Telescope Magnification Calculator

What the telescope magnification calculator does

A telescope's magnification depends on two focal lengths: the telescope's own and that of the eyepiece you put in it. This calculator works out the magnification from those two, and it can also solve for either focal length when you know the magnification you want.

Below is what telescope magnification is, the equation behind it, how to choose eyepieces, and a worked example.

How to use it

1. Choose what to calculate: the magnification, the telescope's focal length, or the eyepiece's focal length.
2. Enter the two values you know, with the focal lengths in millimetres.
3. Press Calculate for the result, or Reset to clear it.

What telescope magnification is

Magnification is how much larger a telescope makes a distant object appear compared with the naked eye. A magnification of fifty means an object looks fifty times bigger across, bringing craters on the Moon or the rings of Saturn into view that the unaided eye could never resolve. It is the number most people first ask about a telescope, and it is set not by the telescope alone but by the combination of the telescope and the particular eyepiece in use.

That last point is the key to understanding it. The same telescope can give wildly different magnifications depending on which eyepiece you slot in, which is why telescopes come with a set of interchangeable eyepieces. Swapping eyepieces is how an observer changes magnification on the fly, zooming in for a close look at a planet or pulling back for a wide view of a star cluster. This calculator captures the relationship that ties the two focal lengths to the resulting magnification.

The equation it uses

The magnification is the telescope's focal length divided by the eyepiece's focal length:

M = f_telescope ÷ f_eyepiece

Here f_telescope is the focal length of the telescope, the distance over which its main lens or mirror brings light to a focus, and f_eyepiece is the focal length of the eyepiece. The longer the telescope's focal length and the shorter the eyepiece's, the greater the magnification. The calculator divides one by the other, or rearranges the relationship to find whichever focal length you need for a target magnification.

Choosing eyepieces

Because the eyepiece focal length sits on the bottom of the fraction, a shorter eyepiece gives a higher magnification. This is the opposite of what many beginners expect, but it follows directly from the formula: halving the eyepiece focal length doubles the magnification. So a 10-millimetre eyepiece magnifies twice as much as a 20-millimetre one on the same telescope.

This is why observers keep a range of eyepieces on hand. A long eyepiece gives low magnification and a wide, bright field of view, ideal for finding objects and viewing large, faint targets like nebulae. A short eyepiece gives high magnification for a detailed look at the Moon, planets, or double stars. The calculator makes it easy to plan a set: pick the magnifications you want, and it tells you which eyepiece focal lengths will deliver them on your telescope.

Why more magnification is not always better

It is tempting to think a telescope is better the more it magnifies, but in practice there is a ceiling, and pushing past it makes the view worse, not better. Magnifying an image also magnifies its blur, and beyond a certain point you are just enlarging a fuzzy, dim picture. The limit is set mainly by the telescope's aperture, the diameter of its main lens or mirror, which governs how much detail it can actually gather. A common rule of thumb puts the highest useful magnification at roughly twice the aperture measured in millimetres.

The atmosphere imposes its own limit. Even on a good night, the shimmering of the air blurs fine detail, and on a turbulent night, high magnification only enlarges that shimmer into a wobbling mess. This is why experienced observers often spend most of their time at modest magnifications, where images are bright, steady, and sharp, and reach for high power only on the steadiest nights and the brightest targets. The calculator tells you the magnification a given eyepiece will give, but the sky and the telescope's aperture decide how much of it is worth using.

Units and precision

The calculator takes the telescope and eyepiece focal lengths in millimetres, the standard unit marked on eyepieces, and returns the magnification as a plain number, conventionally written with an x, as in 100x. The calculation is a simple, exact ratio, and the results carry several significant figures. The magnification itself has no units, since it is a ratio of two lengths.

A worked example

Suppose a telescope has a focal length of 1,000 millimetres, and you fit it with an eyepiece of 10 millimetres focal length.

The magnification is M = f_telescope ÷ f_eyepiece = 1,000 ÷ 10 = 100x, so objects appear a hundred times larger. Switch to a 20-millimetre eyepiece and the magnification drops to 50x, with a wider, brighter field. Switch to a 5-millimetre eyepiece and it climbs to 200x, though whether that sharper zoom is usable depends on the telescope's aperture and the steadiness of the air.

Questions people ask

How do you calculate telescope magnification?

Divide the telescope's focal length by the eyepiece's focal length, M = f_telescope/f_eyepiece. Both are usually measured in millimetres.

Why does a shorter eyepiece magnify more?

Because the eyepiece focal length is on the bottom of the fraction, so a smaller value gives a larger magnification. A 10-millimetre eyepiece magnifies twice as much as a 20-millimetre one.

Is there a limit to useful magnification?

Yes. Beyond about twice the aperture in millimetres, you only enlarge blur and dimness, not detail. The atmosphere often lowers the practical limit further on unsteady nights.

What magnification is best?

It depends on the target and conditions. Low magnification suits wide, faint objects and gives bright, steady views; high magnification suits the Moon and planets on steady nights. Most observing happens at modest powers.

References

A quick note on where the physics comes from. The magnification of a telescope as the ratio of focal lengths is standard optics, set out in OpenStax's University Physics and in Georgia State University's HyperPhysics. The HyperPhysics link is worth a quick click to confirm it lands where you expect.

1. OpenStax, University Physics Volume 3, Section 2.9, Microscopes and Telescopes. https://openstax.org/books/university-physics-volume-3/pages/2-9-microscopes-and-telescopes
2. HyperPhysics, Telescope Magnification. http://hyperphysics.phy-astr.gsu.edu/hbase/geoopt/teles.html
3. NASA Science, Telescopes and how they work. https://science.nasa.gov/mission/hubble/observatory/design/optics/