<p>It is true that a surprisingly large number of stars are smaller (and thus less massive) than the Sun. However, the stars that <em>are</em> bigger than the Sun are often much bigger.</p>

<p>Look at this chart:</p>

<p><a href="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Comparison_of_planets_and_stars_%28sheet_by_sheet%29_%28Apr_2015_update%29.png/640px-Comparison_of_planets_and_stars_%28sheet_by_sheet%29_%28Apr_2015_update%29.png"><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Comparison_of_planets_and_stars_%28sheet_by_sheet%29_%28Apr_2015_update%29.png/640px-Comparison_of_planets_and_stars_%28sheet_by_sheet%29_%28Apr_2015_update%29.png" alt=""></a>
<br>
<sup>Image courtesy of Wikipedia user Jcpag2012 under <a href="https://creativecommons.org/licenses/by-sa/3.0/deed.en">the Creative Commons Attribution-Share Alike 3.0 Unported license</a>.</sup></p>

<p>Notice how small the Sun is compared to some of the other stars. It's <em>tiny</em>! It is indeed a small star - in technical terms a <em>main sequence dwarf</em>.</p>

<p>However, despite its size, it is clear that there are many more stars less massive than the Sun that there are stars more massive than the Sun. Why? There are two reasons:</p>

<ol>
<li>Lower-mass stars live longer.</li>
<li>More low-mass stars can form in a given region than high-mass stars.</li>
</ol>

<p><sup><a href="http://www.astro.caltech.edu/~george/ay20/eaa-stellarmasses.pdf">Encyclopedia of Astronomy and Astrophysics</a></sup></p>

<p>The distribution of masses can be quantified in an <a href="https://en.wikipedia.org/wiki/Initial_mass_function">initial mass function</a>, typically given in the form
$$\xi(m)=km^{-\alpha}$$</p>

<p>When you integrate this over a range of masses, you can find how many stars are within that range. Not surprisingly, this number gets lower and lower as you slide the endpoints to more massive stars. You can see this decrease from the fact that $\xi'(m)&lt;0$, so long as $k&gt;0$ and $\alpha&gt;0$ - which is assumed by the model, according to empirical data.</p>

CC BY-SA 3.0
2016-01-09T23:00:27.433Z
See also https://what-if.xkcd.com/83/ : "Our Sun isn't a grain of sand on a soft galactic beach; instead, the Milky Way is a field of boulders with some sand in between."
j-g-faustus
CC BY-SA 3.0
2016-07-28T21:05:55.373Z
Sorry, but I do not really like this answer because it focuses on spectacular and very rare objects too much. I tend to agree what Sun is medium sized among main-sequence stars.
Free Consulting
CC BY-SA 3.0
2016-07-28T21:11:01.870Z
@FreeConsulting What do you mean by "spectacular and very rare", and why do you object to it?
HDE 226868
CC BY-SA 3.0
2016-07-28T21:29:01.280Z
Because Sun is rather large compared to most abundant stars.
Free Consulting
CC BY-SA 3.0
2016-07-28T21:34:26.610Z
@FreeConsulting I'm aware of that, and stated as much: *However, despite its size, it is clear that there are many more stars less massive than the Sun that there are stars more massive than the Sun.*
HDE 226868
CC BY-SA 3.0
2016-01-09T18:42:43.813Z
2016-01-09T23:14:16.663Z
2016-01-09T23:14:16.663Z
HDE 226868
<p>It is often said that the Sun is a medium size, or even dim star. Is this true?</p>

<p>According to this <a href="http://www.johnstonsarchive.net/astro/nearstar.html" rel="noreferrer">list of stars within 21 light years</a>, there are, out of the closest 121 stars, only six brighter than the Sun. This means that the Sun is in the top 6%. If you also count brown dwarfs, the Sun ranks even higher. </p>

<p>Doesn't this indicate that the Sun is actually a relatively large star?</p>

<p><a href="https://i.sstatic.net/SfyPJ.png" rel="noreferrer"><img src="https://i.sstatic.net/SfyPJ.png" alt="7/121"></a></p>

CC BY-SA 3.0
2016-01-10T03:44:31.937Z
I think your comment is fundamentally correct.  It used to be said that the sun was a medium sized/small star based on preliminary observations.  Better telescopes reversed that observation as many many many more smaller stars became observable.   It's worth pointing out that very few of the stars we can actually see in the sky are smaller than the sun.  None of the visible stars are red dwarfs or smaller.   A similar correction was made on binary stars being the majority.
userLTK
CC BY-SA 3.0
2016-01-10T06:41:56.040Z
Define your terms. By "medium" do you mean mean or median? By "size" do you mean mass or radius?
Mike Scott
CC BY-SA 3.0
2016-01-10T13:25:13.717Z
@MikeScott Just give me any size metric that actually makes the Sun a medium sized star. As for "medium", I meant median.
SE - stop firing the good guys
CC BY-SA 3.0
2016-01-10T15:15:06.527Z
@Hohmannfan If you're using the median as your "medium", then the Sun is bigger than that. But if you're using the more normal mean as your medium, I think the Sun is probably smaller than the mean mass of all stars, and it's certainly smaller than the mean mass of all _known_ stars.
Mike Scott
CC BY-SA 3.0
2016-06-02T11:31:40.697Z
The Sun s about 3 times more massive than a median field star and is more luminous than about 90% of stars. It is only typical in the sense of being on the main sequence, where most stars are.
ProfRob
CC BY-SA 3.0
2016-07-28T21:09:43.767Z
Size doesn't matter as much as temperature for luminosity. Also, red dwarves are most abundant stars.
Free Consulting
CC BY-SA 3.0
2016-08-18T12:27:22.487Z
See also:  [http://physics.stackexchange.com/a/262732/59023](http://physics.stackexchange.com/a/262732/59023) and [http://physics.stackexchange.com/a/262909/59023](http://physics.stackexchange.com/a/262909/59023).  Rob's answer is much more informative, as should be expected (as far as I am concerned, he is the _star whisperer_ on these SE sites).
honeste_vivere
<star><the-sun><size><luminosity>
Is the Sun really a medium size star?
SE - stop firing the good guys
# Is the Sun really a medium size star?

