Field of view & pixel scale calculator

How the numbers are worked out

1. Field of view. 2 × atan(sensor mm ÷ 2 × focal mm) for the width, height and diagonal, in degrees and arcminutes. Focal length is the value the maker states for the configuration you picked — a 0.7× reducer entry already carries the reduced focal length.
2. Image scale. 206.265 × pixel µm ÷ focal mm arcseconds per pixel (206 265 arcseconds in a radian).
3. Resolution limits. Dawes 116 ÷ aperture mm and Rayleigh 138 ÷ aperture mm, in arcseconds — the classic double-star criteria for visible light.
4. Sampling. Pixels per star FWHM = seeing ÷ image scale, for seeing of 1.5, 2, 2.5, 3″. Fewer than 2 is under-sampled (Nyquist), more than 3 is over-sampled, in between is the band most imaging guides recommend. We do not forecast seeing; the four values bracket what typical sites deliver.
5. Fit. A target fits when its catalogue major axis is no longer than the frame's long side and its minor axis no longer than the short side; otherwise the tool says how many panels along the long axis a mosaic needs.
6. Transit month. An object is highest at local midnight when the Sun's right ascension equals its own minus 12 hours; the Sun's RA is 0h at the March equinox and advances 24h per year. Pure geometry, no weather.

Honesty notes: catalogue sizes are visual extents and the faint outer nebulosity a long exposure records can be larger; position angles are not stored, so every object is drawn with its long axis horizontal. Pixel counts are derived from sensor size ÷ pixel size and can differ slightly from the maker's effective-pixel figure. Seeing varies night to night and is not something this site predicts.

Questions people ask

How is the field of view of a telescope and camera calculated?

Field of view = 2 × atan(sensor side ÷ (2 × focal length)). For a 23.5 mm wide APS-C sensor on a 264 mm telescope that is 2 × atan(23.5 / 528) = 5.10°, or 306 arcminutes. The tool uses the focal length as used — after a reducer, if one is selected — and the sensor dimensions from the manufacturer specification.

What is image scale (arcseconds per pixel) and why does it matter?

Image scale = 206.265 × pixel size in µm ÷ focal length in mm. It says how much sky each pixel covers. Compared with the size of a star image in your seeing (its FWHM), it decides whether stars are blocky (under-sampled, fewer than two pixels per FWHM) or spread over too many pixels (over-sampled, more than three).

What image scale is ideal for deep-sky imaging?

Aim for 2–3 pixels across the star FWHM. In 2″ seeing that means 0.67–1.0″ per pixel; in 3″ seeing 1.0–1.5″ per pixel. Short, fast refractors with small pixels are usually under-sampled (fine for wide fields, drizzle helps); long Schmidt–Cassegrains with small pixels are over-sampled (bin 2×2 to recover sensitivity).

What are the Dawes and Rayleigh limits?

They are the classic resolution limits of an aperture for a double star: Dawes = 116 ÷ aperture in mm, Rayleigh = 138 ÷ aperture, both in arcseconds. A 100 mm telescope resolves about 1.2″. In practice the atmosphere (seeing of 1.5–3″) limits deep-sky images far more than the aperture does.

Will M31 or the North America Nebula fit in my frame?

The Andromeda Galaxy is about 178 × 63 arcminutes and NGC 7000 about 120 × 100 arcminutes (catalogue visual extents). A full-frame sensor on a 530 mm telescope gives 233 × 156 arcminutes, so both fit; an APS-C sensor on a 1,000 mm telescope gives 81 × 54 arcminutes and needs a mosaic. The tool draws each target inside your frame to scale.

Where do the angular sizes and best months come from?

Sizes are read from the SEDS Messier database, the NASA Moon fact sheet and catalogue entries, and every row links to the page it was taken from with the date it was read. "Transits at midnight" is derived from the object's right ascension — the month in which it crosses the meridian at local midnight — not copied from anywhere, and it ignores weather and the Moon.

Once the framing is right, the back-focus calculator checks the threads and spacers between the same telescope and camera. For the night itself, the 16-night forecast finds the clear, moonless hours.