Magnification is the number printed on the box, but field of view decides whether you can find anything. A 200 mm telescope at 300× shows a patch of sky smaller than a fifth of a full Moon, and hunting for a galaxy through that patch without knowing how wide it is wastes whole evenings. The true field of view is the angular width of sky visible at the focus, and it is what you compare against a target's published size before going outside.
Arb Digital builds free physics calculators that each own one job. The live telescope magnification calculator is the adjacent page: it owns power, exit pupil, focal ratio and the Dawes limit, and reports a true field as a by-product using the apparent-field-divided-by-magnification shortcut, which it says openly is good to a few per cent. This page starts from the other end. It owns the exact field-stop method manufacturers publish, the imaging case where a rectangular sensor sets the field, sky area in square degrees, and drift time. Use that page for power and exit pupil; use this one for how much sky you are looking at.
What This Telescope Field of View Calculator Does
In visual mode it takes the telescope focal length, the eyepiece focal length and either the field stop diameter or the apparent field, and returns the true field in degrees and arcminutes. In imaging mode it takes the sensor dimensions instead and returns the rectangular field the chip covers, with the image scale in arcseconds per pixel.
Four supporting figures follow. Magnification or image scale sets the resolution you are working at. Sky area in square degrees measures how much you can survey per pointing, and it scales as the square of the field width. Drift time is how long a target takes to cross the field with the drive off — a planning number and the classic test of whether a mount is tracking. Field width in full-Moon widths is the fastest sanity check there is. OpenStax covers the underlying optics of aperture, focal length and magnification in section 6.1, Telescopes, of Astronomy 2e.
One safety point applies to every configuration on this page and it is not negotiable. Never view the Sun through a telescope, camera lens or binoculars without a purpose-made solar filter fitted over the front of the optics. NASA's eclipse viewing safety guidance states plainly that doing so "will instantly cause severe eye injury". Eclipse glasses held behind an eyepiece do not help; the concentrated beam destroys them. Retinal burns are painless as they happen because the retina has no pain receptors, so there is no warning and the damage is permanent. If you want to know where the Sun will be at a given time and place, the sun position calculator gives elevation and azimuth, and it carries the same warning.
How to Use It
- Enter the effective focal length. With a Barlow or reducer in the path, multiply or divide first — a 2× Barlow on a 1,200 mm scope means entering 2,400 mm.
- Enter the eyepiece field stop diameter if you can find it. Most serious eyepiece manufacturers publish it, and it gives the exact field rather than an estimate.
- Otherwise enter the apparent field and leave the field stop at zero. The page will use the approximation and tell you it is doing so.
- Switch to imaging mode and enter the sensor width, height and pixel pitch for a camera at prime focus.
- Set the declination of the object you are planning to observe if you want a meaningful drift time. At the celestial equator drift is fastest; near the pole it slows almost to a stop.
The Formula: Two Ways to Get a True Field
The approximate method divides the eyepiece's apparent field by the magnification. Magnification is the telescope focal length divided by the eyepiece focal length, so
TFOV ≈ AFOV ÷ (Fscope ÷ feyepiece).
The exact method ignores the eyepiece focal length entirely and uses the diameter of the physical aperture inside the eyepiece that crops the image — the field stop. The field stop sits in the focal plane, so its diameter maps directly onto an angle on the sky through the telescope's focal length:
TFOV = 57.2958 × Dstop ÷ Fscope, in degrees, with both diameters in millimetres.
Work the default by hand. A 1,200 mm telescope with a 25 mm eyepiece gives a magnification of 1200 ÷ 25 = 48×. With a 52° apparent field the approximation returns 52 ÷ 48 = 1.083°. With a published 22 mm field stop the exact method returns 57.2958 × 22 ÷ 1200 = 1.050°, or 63.0 arcminutes. The two differ by about three per cent, which is typical, and the exact figure is the one to trust.
For a sensor the geometry is the same but the shape is rectangular, so the exact form uses an arctangent rather than a small-angle ratio: TFOV = 2 arctan(w ÷ 2F). A 23.5 × 15.6 mm chip on the same 1,200 mm telescope covers 1.122° by 0.745°. The image scale follows from the same focal length: arcseconds per pixel = 206.265 × pixel size in micrometres ÷ focal length in millimetres, which for 3.76 μm pixels gives 0.646 arcseconds per pixel.
Why Sky Area Matters More Than Field Width
Field width is a length; sky area is what you are actually surveying, and it goes as the square. Halving the magnification doubles the field width but quadruples the area, which is why a modest drop in power makes such a dramatic difference to how quickly you can sweep for a comet or star-hop to a faint target.
The full Moon is about 0.518° across, covering roughly 0.21 square degrees, and the whole sky is 41,253 square degrees. A one-degree circular eyepiece field is about 0.79 square degrees, so a single pointing shows around one fifty-thousandth of the sky. That is why star-hopping is a skill: at high power you are looking through a straw.
It also explains the difference between eyepiece and sensor fields at the same focal length. An eyepiece view is a circle of area π(θ÷2)²; a sensor field is a rectangle of area width times height. A chip whose diagonal matches an eyepiece's field circle covers less sky, because the circle's corners fall outside the rectangle.
Drift Time, and the Test It Gives You
The sky rotates at the sidereal rate, 15.041 arcseconds per second of time at the celestial equator, which is one degree every four minutes. An object at declination δ drifts more slowly by a factor of cosδ, because circles of constant declination are smaller near the poles.
