🔭Telescope Calculator - Magnification, True Field, Exit Pupil, Resolution, Astrophotography

How to use Telescope Calculator

1. 1Pick an equipment preset, or enter the aperture, focal length and central obstruction, and add a Barlow or reducer if you use one
2. 2Edit the eyepiece list (focal length and apparent field) to see each one's magnification, true field and exit pupil
3. 3Choose a target (Moon, Jupiter, double star, M42…) and see how large it looks in the eyepiece and whether it can be split
4. 4Switch to Astrophotography, pick a sensor or camera lens, and read the image scale, field, sampling and maximum exposure

FAQ

How do I calculate telescope magnification and true field of view?

Magnification M = telescope focal length / eyepiece focal length, multiplied by the Barlow factor if you use one. A 1200 mm telescope with a 10 mm eyepiece gives 120×. The true field is roughly the eyepiece's apparent field divided by the magnification: a 52° eyepiece at 120× shows about 0.43°, a little less than the full Moon (about 0.52°). The exit pupil is aperture / magnification, and it sets the surface brightness of extended objects.

Why is the maximum useful magnification about twice the aperture in mm?

The smallest angle a telescope resolves is about 116″/D (the Dawes limit, with D in millimetres), while the eye comfortably resolves about 1–2′. Enlarging the Dawes limit to that size takes about 2×D. Beyond that you only magnify the diffraction pattern and the blur ('empty magnification'). From the ground, atmospheric seeing usually caps practical magnification at around 250–350×, even for large telescopes.

Is bigger aperture always better? How are light grasp and limiting magnitude found?

Light grasp scales with aperture area: (D/7)² compared with a dark-adapted 7 mm pupil, times (1 − ε²) for a central obstruction. An 8-inch (203 mm) telescope gathers about 800 times more light than the eye and reaches stars of magnitude 13.5–14. Limiting magnitude ≈ naked-eye limit + 2.5·lg(light grasp). Extended objects like nebulae are never brighter per unit area than they look to the naked eye; they are just bigger. They look brightest at low power with a large exit pupil.

What does sampling mean in astrophotography, and how is the image scale found?

Image scale = 206.265 × pixel size (μm) / focal length (mm), in arcseconds per pixel. Seeing and diffraction set the star size (FWHM), and you want 2–3 pixels across one FWHM. Fewer than 2 is undersampled: stars look blocky and detail is lost. More than about 3.5 is oversampled: it wastes field and signal-to-noise, and you could bin pixels. The tool also suggests the focal length that gives ideal sampling.

What is the difference between the 500 rule and the NPF rule?

Both estimate how long you can expose on a fixed tripod before stars start to trail. The 500 rule is t = 500 / full-frame-equivalent focal length. It is simple but ignores pixel size, so it is too generous for high-resolution sensors. The simplified NPF rule t = (35N + 30p)/f adds the f-number N and pixel pitch p, and is stricter. The tool also works out the exact time for stars to drift a chosen number of pixels at 15.04″/s·cos δ, so stars near the celestial pole allow much longer exposures.