Naperville Astronomical Association

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A Barlow Lens, placed between the eyepiece and the telescope, will increase the Resulting Magnification by the power of the Barlow; i.e. if the calculator shows that a certain eyepiece gives 100x in your telescope, and you add a 2x Barlow, the resulting magnification will be 200x (100 x 2).
The other results will also be changed by the same Barlow factor: The Power Per Inch will be doubled (2x), while the the Exit Pupil, True Field, and Field Transit Time will each be halved (divided by 2).



Eye Relief refers to the distance from the outer lens of an eyepiece to the prime spot to place the pupil of your eye (the eyepiece's Exit Pupil). While part of the image may be seen with the eye closer in or farther out, the best image will always be obtained if the eye is at the correct distance.
This distance varies from eyepiece to eyepiece. Eyepieces with longer Eye Relief are easier for eyeglass wearers to use. Eyepieces with very long Eye Relief may be confusing for some people to use, as the image may disappear if the eye comes in too close to the eyepiece.
The eye relief a given eyepiece provides changes some depending on the telescope it is used on. The larger the f Ratio of the telescope, the further the Exit Pupil moves out from the eyepiece; this holds true if the telescope's focal length is "artificially" extended by using a Barlow lens.




narrow AF view

View thru a narrow Apparent Field eyepiece

wide AF view

View thru an eyepiece of the same Focal Length with a wider Apparent Field:
Same magnification, but more sky seen


small 'scope view

Stars thru smaller diameter telescope

larger 'scope view

Stars thru larger telescope at same magnification:
Stars look brighter; fainter ones show up



low power

View at lower magnification

high power

View thru same telescope at higher power:
Both the object and the sky background are reduced in brightness by the same amount; it may be easier to spot the object since it is larger and the sky is blacker, though


small 'scope view

Object thru smaller 'scope

larger 'scope view

Same object thru a larger telescope at same "Brightness Factor":
Object and sky surface brightnesses are the same as in the small 'scope, but magnification is higher


The NAA Telescope Calculator

As a handy tool for the telescope user, we present this JavaScript-driven calculator, which will compute the values of a number of paramaters for any telescope & eyepiece combinations you enter. It starts off with some basic information every telescope user should know for their equipment, and continues into some more esoteric calculations. Enjoy! (And for further information, also see our How Telescopes Work and Choosing a Telescope pages.)

Fill in the numbers in the green boxes below as instructed, then press the "Enter Diameter" button for whichever measurement system you used; the computed values will appear in the other boxes. To try different eyepieces, enter their info in the Eyepiece Specifications field(s), and use the adjacent buttons to re-compute the outputs.

Enter Objective Diameter in inches -or- millimeters



Enter Telescope's Focal Length
(or use Change f number to compute Focal Length from f Ratio and Obj. Dia. in mm)

Focal Length (mm):

f Ratio:

Enter Eyepiece Specifications

Eyepiece Focal Length (mm):

Eyepiece Apparent Field (degrees):
(If unknown, see "Key" below)

Resulting magnification:
Power per inch of aperture:
Exit pupil (mm):
True Field (degrees):
True Field (arcminutes):
Field transit time at 0°declination (sec.):


Objective Diameter: the size of the main light-gathering ("primary") lens or mirror of your telescope (also called the telescope's "aperture").
Focal Length: The Effective Focal Length of your telescope is important to know; it is often listed on a label right on the telescope, sometimes as Fl, and usually in millimeters. It is equal to the Focal Ratio (f number) times the Objective Diameter.
f Ratio: The Focal Ratio (f number) is the Focal Length divided by the Objective Diameter. Just as in camera lenses, telescopes with lower "f numbers" are "faster"; they form brighter (but smaller) images than telescopes of the same diameter with with higher f numbers.
Eyepiece Focal Length: This determines the "power" an eyepiece delivers on a given telescope; the shorter the focal length, the higher the magnification. Usually noted as a number on the eyepiece itself, normally measured in millimeters.
Eyepiece Apparent Field: When you put your eye up to an eyepiece, this is the angular diameter (in degrees) of the circle of view you see through it. It can vary from less than 50° to more than 80°, depending on the eyepiece design. Find this out from the manufacturer or seller of the eyepiece. If that is not possible, Apparent Field can be approximately computed by measuring the diameter of the Field Stop in the eyepiece; it is the aperture (opening) usually located up inside the eyepiece barrel on the telescope side of the eyepiece (but may be internal and not accessible in some wide-field eyepieces). Here is the approximate Field Stop diameter for your eyepiece, based on the Apparent Field entered above; if you replace this number with an actual measurement and click the Enter Measured FS button, we'll recompute your Apparent Field based on this measurement.

