# How to find inverse steradian from $\text{arcmin}^{-2}$ for density of galaxy

I am using a code on EUCLID future mission. The original author of this code has set a value for the density of galaxy equal to :

ng = 354543085.80106884


I think this is expressed in inverse steradian. I think that EUCLID mission has a $$30\text{ arcmin}^{-2}$$ value for density of galaxies.

Is the conversion correct betweeen $$30\text{ arcmin}^{-2}$$ and $$354543085.8010688 \text{ sr}^{-1}$$ ?

and how to do this conversion ?

Indeed, I would like to calculate ng with a density of $$48 \text{ arcmin}^{-2}$$.

Regards

## 1 Answer

There are 60 arc minutes in a degree and $$180/ \pi$$ degrees in a radian.

So 1 radian is 57.2957795 degrees or 3437.746771 arc minutes.

As long as you are talking about units, you can square any of these angular units to obtain solid angle units.

So 1 steradian is 3282.80635 square degrees, or 11818102.860 square arc minutes.

Let's try your theory:

1/354543085.801 steradians is 9.259259E-06 square degrees, or 0.0333333 square arc minutes.

The answer is that it is 1/30th of a square arc minute, so YES it is 30 inverse square arc minutes!

Then 48 per square arcminute is:

$$48 \times 60^2 \times \frac{180^2}{\pi^2} \approx 567268937.282 \ \ \text{sr}^{-1}.$$