(Asked by: username_0 on 2016-01-09)

It is often said that the Sun is a medium size, or even dim star. Is this true?

According to this [list of stars within 21 light years](http://www.johnstonsarchive.net/astro/nearstar.html), there are, out of the closest 121 stars, only six brighter than the Sun. This means that the Sun is in the top 6%. If you also count brown dwarfs, the Sun ranks even higher.

Doesn't this indicate that the Sun is actually a relatively large star?

[![7/121](https://i.sstatic.net/SfyPJ.png)](https://i.sstatic.net/SfyPJ.png)

**Tags:** star, the-sun, size, luminosity
> **Comments:**
> **username_1**: I think your comment is fundamentally correct.  It used to be said that the sun was a medium sized/small star based on preliminary observations.  Better telescopes reversed that observation as many many many more smaller stars became observable.   It's worth pointing out that very few of the stars we can actually see in the sky are smaller than the sun.  None of the visible stars are red dwarfs or smaller.   A similar correction was made on binary stars being the majority.  
> **username_2**: Define your terms. By "medium" do you mean mean or median? By "size" do you mean mass or radius?  
> **username_0**: @MikeScott Just give me any size metric that actually makes the Sun a medium sized star. As for "medium", I meant median.  
> **username_2**: @Hohmannfan If you're using the median as your "medium", then the Sun is bigger than that. But if you're using the more normal mean as your medium, I think the Sun is probably smaller than the mean mass of all stars, and it's certainly smaller than the mean mass of all _known_ stars.  
> **username_3**: The Sun s about 3 times more massive than a median field star and is more luminous than about 90% of stars. It is only typical in the sense of being on the main sequence, where most stars are.  
> **username_4**: Size doesn't matter as much as temperature for luminosity. Also, red dwarves are most abundant stars.  
> **username_5**: See also:  [http://physics.stackexchange.com/a/262732/59023](http://physics.stackexchange.com/a/262732/59023) and [http://physics.stackexchange.com/a/262909/59023](http://physics.stackexchange.com/a/262909/59023).  Rob's answer is much more informative, as should be expected (as far as I am concerned, he is the _star whisperer_ on these SE sites).  

---

## 1 answers

### Answer by username_6 on 2016-01-09. Score: 19 | Accepted answer

It is true that a surprisingly large number of stars are smaller (and thus less massive) than the Sun. However, the stars that *are* bigger than the Sun are often much bigger.

Look at this chart:

[![](https://upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Comparison_of_planets_and_stars_%28sheet_by_sheet%29_%28Apr_2015_update%29.png/640px-Comparison_of_planets_and_stars_%28sheet_by_sheet%29_%28Apr_2015_update%29.png)](https://upload.wikimedia.org/wikipedia/commons/thumb/d/d0/Comparison_of_planets_and_stars_%28sheet_by_sheet%29_%28Apr_2015_update%29.png/640px-Comparison_of_planets_and_stars_%28sheet_by_sheet%29_%28Apr_2015_update%29.png)
  
Image courtesy of Wikipedia user Jcpag2012 under [the Creative Commons Attribution-Share Alike 3.0 Unported license](https://creativecommons.org/licenses/by-sa/3.0/deed.en).

Notice how small the Sun is compared to some of the other stars. It's *tiny*! It is indeed a small star - in technical terms a *main sequence dwarf*.

However, despite its size, it is clear that there are many more stars less massive than the Sun that there are stars more massive than the Sun. Why? There are two reasons:

1. Lower-mass stars live longer.
2. More low-mass stars can form in a given region than high-mass stars.

[Encyclopedia of Astronomy and Astrophysics](http://www.astro.caltech.edu/~george/ay20/eaa-stellarmasses.pdf)

The distribution of masses can be quantified in an [initial mass function](https://en.wikipedia.org/wiki/Initial_mass_function), typically given in the form
$$\xi(m)=km^{-\alpha}$$

When you integrate this over a range of masses, you can find how many stars are within that range. Not surprisingly, this number gets lower and lower as you slide the endpoints to more massive stars. You can see this decrease from the fact that $\xi'(m)<0$, so long as $k>0$ and $\alpha>0$ - which is assumed by the model, according to empirical data.

> **Comments:**
> **username_7**: See also https://what-if.xkcd.com/83/ : "Our Sun isn't a grain of sand on a soft galactic beach; instead, the Milky Way is a field of boulders with some sand in between."  
> **username_4**: Sorry, but I do not really like this answer because it focuses on spectacular and very rare objects too much. I tend to agree what Sun is medium sized among main-sequence stars.  
> **username_6**: @FreeConsulting What do you mean by "spectacular and very rare", and why do you object to it?  
> **username_4**: Because Sun is rather large compared to most abundant stars.  
> **username_6**: @FreeConsulting I'm aware of that, and stated as much: *However, despite its size, it is clear that there are many more stars less massive than the Sun that there are stars more massive than the Sun.*  

---

