boards.straightdope.com/t/why-h-for-plancks-constant/540768/6 "2010-05-26T18:55:18Z")
This is a quote from the German [Wikipedia](http://de.wikipedia.org/wiki/Plancksches_Wirkungsquantum): > [@](#): > > Max Planck führte die Konstante h (von Hilfsgröße) im Jahr 1900 … ein which translates to: Max Planck introduced the constant h (from _Hilfsgröße_) in 1900 … No direct quote from Max Planck himself, but maybe a little more confirmation for the origin. ---
**Author:** ![naita](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/naita/32/5862_2.png) [@naita](https://boards.straightdope.com/u/naita)\ **Post date:** [May 27, 2010, 7:37am UTC](https://boards.straightdope.com/t/why-h-for-plancks-constant/540768/7 "2010-05-27T07:37:21Z")
> [@EinsteinsHund](#): > > This is a quote from the German [Wikipedia](http://de.wikipedia.org/wiki/Plancksches_Wirkungsquantum): > which translates to: Max Planck introduced the constant h (from _Hilfsgröße_) in 1900 … > > No direct quote from Max Planck himself, but maybe a little more confirmation for the origin. The cite for that whole sentence is Planck’s orignal presentation which seems to available here: [http://www.christoph.mettenheim.de/planck-energieverteilung.pdf](http://www.christoph.mettenheim.de/planck-energieverteilung.pdf) As far as I can determine from a quick browse, Planck in no way mentions any reasoning for chosing the letter h, but just introduces it as a natural constant fitting the formula. But my German is rusty and it was a quick browse, so I might have missed something. ---
**Author:** ![UDS](https://avatars.discourse-cdn.com/v4/letter/u/ecae2f/32.png) [@UDS](https://boards.straightdope.com/u/UDS)\ **Post date:** [May 27, 2010, 7:53am UTC](https://boards.straightdope.com/t/why-h-for-plancks-constant/540768/8 "2010-05-27T07:53:50Z")
A google search for _Hilfsgröße Planck_ yields 1,330 results, most of them - unsurprisingly - in German. My German is not good, but from the snippets on the first couple of pages of search results, most of them seem to be affirming that this is the etymology of ‘h’. So it seems that this understanding is at least widespread. ---
**Author:** ![BigT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bigt/32/12044_2.png) [@BigT](https://boards.straightdope.com/u/BigT)\ **Post date:** [May 27, 2010, 9:19am UTC](https://boards.straightdope.com/t/why-h-for-plancks-constant/540768/9 "2010-05-27T09:19:13Z")
> [@UDS](#): > > A google search for _Hilfsgröße Planck_ yields 1,330 results, most of them - unsurprisingly - in German. My German is not good, but from the snippets on the first couple of pages of search results, most of them seem to be affirming that this is the etymology of ‘h’. So it seems that this understanding is at least widespread. Of course, if you used another word, and got even more results (1,330 is piddly on Google), that might be better. I used the “English Only” feature, and I found the 34 results agreed, but that is definitely a small number. ---
**Author:** ![Normm](https://avatars.discourse-cdn.com/v4/letter/n/59ef9b/32.png) [@Normm](https://boards.straightdope.com/u/Normm)\ **Post date:** [November 29, 2011, 8:08pm UTC](https://boards.straightdope.com/t/why-h-for-plancks-constant/540768/10 "2011-11-29T20:08:14Z")
> [@Pacomalino](#): > > I’ve wondered for a long time why Planck’s constant is called, ‘h’. Apparently Planck used the letter “b” in his paper. So it could have been German physicists that decided that “h” was a good choice. But I thought it was because mathematicians like to use the letter “h” for the small quantity in limits (since at least Cauchy). In Planck’s analysis “h” was supposed to go to zero in the limit, but instead a finite value corresponded to physical reality. Now why Cauchy chose “h” I don’t know. Presumably it corresponds to some word in French or Latin. ---
**Author:** ![IAmBroom](https://avatars.discourse-cdn.com/v4/letter/i/977dab/32.png) [@IAmBroom](https://boards.straightdope.com/u/IAmBroom)\ **Post date:** [March 8, 2012, 6:31pm UTC](https://boards.straightdope.com/t/why-h-for-plancks-constant/540768/11 "2012-03-08T18:31:54Z")
(deleted) ---
**Author:** ![IAmBroom](https://avatars.discourse-cdn.com/v4/letter/i/977dab/32.png) [@IAmBroom](https://boards.straightdope.com/u/IAmBroom)\ **Post date:** [March 8, 2012, 6:35pm UTC](https://boards.straightdope.com/t/why-h-for-plancks-constant/540768/12 "2012-03-08T18:35:21Z")
[According to Wikipedia](http://en.wikipedia.org/wiki/Planck_constant), the ‘h’ refers to the initial of the man who first predicted it in 1860: Robert Baldwin Hayword. Planck was the first to determine its value, 40 years later. ---
