Telescope Magnification & Field of View Calculator

How Telescope Magnification Works

A telescope uses its main optical element (a lens or mirror) to focus incoming light into an image at its focal plane. This element has a focal length, usually printed on the tube or in the manual. An eyepiece, which also has its own focal length, then magnifies that focused image so your eye can see fine detail.

In simple terms, magnification tells you how many times larger an object appears through the telescope compared with the naked eye. Higher magnification shows more detail, but also narrows the field of view and can make the image dimmer and shakier.

The basic formula for magnification is:

Magnification

M = F_t / F_e

where:

• F_t is the telescope focal length (in millimetres).
• F_e is the eyepiece focal length (in millimetres).
• M is the magnification (a unitless ratio, often written as “×”).

Example: if your telescope focal length is 1000 mm and your eyepiece focal length is 25 mm, then:

M = 1000 / 25 = 40×

Through this setup, objects appear about 40 times larger in angular size than they do with the unaided eye. Swapping eyepieces changes the magnification. Shorter focal length eyepieces give higher magnification; longer focal length eyepieces give lower magnification and a wider patch of sky.

Apparent vs. True Field of View

Eyepiece specifications often list an apparent field of view (AFOV) in degrees. This is roughly the angle your eye sees when you look into the eyepiece alone, not attached to any particular telescope. Common AFOV values include around 40–50° for simple designs, 60–70° for wide-field eyepieces, and 80° or more for ultra-wide designs.

What observers usually care about at the telescope, however, is the true field of view (TFOV): how much of the actual sky (in degrees) is visible through the scope–eyepiece combination. The true field is smaller than the apparent field because magnification stretches the image.

A widely used approximation relates TFOV to AFOV and magnification:

True Field of View (approximate)

TFOV ≈ AFOV / M

where:

• AFOV is the apparent field of view of the eyepiece (in degrees).
• M is the magnification calculated from the focal lengths.
• TFOV is the approximate true field of view on the sky (in degrees).

Example: if an eyepiece has AFOV = 50° and the magnification with your telescope is 40×, then:

TFOV ≈ 50 / 40 = 1.25°

You would see a patch of sky about 1.25 degrees across—slightly more than twice the apparent diameter of the full Moon (about 0.5°).

Exit Pupil and Image Brightness

If you also know your telescope’s aperture (the diameter of the main lens or mirror), you can calculate the exit pupil. This is the diameter of the beam of light that emerges from the eyepiece and enters your eye.

The exit pupil connects image brightness, contrast, and how comfortable the view appears. For extended objects like nebulae and galaxies, the apparent surface brightness in the eyepiece depends strongly on exit pupil.

The exit pupil is given by:

Exit Pupil

EP = D / M

where:

• D is the telescope aperture (in millimetres).
• M is the magnification.
• EP is the exit pupil diameter (in millimetres).

Typical dark-adapted pupil diameters for adults range from about 5 mm to 7 mm, depending on age, lighting, and individual variation. If the calculated exit pupil is larger than your eye’s pupil, some of the light from the telescope never reaches your retina—it is effectively wasted. If the exit pupil is very small (for example, 0.5–1 mm), the image can appear dim and may show floaters in your eye more prominently.

Observers often target exit pupils in these rough ranges:

• 4–6 mm: bright, wide-field views of large nebulae, open clusters, and the Milky Way star fields.
• 2–3 mm: a good compromise for many deep-sky objects, balancing brightness and contrast.
• 1–2 mm: common range for lunar and planetary observing where higher magnification is needed.
• < 1 mm: very high powers, mainly for splitting tight double stars or occasional planetary detail when the atmosphere is extremely steady.

Interpreting the Calculator Results

This calculator asks for:

• Telescope focal length (in millimetres).
• Eyepiece focal length (in millimetres).
• Eyepiece apparent field of view (in degrees).
• Telescope aperture (optional, in millimetres) if you want the exit pupil.

From these inputs it returns:

• Magnification (M), showing how many times larger objects appear than with the naked eye.
• True field of view (TFOV), the approximate patch of sky you see, measured in degrees.
• Exit pupil (EP), the diameter of the beam of light reaching your eye (shown only if you provide aperture).

Use these outputs together, rather than in isolation:

• If magnification is very high but the exit pupil is tiny, the image may be dim and sensitive to poor atmospheric seeing.
• If the true field of view is very small but you want to frame a large object (for example, the Pleiades or the Orion Nebula), you may need a longer focal length eyepiece or one with a larger AFOV.
• If the exit pupil is larger than about 6–7 mm, you are probably not using the full light-gathering potential of your telescope.