Approximate Eyepiece Field Stop diameter (mm):

Magnification (power): How many times larger (in angular size) an object looks through the telescope than it would look to the unaided eye. For example, at 50x (fifty power, fifty times magnification), the Moon (or whatever you're looking at) looks fifty times bigger across than it does to the naked eye.
Exit pupil: The diameter of the beam of focused light shining out of the eyepiece. This figure is important, because if the beam is larger across than the pupil (the dark window) into your eye, some of the light from the telescope won't make it in for you to see it. In that case, your telescope would be performing like a smaller telescope (sometimes much smaller). See the section below for more information on your pupil size!
True Field: The angular diameter of the part of the sky you can observe through the telescope. In other words, if the Moon is one-half degree across, it will just fill the view through a telescope/eyepiece combination which delivers a true field of .5°. Can be measured in Degrees or Minutes of Arc (arcminutes).
Field Transit Time: A product of the True Field, this is how long it will take a star, located near the celestial equator, to drift across the center of the field from one edge to the other (when the telescope is not clock driven to follow the sky). This gives you some idea of how fast something will drift to the edge from the center of the field (half of the full Field Transit Time).

So, What Will I See?

The above computations are a good start to exploring the properties of various telescope/eyepiece combinations, and are especially important to make when you are selecting new eyepieces for a telescope (to make sure the resulting system will really be useful). To go beyond the basics, and explore what you should be able to see through your telescope, continue on below.
It is important to note that there are a number of factors which effect what one will actually see through a telescope, including: the condition of the atmosphere as far as its clarity (transparency) and steadiness (seeing); the amount of light pollution in your sky and in your immediate neighborhood; the quality of the optics in your telescope, eyepiece, and indeed, those in your eye itself. These variables cannot all be accounted for here, but you may find some of these theoretical calculations helpful. Be sure your telescope & eyepiece information is filled in correctly above; you can go back and alter it anytime you want, too.

1: Determine your pupil size

To best match your telescope/eyepiece combination for your use, you have to know how wide the pupil of your eye can open in the dark. On average, this maximum decreases as we age; while the average teenager's pupil can dilate to 7.5mm, the average 78 year old's eye can only reach about 5mm. Enter your age below, and this program will show an average value for your age group. If you actually know what your maximum pupil dilation is, you can correct the figure (your actual measurement might vary as much as a millimeter from the estimated value).

Your age gives you an approximate maximum pupil diameter of mm
An Objective with a diameter of (mm) is equivalent in area to about  of your eyes
This corresponds to an approximate gain in magnitudes of for stars

Remember your maximum pupil diameter when studying eyepiece/telescope combinations with the top table. Again, if the Exit Pupil a given combination delivers is larger than the maximum diameter of your eye's pupil, not all of the light the telescope gathers and focuses will make it in to your eye to be seen -- you'll be wasting some of the money you paid to get that large a telescope!

2: Theoretical Magnitude limits your telescope

Based on the telescope information entered in above, the tables below gives some figures for what its performance capabilities might be. The actual performance you will get, as noted above, will be dependent on not only these theoretical limits (which you may actually surpass under the right conditions), but also on variables in the atmospheric conditions, your eyesight and observing skill, and the quality of your optics. Magnitude is the measurement of the brightness of an astronomical object; the lower the number, the brighter the object is (the faintest stars you can see in from in town may be 3rd magnitude, while out in the country you might see 6th magnitude ones; the brightest stars actually have negative magnitudes-- Sirius' is -1.4).

Your currently selected telescope has a theoretical limiting magnitude of   for stellar objects

This value is complicated by the fact that magnification also dims the brightness of the sky background, increasing the contrast of stellar objects to the background. When stars are magnified (within the "optimum" magnification range of a telescope, as described in Section 4, below), they remain as "points", so changing magnification within that range does not strongly effect the apparent brightness of stars and other stellar objects. Therefore, the actual limiting magnitude for stellar objects you can achieve with your telescope may be dependent on the magnification used, given your local sky conditions.

Other types of objects are rated with the same magnitude scale, based on the total amount of their light that reaches us; if the object is large, though, that light is spread out over an area. In other words, an 8th magnitude star and an 8th magnitude galaxy put equal amounts of light into your eyepiece, but the light from the star is concentrated into a bright "point", while that of the galaxy is spread over a larger area, and will be harder to see.

