How Magnification Works

A telescope brings distant objects into view by using lenses or mirrors to focus light. The primary optical element has a focal length, denoted , which represents the distance over which incoming parallel rays are brought to a point. An eyepiece with focal length $\mathrm{F_e}$ magnifies that image so your eye can see it. The ratio of these focal lengths provides the magnification:

If the telescope focal length is 1000 mm and the eyepiece is 25 mm, the magnification is 40×. Every object appears 40 times larger in angular size than it would to the naked eye. Changing eyepieces effectively swaps the magnification. Shorter focal lengths yield higher powers, while longer eyepieces offer wider views.

Apparent vs. True Field of View

Eyepiece manufacturers often quote an apparent field of view (AFOV), the angle your eye sees looking through the eyepiece alone. The real question is how much of the sky, or true field of view (TFOV), you can observe when that eyepiece is combined with a telescope. The TFOV shrinks by the same factor as magnification, following:

This approximation works well for most setups. An eyepiece with a 50° AFOV in a 40× telescope will show about 1.25° of the sky. Wide-field eyepieces, boasting apparent fields of 68°, 82° or more, provide expansive vistas even at high powers.

Exit Pupil Considerations

If you also know your telescope’s aperture $D$, you can estimate the exit pupil—the diameter of the beam of light leaving the eyepiece. It equals the aperture divided by magnification:

The exit pupil should match your eye’s dilation for comfortable viewing. In dark conditions, an adult may reach a pupil size of 6 or 7 mm. If the exit pupil exceeds this size, light is wasted. If it is too small, the view becomes dim. Telescopes used for deep-sky observing often target 4–5 mm for a balance of brightness and contrast.

Using This Calculator

Enter the focal lengths of your telescope and eyepiece, plus the eyepiece’s apparent field of view. If you specify the aperture, the script also returns the exit pupil. Clicking the Calculate View button computes the magnification and TFOV. The copy button lets you transfer the results elsewhere, such as a note-taking app or an observing log.

Because the calculation uses simple ratios, it runs entirely in your browser with no external scripts or network requests. You can experiment freely with hypothetical eyepieces to plan your next purchase or to compare two telescopes side-by-side.

Example Table

Suppose your telescope has a focal length of 1200 mm and an aperture of 200 mm. The table lists magnifications, true fields, and exit pupils for several eyepiece focal lengths with a 68° apparent field.

Eyepiece Focal (mm)	Magnification	True FOV (°)	Exit Pupil (mm)
35	34×	2.0	5.9
25	48×	1.4	4.2
18	67×	1.0	3.0
10	120×	0.57	1.7
5	240×	0.28	0.8

Practical Observing Tips

High magnification is tempting, but turbulence in Earth’s atmosphere often limits usable power. A common rule of thumb is about 50 times the telescope’s aperture in inches on a night of good seeing. For a 200 mm (8 inch) scope, that means around 400× is typically the practical upper limit. Lower powers reveal larger swaths of the Milky Way, double star systems, and extended nebulae. Larger exit pupils also reduce floaters and provide a brighter image.

True field of view helps frame celestial objects. The full Moon spans about 0.5°; many star clusters extend a degree or more. Knowing your TFOV ensures the entire target fits comfortably within the eyepiece. Wide-field views are especially striking for objects like the Andromeda Galaxy, which covers about 3° of sky counting its faint outer arms.

Limits and Assumptions

The formulas above assume a simple optical path. Some telescopes use focal reducers or Barlow lenses that change the effective focal length, altering magnification. Complex eyepiece designs may deviate slightly from the AFOV approximation. Nevertheless, these calculations give reliable first-order estimates for most amateurs. Keep in mind that poorly collimated optics or mismatched components can degrade the image regardless of the computed numbers.

Historical Perspective

Telescope magnification became a prominent selling point during the early days of commercial telescope production. Cheap telescopes were often advertised with impossibly high magnifications to entice novices. Experienced observers know that clarity, stability, and field of view are just as important. This calculator encourages a measured approach—quantifying what each eyepiece will deliver so you can make informed decisions rather than chasing unrealistic claims.

Summary

By comparing your telescope and eyepiece focal lengths, you can instantly assess how large celestial objects will appear and how much of the sky fits in view. This simple tool demystifies the relationships between magnification, field of view, and exit pupil. Experiment with different values and plan your next stargazing session with confidence.