What are degrees, arc minutes and arc seconds?

How do skywatchers measure distances in the night sky? Here’s how to understand it when they speak of objects as being several degrees (or several arc minutes or arc seconds) apart.

Five hands with fingers extended in various configurations, showing different widths.

Use this “handy” guide to measure degrees on the dome of the sky. Image via Fort Worth Astronomical Society.

The handiest measuring stick for the sky’s dome is the one on the end of your arm. You can use the width of your pinky, fist and more to gauge the distance between sky objects. That comes in handy when you’re observing conjunctions between planets, or close planets and stars, or planets and stars and the moon, plus many other space objects. You’ll often find these objects described as being a certain number of degrees, arc minutes or arc seconds apart.

Just how far apart is that?

To begin with, from one side of the sky all the way across to the other horizon measures 180 degrees, or half a circle. Therefore, from horizon to zenith, the point straight above your head, should be 90 degrees (this is assuming a flat horizon – not a hilly or mountainous region).

The general rule amateur astronomers use is that the width of your fist held at arm’s length equals about 10 degrees. You may look at your fist and the fist of a small child and wonder how both can measure 10 degrees, but the size of peoples’ fists is generally proportional to the length of their arms. Thus, a child with a small fist and small arm will measure approximately 10 degrees from their perspective, just as an adult with a larger fist and longer arm measures 10 degrees from their point of view.

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If you want to do a rough check, extend your arm and fist out toward a flat horizon. Then place your other arm and fist on top of the first, and alternate, trying not to wobble, until you have counted nine fists. Your ninth fist should be pointing straight up (the zenith is at 90 degrees).

For degrees smaller than 10, focus on just your fingers. At arm’s length, a pinky measure about 1 to 1.5 degrees, and your three middle fingers measure about 5 degrees. For larger degrees, you’ll need to stretch those fingers out. To find 15 degrees, use your index finger and pinky spread apart, and to find 25 degrees, look at the span between your pinky and thumb spread apart.

View along arm with hand with fingers extended.

You can measure 15 degrees of sky by the span between your pinky and index finger. Image via Sharon Kizer.

The Big Dipper is a good target to use in checking your hand measurements. The end two stars in the bowl, the ones that are used to find Polaris, are about 5 degrees apart. The top two stars in the bowl of the Big Dipper are 10 degrees apart. And finally, using the same far star in the bowl of the Big Dipper that you used for the first two tests (Dubhe, the spot at which water would pour out if it were a real dipper) plus the end star in the handle will measure 25 degrees.

How wide do you think the full moon looks – how many degrees would you expect it to measure? 5 degrees? 2? 1? Most people overestimate its size, but in actuality, the full moon is a mere half degree across. How about the sun? While instinctually you might want to say the sun is larger, because its actual size is huge if put side-by-side with the moon, we know that the amount of sky the sun and moon take up is equal – a half degree. We know this without even having to check out the sun with our half-pinky measurement, because we know that during total solar eclipses the moon temporarily slips just in front of the sun, blocking all of its light for a fleeting few minutes.

The sun nearly blocked by the black moon.

Both the sun and moon measure a half degree in our sky, which becomes clear when we see the moon cover the sun in a total solar eclipse. Image via Michael Rodriguez.

Once you have a good grasp of degrees, if you want to estimate smaller measurements, you need to know that degrees are further divided by arc minutes. There are 60 arc minutes in 1 degree, therefore the moon and sun are each 30 arc minutes across. Arc minutes can also be divided. 60 arc seconds make up 1 arc minute. Going back to the Big Dipper, the stars in the bend of the handle are a double star system named Mizar and Alcor and are separated by just 12 arc minutes. People with good eyesight can see the two separate stars without optical aid. Stars closer than this usually require binoculars or a telescope to split. Mizar has another companion that is even closer than Alcor. Mizar’s double star is a mere 14.4 arc seconds away. Arc minutes are written with the same symbol as feet (‘) and arc seconds are written with the inch notation (“).

Star field with prominent Big Dipper stars in deep blue sky over icy lake.

View at EarthSky Community Photos. | Jim Peacock captured this photo of the Big Dipper on January 3, 2021, over the horizon of a freezing bay of Lake Superior in northern Wisconsin. Thanks, Jim! The 2 so-called Pointer Stars in the Dipper’s bowl (the 2 stars farthest from the Dipper’s handle) – used to find Polaris, the North Star – are about 5 degrees apart. The top 2 stars in the bowl of the Big Dipper are 10 degrees apart.

Two very bright, very close stars in a star field with a degree ruler at the bottom.

Here are Mizar and Alcor, a naked-eye double star you can with your eye alone, second to last in the handle of the Big Dipper. They are 12 arc minutes apart. Image via Fred Espenak/ astropixels.com.

You can tell how long until the sun will set by measuring its distance from the horizon. The sun moves about 15 degrees across the sky in an hour. Moving 15 degrees an hour for 24 hours would equal 360 degrees, or a full day from sunset to sunset. (Of course, the sun is not really moving, it is only appearing to move in the sky as Earth turns.) Remember that unless you are at the equator, the sun is not moving in a beeline toward the horizon. The sun sinks downward at angle that gets steeper the closer to the poles you’re located.

Multiple suns, dimming, in a nearly vertical line over the domes of the sihouetted Taj Mahal.

View larger. | Abhinav Singhai created this beautiful composite image of the sunset over the Taj Mahal. The sun crosses 15 degrees of sky every hour, which can help you estimate how long until sunset.

Bottom line: Degrees, arc minutes and arc seconds are all useful units of measurement in astronomy. Sometimes your own hand – held at arm’s length – can help. For example, your fist held at arm’s length measures 10 degrees on the sky’s dome. Your pinky at arm’s length measures one degree.

Kelly Kizer Whitt