For such extended objects, the object's surface brighness decreases at the same rate the sky's does as magnification is increased, so there is no improvement in contrast from magnification (as opposed to stellar objects, as noted above). Instead of listing a limiting magnitude for extended objects (since that would actually have to be based on an object's brightness per unit surface area, not its total magnitude), we'll give a "Brightness Factor" for the achieved surface brightness of an object viewed through your telescope, comparing to its surface brightness through the 'scope to what you'd see with your your unaided eye. Surprisingly, our telescopes are not providing (once the image is magnified) a higher surface brightness than the unaided eye does; all that light gathering power is going into providing a bigger image!

For extended objects, your currently selected telescope/eyepiece combination delivers a Brightness Factor of , compared to your unaided eye (pupil diameter).

If the above factor is 1, when you look at the Moon (for example) through the telescope, the image there will have the same average surface brightness per square arc second as the Moon does to your unaided eye (although the image will be much larger in angular size, of course, through the telescope). If the value is less than 1, the surface of the Moon (or whatever object) will be dimmer by that factor per unit of surface area than it appears to your unaided eye. If the value is over 1.0, then the exit pupil for your selected telescope/eyepiece combination is larger than your eye's pupil, and this would cause light loss, bringing the achieved Brightness Factor back down to 1 (or potentially less, especially in reflecting telescopes with central obstructions).

As you change the eyepiece values, note that the brightness factor will go down at higher powers, and up at lower ones. As noted on the illustrations at left, even though higher magnifications will make extended objects look fainter, they can still be useful in observing some fainter objects because (1) the eye can spot moderately large faint objects with more ease than it can tiny ones, and (2) it may be easier to spot a faint object against a blacker sky (even if the actual sky/object contrast is no greater).

Overall, the Brightness Factor can give some guideline as to how relatively bright a particular object will look in different telescopes and at different magnifications (all other observing conditions being the same).

3: Theoretical Resolution limits for your telescope

The Resolving Power for a telescope tells what the size of the smallest details which can be seen through it, atmospheric conditions allowing. Beyond a certain point (usually accepted to be 0.5 arc seconds for locations at our altitude), the atmosphere always prohibits seeing any smaller details, even if the telescope's optics could deliver them. Indeed, our seeing often creates a resolution limit well above this level. As an example of resolving power, if you can look at two stars (of similar brightness) which are just 1 arc second apart in the sky, and see the two separated (not blurred together into one point of light), your telescope is resolving 1 arc second detail. Again, the figure shown is based on the telescope information entered above, and actual performance will vary with other factors as noted earlier.

Your currently selected telescope has a theoretical resolving power of seconds of arc (computed Dawes' Limit, .5sec "ceiling")

Just for fun, let's apply that theoretical resolving power we've computed to an astronomical object, our Moon. What is the smallest feature you can theoretically resolve on the lunar surface, near the center of the Moon's face, if your observing conditions, telescope optics, and eyes are all top-notch?

For your currently selected telescope, the smallest features you could theoretically
ever see on the Moon would be about   miles across.

4: Other eyepiece considerations

Experienced observers have found that using eyepieces which deliver Exit Pupils in the range of 2-4mm usually give the best images, especially when observing faint objects. Indeed, diffuse, low brightness objects may sometimes be seen within this range, and invisible outside of it. For brighter objects, such as the planets, higher magnifications may be desirable, but the sharpest appearing views will still probably be found within this range. For larger objects, which need a larger True Field for you to see their full extent, lower magnifications can certainly be used (watch out for oversized Exit Pupils, though!); but for the "prettiest picture", you might want to consider using an eyepiece within this range which has a larger Apparent Field to reach your desired True Field.

For your currently selected telescope,
this "optimum" magnification range is   to power,
corresponding to   to mm eyepiece focal lengths.
For your currently selected telescope, and based on your pupil size as entered above, the minimum magnification you can use without losing light (without the eyepiece's exit pupil being larger than yours) is   power, with a mm eyepiece.
For the highest magnifications, most observers find a practical top limit where the eyepiece
gives an Exit Pupil of 0.5mm; on this telescope,
that would be   power, with a mm eyepiece (or an equivalent eyepiece/Barlow lens
combination). Enter that eyepiece in the table at page top for more information.

5: Esoterica

For your currently selected telescope, the minimum Airy Disk diameter
(theoretical star image size) is   arc seconds (in yellow light).

For your currently selected telescope, the image scale at prime focus is
arc minutes per mm.