So the time for an object to cross a field of width θ degrees is roughly t = θ × 240 ÷ cosδ seconds. The default 1.050° field at the equator gives about 252 seconds, or four minutes and twelve seconds. The same field at declination 60° gives twice that, because cos 60° is 0.5.
That number is more useful than it looks. It is the standard way to check whether a mount is genuinely tracking: centre a star, wait, and if it stays put for far longer than the drift time the drive is working. It also sets a hard ceiling on untracked exposures at prime focus, and it is how visual observers with undriven Dobsonians plan their observing — nudge, look, nudge again. For the diffraction limit that decides what detail can be resolved inside that field, the angular resolution calculator covers the Rayleigh and Dawes criteria.
Where These Numbers Stop Being Exact
The field stop method is geometrically exact but assumes the field stop is genuinely at the focal plane and that you have the real diameter. Some manufacturers publish a nominal figure, some publish the apparent field instead, and some publish neither. Where a published field stop is unavailable, measuring the drift time of an equatorial star and inverting the relation above gives the true field to better than a per cent, which is a genuinely useful field technique.
The apparent-field approximation carries a second-order error from distortion. Wide-field eyepieces are designed with deliberate angular magnification distortion to control the rectilinear distortion that makes panning uncomfortable, and that shifts the effective mapping between apparent and true field. The error grows with apparent field, so a 100° eyepiece is where the approximation is worst and the field stop figure matters most.
Two further limits apply. At very low magnification the exit pupil can exceed the observer's dark-adapted pupil, wasting the outer part of the light cone — the telescope magnification calculator handles that. And a sensor larger than the telescope's corrected image circle shows vignetting and aberrated corners long before it runs out of geometric field, an optical limit this page does not model. Degrees, arcminutes, arcseconds and radians convert in the angle converter.
Arb Digital builds free tools like this one because useful pages earn attention. If you want tools, calculators or content built for your own audience, we can help.
Browse All Free Tools Talk to Arb DigitalCommon Mistakes to Avoid
- Confusing apparent and true field — apparent field is a property of the eyepiece alone, typically 50° to 100°. True field is what the telescope and eyepiece show together, and it is always far smaller.
- Forgetting the Barlow or reducer — these change the effective focal length, and the field changes with it. Enter the focal length after the accessory, not the bare telescope figure.
- Comparing field width when you mean sky area — area scales as the square of width, so a field twice as wide surveys four times as much sky, not twice as much.
- Assuming a sensor's diagonal field is its usable field — the telescope's corrected image circle, not the geometry, usually decides how much of a large chip produces round stars.
- Pointing any optic at the Sun without a front-mounted solar filter — this causes instant, painless and permanent retinal damage. Filters that screw into an eyepiece are not adequate and are not used by anyone who understands the risk.
Related Free Tools From Arb Digital
For power, exit pupil, focal ratio and the resolution limit of the same instrument, use the telescope magnification calculator. The angular resolution calculator covers the diffraction limit that sets the finest detail visible inside the field. The sun position calculator gives solar elevation and azimuth for planning, the moon phase calculator tells you how much moonlight to expect, and the synodic period calculator works out when two bodies return to the same alignment. If you have a measured parallax, the stellar parallax calculator turns it into a distance. Everything Arb Digital publishes is on the free online tools hub.
Frequently Asked Questions
It is the angular width of the patch of sky visible at the focus, measured in degrees or arcminutes. It depends on the telescope's focal length and on the eyepiece or sensor at the focus, and it is always much smaller than the eyepiece's own apparent field.
The exact method divides the eyepiece field stop diameter by the telescope focal length and multiplies by 57.2958 to get degrees. The approximate method divides the eyepiece apparent field by the magnification, which is accurate to a few per cent for ordinary eyepieces.
Apparent field is the angular width of the illuminated circle as it appears to the eye looking into the eyepiece, and it is a property of the eyepiece alone. True field is the actual angle on the sky that circle corresponds to once the telescope's magnification is applied.
Use the sensor dimensions rather than an eyepiece. The field in degrees is twice the arctangent of half the sensor dimension divided by the focal length, computed separately for width and height because the chip is rectangular.
It is how much sky one pixel covers, and it equals 206.265 multiplied by the pixel size in micrometres and divided by the telescope focal length in millimetres. It sets the sampling of the image and is the figure to compare against the seeing and the diffraction limit.
The sky moves one degree every four minutes at the celestial equator, so a field of a given width in degrees takes roughly that width times 240 seconds to cross. Objects at higher declination drift more slowly, by a factor of one over the cosine of the declination.
No. Eclipse glasses are made for the naked eye only. Viewing the Sun through a telescope, camera lens or binoculars without a purpose-made filter fitted over the front of the optics causes instant and permanent eye injury, and the concentrated beam will destroy a filter held behind the optics.
Because sky area scales as the square of the field width. Halving the magnification roughly doubles the field width and therefore quadruples the area surveyed, which is why finding faint objects is done at low power before switching to high power to examine them.
This tool is provided for educational and observing-planning use. It computes geometric fields only and does not model vignetting, the telescope's corrected image circle, eyepiece distortion or atmospheric refraction. Never observe the Sun through any optical instrument without a purpose-made full-aperture solar filter fitted over the front of the optics; the resulting retinal injury is instant, painless and permanent.
