How this instrument works
Magnification is nothing more than a ratio of focal lengths: divide the telescope's focal length by the eyepiece's, M = F_tele ⁄ F_eye. A 1,000 mm telescope paired with a 10 mm eyepiece delivers 100×, full stop — the objective's aperture and the telescope's price tag play no part in that number. Only the two focal lengths decide how large the image appears.
True field of view answers a different question: not how big the image looks, but how much actual sky fits inside it. Every eyepiece carries a fixed apparent field of view, AFOV, built into its optical design — picture it as the angular width of the little window you look through. Divide that window's width by the magnification and the result is TFOV = AFOV ⁄ M. Higher power always narrows what you see, because the same window is being stretched over a smaller patch of real sky.
The division is a well-behaved approximation, accurate to within a percent or two for ordinary eyepieces, but it loosens for ultra-wide designs above roughly 70° AFOV, where lens distortion means the simple ratio slightly underestimates what a manufacturer measures directly on an optical bench. Amateur observers lean on this arithmetic before a night at the eyepiece: choosing between a wide, dim view of a sprawling nebula and a tight, bright view of a planet's cloud bands is really a choice of which Eyepiece focal length produces the True field of view a given target needs.
- Enter your telescope's focal length in the Telescope focal length field — check the tube or the spec sheet; a common beginner scope is 1,000 mm.
- Enter the eyepiece's own focal length in the Eyepiece focal length field, printed on its barrel, typically somewhere between 4 mm and 32 mm.
- Enter the eyepiece's advertised angular window into Eyepiece apparent field of view — fixed by the eyepiece's design, not your telescope, and usually printed on its box or spec sheet.
- Read Magnification, × for the power this pairing delivers, and True field of view for the actual angular width of sky visible through the eyepiece.
- Compare that True field of view figure against the target's known angular size — the full Moon runs about 0.52° across — to judge whether the eyepiece frames it comfortably.
Worked example — a 10 mm eyepiece in a 1,000 mm scope
Take a common 8-inch Newtonian with a 1,000 mm focal length and a 10 mm eyepiece advertised at a 50° apparent field of view — an ordinary Plössl. Magnification comes first: M = 1,000 ⁄ 10 = 100×. That number alone says nothing about how much sky is visible, only how much the image has been enlarged.
TFOV follows by dividing the eyepiece's own 50° window by that same 100×: TFOV = 50° ⁄ 100 = 0.5°. The full Moon spans about 0.52° across, so this pairing frames it with almost no margin to spare — step up to a longer eyepiece, or drop the magnification, and the Moon's disc starts to spill past the edge of the frame.
Questions
Why does higher magnification shrink the field of view?
Because TFOV is the eyepiece's fixed AFOV divided by magnification, and that ratio only shrinks as magnification climbs — the same window of sky gets stretched over a smaller and smaller patch. Double the power and what you see is cut in half; the eyepiece's own AFOV never changes, only how much sky that fixed window is made to cover.
Where do I find an eyepiece's apparent field of view?
It is printed on the eyepiece's spec sheet or box, not something you calculate — AFOV is fixed by the optical design, typically 40–50° for a simple Plössl, 60–70° for a wide-angle design, and up to 100° for premium hyper-wide eyepieces. If the packaging omits it, the manufacturer's own product page almost always lists the figure.
Is TFOV = AFOV ⁄ M exact for every eyepiece?
It is a close approximation for eyepieces under roughly 60° AFOV, but it drifts for wide-angle designs beyond that, where barrel distortion means the simple ratio slightly underestimates TFOV. Makers of ultra-wide eyepieces often publish a separately measured true field of view for this reason, worth checking against this formula's output once AFOV climbs past about 70°.
Does the telescope's aperture change the field of view?
No — that depends only on the two focal lengths and the eyepiece's AFOV, not on aperture, the diameter of the main mirror or lens. A 90 mm and a 250 mm telescope sharing a 1,000 mm focal length and the same eyepiece produce an identical TFOV; aperture instead governs how much light is gathered and how faint an object can be seen.
What eyepiece do I need to fit a whole nebula or constellation?
Work backwards from the target's known angular size: pick a Magnification, × low enough — meaning a longer Eyepiece focal length — that True field of view comfortably exceeds the object. The Andromeda Galaxy spans roughly 3° end to end, so a scope needs a TFOV near 3° or wider, which usually means low power paired with a wide-angle eyepiece, to fit the whole thing in one view.
How does a Barlow lens change these numbers?
A 2× Barlow effectively halves the eyepiece focal length feeding into the magnification formula, so Feye is divided by the Barlow's factor before M is computed — a 10 mm eyepiece behind a 2× Barlow behaves like a 5 mm eyepiece, doubling magnification and halving TFOV. The eyepiece's own AFOV is unaffected by the Barlow; only the magnification, and hence what you see, changes.