How to use the telescope magnification calculator
- Enter the aperture of the telescope, the width of its main mirror or lens, in millimeters.
- Enter the focal length of the telescope and the focal length of the eyepiece, both in millimeters.
- Open the advanced options to enter the apparent field of the eyepiece and a Barlow lens factor.
- Read the magnification, the exit pupil, the true field of view, the focal ratio and the resolving limits, with a note on whether the magnification is in the usual range.
Formula
magnification = telescope focal length x Barlow factor / eyepiece focal length
exit pupil = aperture / magnification
true field = apparent field / magnification
focal ratio = focal length x Barlow factor / aperture
Dawes limit = 116 / aperture in mm (arcseconds)
The Rayleigh limit is 138 / aperture in mm. The rules of thumb for the useful magnification range are an exit pupil of about 7 mm at the low end and a magnification of about twice the aperture in millimeters at the high end.
A 150 mm telescope with a 25 mm eyepiece
A telescope with a 150 mm aperture and a 750 mm focal length has a focal ratio of f/5. With a 25 mm eyepiece that has a 52 degree apparent field, the magnification is 750 / 25 = 30x. The exit pupil is 150 / 30 = 5.0 mm and the true field is 52 / 30 = 1.733 degrees, about 104 arcminutes. The Dawes limit is 116 / 150 = 0.77 arcseconds.
A 2x Barlow lens doubles the magnification to 60x, halves the exit pupil to 2.5 mm and narrows the true field to 0.867 degrees. An 80 mm refractor with a 400 mm focal length and a 10 mm eyepiece gives 40x and a 2.0 mm exit pupil, well inside the range of about 11x to 160x for that aperture.
What the exit pupil tells you
The exit pupil is the width of the beam of light that leaves the eyepiece. A wide pupil gives a bright, wide view of faint extended objects, while a narrow one gives a dim, high-power view suited to the moon and planets. If the exit pupil is wider than your own pupil, some of the light is wasted, and many people find a pupil near 2 to 5 mm a good place to start.
Limits of the rules of thumb
The Dawes and Rayleigh figures describe the finest detail a perfect telescope could separate under steady air. The air, the optics and your eyes almost always set the practical limit lower. A higher magnification does not add detail beyond that limit. It only makes the image larger and dimmer.
More waves and light tools
For related tools on light and sound, try the Doppler Effect Calculator, Speed of Sound Calculator and Sabine Reverberation Time Calculator.
Assumptions and limits
- The telescope and eyepiece are of good quality with no focal length error.
- The apparent field of the eyepiece is a single figure from its maker.
- A Barlow lens multiplies the focal length of the telescope by its stated factor.
- Resolving limits describe a perfect telescope in steady air.
- The aperture, focal lengths and apparent field in the form are examples to replace with your own.
Frequently asked questions
What is the best magnification?
There is no single best value. It depends on the object, the sky and your telescope, so many observers keep several eyepieces and change them as conditions change.
What is the apparent field of an eyepiece?
It is how wide the view looks to your eye through that eyepiece, in degrees. Dividing it by the magnification gives the true field, the width of sky you see.
Why does the page warn about the magnification range?
Beyond about twice the aperture in millimeters the image gets dim and soft without showing more detail, and below the aperture divided by 7 the exit pupil is wider than most eyes can use. Both are rules of thumb, not hard limits.
Does the focal ratio change the magnification?
No. The focal ratio is the focal length divided by the aperture, and it affects how bright and how wide a field the telescope gives for a given eyepiece, not the magnification itself.