In a previous post, we looked at cosmic distances and how they are measured. In this post, we'll look at angular distances as objects appear in the sky, and how to apply this to your observing. For this we use a system of degrees, minutes, and seconds of arc.
There are many resources on the internet that describe this system, so I'll only cover the basics. What we're interested in as visual observers is being able to translate numbers given to us in an app, article, or data source to what we see in the sky, especially in the telescope.
Because there are 360 degrees in a circle, the sky as we see it is always half of that, or 180 degrees. We are standing on the other half, as if we are standing in the middle of a globe. The zenith is 90 degrees overhead, so if the altitude of Jupiter is 45 degrees for our location at a given time, it will be halfway up the sky and good for observing if it's clear with steady air (seeing). At 20 degrees, things are a bit low and murky, subject to poor seeing and probably horizon light glow.
Left: If we are using an altitude-azimuth mount like a Dobsonian, a degree in altitude is the same no matter how high we point our scope because all the circles of altitude are the same size. Think of these as lines of longitude.
But only if the scope is horizontal and pointed at the horizon is a degree of azimuth the same distance as a degree of altitude, because it's the only full diameter horizontal circle. As we point the scope higher up in the sky, the circles of azimuth, similar to lines of latitude, get smaller as we approach the zenith, so the apparent distance in the sky for the same number of degrees of azimuth is shorter. The higher we point the tube of the telescope, the smaller the arc it describes as it swings in the same number of degrees of azimuth.
As a result, we use a standard angular measurement of apparent distance essentially equal to degrees, minutes, and seconds of arc equivalent to any altitude circle (like a meridian of longitude, or our azimuth circle at the horizon only—essentially both great circles), regardless of what direction we are moving in, and we call them degrees, arcminutes ('), and arcseconds (").
Practical application
An easy rough estimate can be done with your outstretched hand.
1 degree is about the width of your pinky
5 degrees is about the width of your three middle fingers
10 degrees is about the width of your fist
20 degrees is about the width of your outstretched hand.
This can vary considerably depending on the size of your hands and length of your fingers, but it's close enough for rough estimates. You can check how your own hand measures up by looking up the distances between bright stars that fit these measurements using an app such as Sky Safari Pro, Stellarium, or Cartes du Ciel.
When looking in binoculars or a telescope, your best bet is to know the field of view (FOV), or diameter of the portion of sky that you can see in your particular instrument, measured in degrees for binoculars and widefield eyepieces, and in arcminutes in higher power eyepieces. This will be fixed in non-zoom binoculars and will change depending on what eyepiece you use in the telescope. This is called the "true field of view" (TFOV) (or "actual field of view" in Stellarium), as opposed to the "apparent field of view" (AFOV), which is the angle of "wideness" of your view based on the optics you are using.
Left: The circle represents the true field of view (TFOV) in typical wide angle 10x50 binoculars. This diameter represents about 6.5 degrees of angular distance in the sky. (Chart adapted from Cartes du Ciel).
Some eyepieces have a narrow AFOV because of their design, and it's like looking down a tube, whereas others have a wide, sometimes very wide, field of view, described as like looking through a "porthole" or on a "spacewalk," where you can't see the interior edge of the eyepiece, the field stop, at all without peering into the eyepiece almost sideways.
To recap, the AFOV is the apparent angle of wideness that you experience, but the TFOV is the actual angular measurement of distance in the sky that you are able to see, and that is what we're more concerned with here. Knowing this makes it easier to compare what you are seeing in your binoculars or telescope to your chart or unaided eye view.
Calculating TFOV in the telescope
TFOV must be calculated for each combination of telescope and eyepiece. You can use a variety of methods to calculate TFOV, with varying degrees of accuracy:
The easy calculated method
This method gives you a rough estimate because it is dependent upon the manufacturer specs being exactly correct, which is not always the case.
AFOV (provided by manufacturer or vendor) / MAGNIFICATION = TFOV (in degrees; multiply this by 60 for arc minutes)
Example: 60 / 30 (*see below for this calculation) = 2 degrees or 120 arc minutes
The published AFOV is often not completely accurate but usually fairly close.
*Magnification is calculated as follows:
FOCAL LENGTH OF TELESCOPE (in mm) / FOCAL LENGTH OF EYEPIECE (in mm)
Example: 750 / 25 = 30x
Both of the focal lengths above are provided by the manufacturers or vendors and are usually marked in millimeters somewhere on the telescope near the focuser and on the barrel of the eyepiece.
The more precise calculated method
This method relies upon the manufacturer or vendor to provide the field stop diameter. Unfortunately, aside from Televue eyepieces, these are not easy to find (check out Don Pensack's 2025 Eyepiece Buyer's Guide, which lists many, or it can be calculated or measured with calipers). If you have it, here is the formula:
EYEPIECE FIELD STOP DIAMETER / TELESCOPE FOCAL LENGTH x 57.3 = TFOV (in degrees; multiply this by 60 for arc minutes)
Example (for the Celestron Xcel-LX 24mm eyepiece pictured above and a 750mm focal length telescope):
25 (provided by manufacturer) / 750 = .033 x 57.3 = 1.89 degrees or 113 arc minutes
The drift method
This one must be done in the field with the telescope - eyepiece combination for which you wish to find the TFOV. Rather than go into the details, David Knisely provided an excellent description in this post from the Cloudy Nights forum. He also provides descriptions of some of the other methods.
The app or chart method
This one is also accomplished in the field and is another rough estimate. Again, With the telescope - eyepiece combination for which you wish to find the TFOV, locate any two easily identifiable stars that just fit on the edges of a full diameter of the eyepiece field of view, and measure the distance between those stars in the app. This is inherently inaccurate because you have to eyeball it, but it will give you a number close enough for casual observing.
Using TFOV in starhopping
Once you're comfortable with this, your navigation skills will improve immensely.