Worked Example Calculation

Consider a telescope with:

• Telescope focal length F_t = 1200 mm
• Telescope aperture D = 200 mm

Suppose you have an eyepiece with:

• Eyepiece focal length F_e = 20 mm
• Apparent field of view AFOV = 68°

Step 1: Magnification

Use the magnification formula:

M = F_t / F_e = 1200 / 20 = 60×

The telescope–eyepiece combination gives 60 times magnification.

Step 2: True field of view

Apply the TFOV approximation:

TFOV ≈ AFOV / M = 68 / 60 ≈ 1.13°

You will see a patch of sky roughly 1.1 degrees across—about twice the width of the full Moon.

Step 3: Exit pupil

Now calculate the exit pupil:

EP = D / M = 200 / 60 ≈ 3.3 mm

An exit pupil of about 3.3 mm is a very comfortable size for many deep-sky objects, providing a good balance of brightness and contrast.

You can use this same process with any set of inputs: enter the values into the calculator, then review the magnification, TFOV, and exit pupil to see whether the combination suits your target (planets, Moon, star clusters, galaxies, wide-field sweeping, and so on).

Example Eyepiece Combinations

The table below shows example results for a 1200 mm focal length, 200 mm aperture telescope with a 68° AFOV eyepiece at different eyepiece focal lengths.

These numbers are illustrative, but they show how changing only the eyepiece focal length affects magnification, field of view, and exit pupil:

• At 30 mm, the view is wide and bright, ideal for large nebulae and sweeping star fields.
• At 12–8 mm, magnification and contrast increase, making this range good for smaller galaxies, globular clusters, and lunar detail.
• At 5 mm, magnification is high and the exit pupil small; views will be sensitive to atmospheric stability but can show fine planetary or double-star details when conditions allow.

Practical Observing Guidelines

You can use the calculator outputs to help choose appropriate eyepieces for different types of targets:

• Wide-field and large objects (Milky Way, large open clusters, big nebulae): look for low magnification (large eyepiece focal length), true fields of view larger than about 1°, and exit pupils around 4–6 mm.
• General deep-sky observing (many galaxies and nebulae): a magnification range that gives 2–3 mm exit pupils is often a good starting point.
• Moon and planets: try magnifications that yield 1–2 mm exit pupils, adjusting based on how steady the atmosphere appears on a given night.
• Double stars and very small details: very high magnification (exit pupils below 1 mm) can be useful, but only when seeing conditions are excellent and the optics are well collimated.

Assumptions and Limitations

The formulas and results provided by this calculator rest on several simplifying assumptions:

• Approximate TFOV formula: The relationship TFOV ≈ AFOV / M is an approximation that works reasonably well for many eyepieces. In reality, the exact true field is more accurately determined by the eyepiece’s field stop diameter and the telescope focal length. Some eyepiece designs or configurations may deviate from the simple estimate.
• Ideal optics: The calculator assumes perfect, aberration-free optics. It does not account for coma, field curvature, astigmatism, chromatic aberration, or other distortions that can affect edge sharpness and perceived field of view.
• Visual use only: The results are intended for visual observing. For astrophotography, the concepts of image scale, sensor size, and sampling are more relevant than eyepiece AFOV, and this tool does not model those factors.
• Units and values: All inputs assume millimetres for focal lengths and aperture, and degrees for apparent field of view. Entering values in other units will produce incorrect results.
• Observer’s eye: Exit pupil interpretations assume a dark-adapted human eye with typical pupil sizes. Individual eyes vary, and pupil size decreases with age. The calculator does not attempt to model these personal differences.
• Accessories not modeled: Additional optics, such as Barlow lenses, focal reducers, or binoviewers, change the effective focal length of the system. To use those configurations accurately, you should manually adjust the telescope focal length in the inputs to reflect the effective value.
• Atmospheric seeing and transparency: The calculator cannot account for the quality of the night sky. Poor seeing or light pollution can make very high magnifications impractical even if the numeric results look promising.

Because of these limitations, treat the outputs as practical guidelines and planning tools rather than exact predictions. Use them to compare different eyepieces, explore how magnification and field of view trade off against each other, and choose sensible starting points for real observing sessions. Final choices should be guided by what you actually see at the eyepiece under your local conditions.