Refracting Telescope Magnification Formula

This calculator works out the magnification of a refracting telescope. You enter the telescope’s focal length (in mm) and the eyepiece’s focal length (in mm), and it returns the magnification factor—how many times larger the object appears compared to the naked eye. The formula is simply telescope focal length divided by eyepiece focal length.

Formula

The magnification M of a refracting telescope is given by:

M = F_telescope / F_eyepiece

• M – magnification (dimensionless, often written as “×” or “power”)
• F_telescope – focal length of the objective lens (the large front lens), in millimeters (mm)
• F_eyepiece – focal length of the eyepiece, in millimeters (mm)

Both focal lengths must be in the same unit (usually mm). The result is a pure number—it has no unit.

Worked Example

Using the default values from the calculator: a telescope with a focal length of 900 mm and a 25 mm eyepiece.

1. Write down the formula: M = F_telescope / F_eyepiece
2. Plug in the numbers: M = 900 mm / 25 mm
3. Divide: M = 36

The magnification is 36×. The object appears 36 times larger in angular size than it does with the unaided eye.

Why the Formula Works

A refracting telescope uses a large objective lens to gather light and form a real image at its focal plane. The eyepiece then acts like a magnifying glass to enlarge that image. The angular magnification is the ratio of the angle subtended at the eye with the telescope to the angle without it. For small angles, that ratio equals the focal length of the objective divided by the focal length of the eyepiece. This is a fundamental optical relationship that applies to all refractors, regardless of their aperture or design.

The focal length of the objective is usually printed on the telescope tube or in the manual (e.g., 700 mm, 900 mm). Eyepieces are marked with their focal length in millimeters (e.g., 10 mm, 20 mm, 25 mm). Simply divide the two.

How to Choose the Right Eyepiece

To get a desired magnification, rearrange the formula: Eyepiece focal length = Telescope focal length / Desired magnification.

For example, with a 900 mm telescope:

• To get 50×, use a 18 mm eyepiece (900/50 = 18).
• To get 100×, use a 9 mm eyepiece (900/100 = 9).
• To get 200×, use a 4.5 mm eyepiece (900/200 = 4.5).

Most telescopes come with one or two eyepieces, but you can buy additional ones with different focal lengths. Lower magnification (longer eyepiece focal length) gives a wider field of view and a brighter image—good for deep-sky objects and finding targets. Higher magnification (shorter eyepiece) is better for the Moon and planets, but the image gets dimmer and more sensitive to atmospheric turbulence.

Common Mistakes and Limits

The most common mistake is mixing units—for instance, using the telescope focal length in millimeters and the eyepiece focal length in inches. Always convert to the same unit before dividing.

Another mistake is assuming higher magnification is always better. Every telescope has a maximum useful magnification, roughly 2× the aperture in millimeters (or 50× per inch of aperture). For a 60 mm refractor, that’s about 120×. Beyond that, the image becomes too dim and blurry to be useful. The formula gives the geometric magnification, but the actual resolving power is limited by the aperture and the atmosphere.

The formula also assumes the eyepiece is the only magnification element. If you use a Barlow lens (which multiplies the effective focal length) or a focal reducer, you must account for that factor. For example, a 2× Barlow doubles the effective focal length of the telescope, so the magnification doubles.

Practical Considerations for Refractors

Refracting telescopes are known for crisp, high-contrast images because they use lenses instead of mirrors. However, they can suffer from chromatic aberration—color fringing around bright objects—especially in achromatic designs. This does not affect the magnification formula, but it can limit how much you can usefully magnify before the color errors become distracting.

When observing, let the telescope cool to the outside temperature before using high magnification. Air currents inside the tube can distort the image. Also, use a sturdy mount; at high magnification, even small vibrations become very noticeable.

Frequently Asked Questions

What does “power” mean on a telescope?

“Power” is just another word for magnification. A 50× telescope makes objects appear 50 times larger than they do with the naked eye. The power is always the telescope focal length divided by the eyepiece focal length.

Can I use any eyepiece with my refractor?

Most refractors accept standard 1.25-inch or 2-inch eyepieces. Check the focuser diameter. You can also use eyepieces from other brands as long as the barrel size matches. Avoid forcing an eyepiece that doesn’t fit.

Why does high magnification make the image blurry?

High magnification enlarges the image, but it also enlarges atmospheric turbulence and any optical imperfections. If the seeing is poor, the image will appear to boil or shimmer. Also, if you exceed the maximum useful magnification (about 2× aperture in mm), the image becomes dim and soft.

Does a Barlow lens change the magnification?

Yes. A Barlow lens is placed between the eyepiece and the telescope. It increases the effective focal length of the telescope by its factor (e.g., 2× or 3×). So the magnification becomes (telescope focal length × Barlow factor) / eyepiece focal length.

How do I find the focal length of my telescope if it’s not written?

Look for a label on the tube or the focuser. If it’s missing, check the manual or the manufacturer’s website. You can also measure it approximately: the focal length is the distance from the objective lens to the point where a distant object comes to focus. This is usually close to the length of the tube, but not exactly.

Is magnification the same as zoom?

No. Magnification is a fixed ratio for a given eyepiece. Zoom eyepieces have a variable focal length, so they change magnification continuously. The formula still applies—you use the current focal length of the zoom eyepiece.

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in t | Telescope focal length | mm | 900 | 0
in e | Eyepiece focal length | mm | 25 | 0
out m | Magnification | x | t / e | 0