**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\ **Post date:** [March 8, 2012, 7:23pm UTC](https://boards.straightdope.com/t/why-h-for-plancks-constant/540768/13 "2012-03-08T19:23:38Z")
While I’m not discounting this possibility, I find it a little suspicious that this statement about Mr. Hayward was only added to the Wikipedia article [earlier today](http://en.wikipedia.org/w/index.php?title=Planck_constant&diff=prev&oldid=480813751), without any citation. I’ll dig around online a little more and see if I can find any proof of it, though. ETA: The same wiki user also added this claim to the page on [areal momentum](http://en.wikipedia.org/w/index.php?title=Specific_relative_angular_momentum&diff=next&oldid=480810250). There’s a citation there, which I’m looking over now. ---
**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\ **Post date:** [March 8, 2012, 7:42pm UTC](https://boards.straightdope.com/t/why-h-for-plancks-constant/540768/14 "2012-03-08T19:42:22Z")
The citation in the “areal momentum” article just talks about angular momentum; it seems to only be a coincidence that Hayward used the symbol _h_ to denote it, and it’s fairly clear that he viewed _h_ (the angular momentum as a continuous quantity rather than a discrete one (since he takes derivatives with respect to it. Moreover, Planck’s initial paper had nothing to do with angular momentum; he was concerned with the energies of oscillators in a blackbody. All in all, I remain unconvinced that Hayward had anything to do with Planck’s constant as we understand it today. ---
**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\ **Post date:** [March 8, 2012, 7:57pm UTC](https://boards.straightdope.com/t/why-h-for-plancks-constant/540768/15 "2012-03-08T19:57:37Z")
> [@MikeS](#): > > All in all, I remain unconvinced that Hayward had anything to do with Planck’s constant as we understand it today. Looking at [the talk page for Planck’s constant](http://en.wikipedia.org/wiki/Talk:Planck_constant#Verging_on_an_edit_war), it seems that I’m not the only one who is unconvinced. (For the record, I’m “Johnny Assay” over there.) ---
**Author:** ![IAmBroom](https://avatars.discourse-cdn.com/v4/letter/i/977dab/32.png) [@IAmBroom](https://boards.straightdope.com/u/IAmBroom)\ **Post date:** [March 9, 2012, 1:52pm UTC](https://boards.straightdope.com/t/why-h-for-plancks-constant/540768/16 "2012-03-09T13:52:31Z")
> [@MikeS](#): > > While I’m not discounting this possibility, I find it a little suspicious that this statement about Mr. Hayward was only added to the Wikipedia article [earlier today](http://en.wikipedia.org/w/index.php?title=Planck_constant&diff=prev&oldid=480813751), without any citation. Wow… Yep, I understand your suspicion, but for the record: I haven’t edited that page, nor did I know of this. Giving my Wikipedia login (my real name) wouldn’t help, since there’s sock-puppet accusations afloat now… Anyway, that _was_ weird timing. I got to this page, and thence that article, from a recent article about an experiment that (supposedly) validated a new (2003) formulation of the Heisenberg Uncertainty Formula. Naturally, I can’t find the damned article _now_, but [here’s a reference](http://physicsworld.com/cws/article/news/48378)to the reformulation. What continues to boggle my mind is that there’s a sudden edit storm on Wikipedia (nothing odd yet…) about the HUP (OK, a bit odd) the very day I cite it. :smack: Honest, I didn’t do it! ☹ ---
**Author:** ![IAmBroom](https://avatars.discourse-cdn.com/v4/letter/i/977dab/32.png) [@IAmBroom](https://boards.straightdope.com/u/IAmBroom)\ **Post date:** [March 9, 2012, 2:05pm UTC](https://boards.straightdope.com/t/why-h-for-plancks-constant/540768/17 "2012-03-09T14:05:31Z")
And, for the record, the 2003 reformulation was by Masanao Ozawa, and not this [nutbag](http://forums.macrumors.com/archive/index.php/t-98198): [BinXin Gong](http://theoryandscience.icaap.org/content/vol004.002/13_letter_gong.html). Ozawa’s team’s experiment paper is [here](http://www.nature.com/nphys/journal/vaop/ncurrent/abs/nphys2194.html) (paywall). ---
**Author:** ![MikeS](https://avatars.discourse-cdn.com/v4/letter/m/919ad9/32.png) [@MikeS](https://boards.straightdope.com/u/MikeS)\ **Post date:** [March 9, 2012, 9:26pm UTC](https://boards.straightdope.com/t/why-h-for-plancks-constant/540768/18 "2012-03-09T21:26:24Z")
No worries, I believe you that it was just a strange coincidence. In any event, it drew additional eyes to the article, and so it got corrected more quickly. ---
**Author:** ![John\_Mace](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/john_mace/32/185_2.png) [@John\_Mace](https://boards.straightdope.com/u/John_Mace)\ **Post date:** [March 9, 2012, 10:20pm UTC](https://boards.straightdope.com/t/why-h-for-plancks-constant/540768/19 "2012-03-09T22:20:57Z")
Real physicists use ħ, not h (“h-bar” = h/2π). 🆒 ---
**Author:** ![Chipacabra](https://avatars.discourse-cdn.com/v4/letter/c/e19b73/32.png) [@Chipacabra](https://boards.straightdope.com/u/Chipacabra)\ **Post date:** [March 9, 2012, 10:59pm UTC](https://boards.straightdope.com/t/why-h-for-plancks-constant/540768/20 "2012-03-09T22:59:24Z")
You still use π?😉 [Next page](https://boards.straightdope.com/t/why-h-for-plancks-constant/540768.md?page=2)