<p>The transverse size is the angular size in radians times the distance, or <span class="math-container">$\frac{π}{10800}$</span> times the angular size in arc minutes times the distance. (The values you quoted are in arc minutes.) The radius is half that.</p>
<p>Technically you should probably take the tangent of the angular radius, but for the sizes encountered in astronomy, it's unnecessary. Even for Andromeda, the difference is less than 0.1%.</p>
<p>Technically the distance you should use is the <a href="https://en.wikipedia.org/wiki/Distance_measures_(cosmology)" rel="nofollow noreferrer">angular diameter distance</a>, but the distinction between that and any other distance measure is less than 1% at distances under 100 million light years.</p>

CC BY-SA 4.0
2021-10-30T17:35:26.233Z
Would you mind giving an example of a calculation please?
MiscellaneousUser
CC BY-SA 4.0
2021-10-28T21:28:31.233Z
2021-10-28T21:28:31.233Z
benrg
<p>Is there a formula for calculating the size of a galaxy or even a nebula if you have the Angular Size.  For example, M31 has an angular size of     199.53 70.79 35 (Opt) D</p>
<p>M31 should be 200,000 light Years or Whirlpool Galaxy 10.00 7.59 163 (Opt) D should equate to 30,000 Light Years.</p>
<p>Or Even the Orion Nebula 5.5 5.5 90 (Rad) D to be 12 Light Years.</p>
<p>The angular sizes come from Simbad as sources.</p>
<p><a href="https://simbad.u-strasbg.fr/simbad/sim-id?Ident=Andromeda%20Galaxy" rel="nofollow noreferrer">https://simbad.u-strasbg.fr/simbad/sim-id?Ident=Andromeda%20Galaxy</a><br />
<a href="https://simbad.u-strasbg.fr/simbad/sim-id?Ident=Whirlpool%20Galaxy" rel="nofollow noreferrer">https://simbad.u-strasbg.fr/simbad/sim-id?Ident=Whirlpool%20Galaxy</a><br />
<a href="https://simbad.u-strasbg.fr/simbad/sim-id?Ident=Orion%20Nebula" rel="nofollow noreferrer">https://simbad.u-strasbg.fr/simbad/sim-id?Ident=Orion%20Nebula</a></p>
<p>Any help on the formula if there is one or if not, is it based on observation?  Thanks in advance</p>

CC BY-SA 4.0
2021-10-28T13:11:24.660Z
Errrr, you multiply by the distance.
ProfRob
<galaxy><nebula>
Can you calculate the radius of a galaxy from Angular Size?
MiscellaneousUser
# Can you calculate the radius of a galaxy from Angular Size?

(Asked by: username_0 on 2021-10-28)

Is there a formula for calculating the size of a galaxy or even a nebula if you have the Angular Size. For example, M31 has an angular size of 199.53 70.79 35 (Opt) D

M31 should be 200,000 light Years or Whirlpool Galaxy 10.00 7.59 163 (Opt) D should equate to 30,000 Light Years.

Or Even the Orion Nebula 5.5 5.5 90 (Rad) D to be 12 Light Years.

The angular sizes come from Simbad as sources.

<https://simbad.u-strasbg.fr/simbad/sim-id?Ident=Andromeda%20Galaxy>  
<https://simbad.u-strasbg.fr/simbad/sim-id?Ident=Whirlpool%20Galaxy>  
<https://simbad.u-strasbg.fr/simbad/sim-id?Ident=Orion%20Nebula>

Any help on the formula if there is one or if not, is it based on observation? Thanks in advance

**Tags:** galaxy, nebula
> **Comments:**
> **username_1**: Errrr, you multiply by the distance.  

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## 1 answers

### Answer by username_2 on 2021-10-28. Score: 2

The transverse size is the angular size in radians times the distance, or $\frac{π}{10800}$ times the angular size in arc minutes times the distance. (The values you quoted are in arc minutes.) The radius is half that.

Technically you should probably take the tangent of the angular radius, but for the sizes encountered in astronomy, it's unnecessary. Even for Andromeda, the difference is less than 0.1%.

Technically the distance you should use is the [angular diameter distance](https://en.wikipedia.org/wiki/Distance_measures_(cosmology)), but the distinction between that and any other distance measure is less than 1% at distances under 100 million light years.

> **Comments:**
> **username_0**: Would you mind giving an example of a calculation please?  

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