What Is Angular Size?

How good are your eyes at seeing really tiny things that are really far away? How much better is the Hubble Space Telescope at doing the same thing? What do these two questions have to do with the mathematical concept of angular size? Keep on reading to find out!

Jason Marshall, PhD
4-minute read
Episode #204

TelescopeHow big is the Sun? As you probably know, it's huge. Really huge. In fact, it's so big that you could fit about 1,300,000 Earths inside of it! But that's not what I mean, so let's try again:

How big does the Sun look to you and me from our cozy vantage point here on Earth? 

Although this seems like a simple question, it's tougher than you might think. After all, we can't answer it using normal size units like miles or kilometers. Because I'm not asking how big it really is in real physical units. Rather, I'm asking how big it appears to be?

How can we answer that? Here's a clue: It has something to do with an idea in math called angular size. And, as we'll soon find out, once we understand that idea, we'll also understand some amazing facts about human eyes and how they compare to the largest, most incredible telescopes ever built..

Degrees, Minutes, and Seconds

Before we start talking about the idea of angular size, how we use it to quantify how big the Sun looks, and what it tells us about human eyes and giant telescopes, we need to quickly review how we measure angles. As you probably already know, there are 360 degrees in a circle—which is why your favorite semi-circular protractor in elementary school had 180 degree marks on it.

What you may not already know is that the degree is not the smallest unit we use to measure angles. And thank goodness for that because there are many times in life (especially if you're an astronomer) where we need to measure angles that are much smaller than 1 degree.

The degree is not the smallest unit we use to measure angles.

If we divide each degree up into 60 evenly spaced pieces, those pieces each represent an angle that is 1 arcminute across. If we further divide an arcminute up into 60 yet smaller evenly spaced pieces, those pieces each represent an angle that is 1 arcsecond across.

So we can measure angles by specifying the number of degrees, arcminutes, and arcseconds that they span. Notice that an arcsecond is an extremely tiny angle—it's 1/3,600th of a degree. And it's not like a degree is a very big angle to begin with!


About the Author

Jason Marshall, PhD

Jason Marshall is the author of The Math Dude's Quick and Dirty Guide to Algebra. He provides clear explanations of math terms and principles, and his simple tricks for solving basic algebra problems will have even the most math-phobic person looking forward to working out whatever math problem comes their way.