The dimensions for most astronomical objects are given in degrees of arc in most cases. While the apparent size of an object is interesting, it’s sometimes useful to convert the apparent size into something more understandable like light years. For example, Messier 20’s apparent size is 28 arcminutes, but what does that translate to in terms of actual size in light years?

To solve for the size of an object, you need to know its distance and its apparent size in degrees.

Using Messier 20, its distance is about 4,100 light years and its apparent size is 28 arcminutes. This is how to solve for the size:

  1. Convert 28 arcminutes into degrees:

    28 / 60 = 0.466667

  2. If you have a value for arcseconds, convert it to degrees as follows:

    arcseconds / 3600 = degrees of arc

  3. Add the numbers from step 1 and 2
  4. Convert the degrees of arc into radians as follows:

    0.466667 * (3.141592 / 180) = 0.008144

  5. Multiply the distance by the number you got for #4:

    4100 * 0.008144 = 33.394

Since the distance is in light years, the answer is also in light years, so Messier 20’s size is about 33.4 light years.

Note that if the apparent size of the object includes the angle in hours, add that number to numbers 1 and 2 in step 3.

Conclusion

In this article, you learned how to solve for linear size, given an object’s apparent angular size and distance.