Eyepiece Calculator: Field of View and Exit Pupil

A 25 mm eyepiece in a 1200 mm telescope gives 48x. Divide 1200 by 25.

The aperture behind that focal length is 203 mm (8 in). Exit pupil is 4.23 mm, from 203 ÷ 48.

At 52° apparent, true field of view is 1.08°, or 2.1 Moon widths at 0.52°. The calculator above opens on these numbers. Sky & Telescope's formulas, checked Oct 17, 2026.

Magnification is telescope focal length divided by eyepiece focal length. On the default, 1200 ÷ 25 = 48x. The magnification calculator is the page for a separate power check.

A 60 mm (2.4 in) department-store refractor box often says 675x. That is 900 mm × 3 (the 3x Barlow in the box) ÷ 4 mm. The ceiling for 60 mm is 2 × 60 = 120x, so 675x is unusable, about 5.6 times past it.

The table below works the same four inputs by hand. Magnification = focal length ÷ eyepiece. Exit pupil = aperture ÷ magnification, and also eyepiece ÷ focal ratio. Here 1200 ÷ 203 = f/5.91, so 25 ÷ 5.91 = 4.23 mm. True field ≈ apparent field ÷ magnification = 52 ÷ 48 = 1.08°. A field stop is a separate sum: 57.3 × stop mm ÷ focal length mm.

Exit pupil is the beam diameter leaving the eyepiece. Divide aperture by magnification. On the default, 203 ÷ 48 = 4.23 mm.

The second path divides eyepiece focal length by focal ratio. Here 1200 ÷ 203 = f/5.91. The tube's f/6 label is the round number.

Then 25 ÷ 5.91 = 4.23 mm. Both exit-pupil paths agree. Use the millimeters on the tube, and keep the f/ label off the inputs.

Divide 25 by a rounded f/6 and the beam comes out 4.17 mm. That 0.06 mm gap is the label, not a second optic.

We flag an exit pupil under 0.5 mm. You are past the useful ceiling, which is about 2× the aperture in millimeters.

On this 203 mm default, 2 × 203 = 406x. A 2 mm eyepiece forces 1200 ÷ 2 = 600x. Then 203 ÷ 600 = 0.34 mm.

That 2 mm row fails both checks: power is past 406x and the beam is under 0.5 mm. The calculator shows the ceiling warning. The field at 52° shrinks to 0.09°.

We also flag an exit pupil over 7 mm. Minimum useful power is aperture ÷ 7, the 7 mm planning pupil in the Sky & Telescope notes.

On the default, 203 ÷ 7 = 29x. A 7 mm beam wants about a 41 mm eyepiece (a 2 in barrel), because 7 × 5.91 = 41.4.

The spill shows up on a faster tube. Take a 130 mm (5.1 in) f/5. Focal length is 650 mm. Fit a 40 mm eyepiece.

Power is 650 ÷ 40 = 16.25x, listed as 16.3x. Exit pupil is 40 ÷ 5 = 8.0 mm. The floor is 130 ÷ 7 = 18.6x, so 16.3x sits under it.

True field of view is the sky patch, in degrees. Apparent field is the angle at the eyepiece glass. Divide before you compare them.

A 52° eyepiece at 48x covers 52 ÷ 48 = 1.08°. Type 82° on the 1.25 in barrel and the calculator caps that 48x view at 1.29°, not 82 ÷ 48 = 1.71°. Switch the barrel to 2 in and 1.71° fits under the 46 mm cap.

82° is the apparent field, the angle you see at the eyepiece. In a 1.25 in barrel the 27 mm stop holds that 48x view to 1.29°.

The calculator caps a 1.25 in barrel at 27 mm and a 2 in barrel at 46 mm, and it says so under the result. A printed field stop, typed in millimeters, is used as-is.

Tele Vue lists a 27 mm maximum stop for a 1.25 in barrel, and 46 mm for a 2 in barrel. We checked that note on Oct 17, 2026.

On 1200 mm, 57.3 × 27 ÷ 1200 = 1.29°. The 46 mm stop gives 57.3 × 46 ÷ 1200 = 2.20°. Those are barrel caps, not a guess for one model.

A 32 mm Plössl at 52° claims 52 ÷ 37.5 = 1.39°, and 1200 ÷ 32 = 37.5x. The 27 mm stop pulls the sky patch back to 1.29°. The calculator shows 1.29° and the cap note.

A real 32 mm Plössl prints about 48°–50° because the 27 mm stop allows no more. At 48°, 48 ÷ 37.5 = 1.28°, inside the cap.

52° is the calculator's default, the number many low-cost Plössls print. Tele Vue's Plössl class is 50°. Then 50 ÷ 48 = 1.04°.

1. Type focal length, eyepiece focal length, apparent field, and aperture.

2. Read power, exit pupil, and true field. Check 0.5 mm and 7 mm.

3. If the maker prints a field stop, type it. The calculator uses 57.3 × stop ÷ focal length and skips the barrel cap. Sky & Telescope calls apparent field ÷ power rough. With no printed stop, pick the barrel: 27 mm for 1.25 in, or 46 mm for 2 in.

Our assumptions

Aperture rows use 203 mm for 8 in, 152 mm for 6 in, 102 mm for 4 in, 127 mm for a 5 in Mak, and 130 mm for the f/5 spill case.

Focal lengths are 1200 mm, 663 mm, 1500 mm, and 650 mm. Working focal ratio is focal length ÷ aperture, so the 1200 mm tube is f/5.91.

Apparent field stays 52° until you replace it. A printed stop is typed in and used as 57.3 × stop ÷ focal length, with no barrel cap. With no printed stop, the barrel caps the field: 27 mm at 1.25 in, or 46 mm at 2 in.

The Moon disk is 0.52°. Las Cumbres lists about 31 arcmin, which is 0.52°, checked Oct 17, 2026. The calculator uses that same diameter.

Max useful power is 2 × 203 = 406x. The inch form is 50 × 8 = 400x. Min useful power is aperture ÷ 7, from the 7 mm pupil. The field calculator shows the max, not the min.

The Suburban sky and dark sky section below uses Bortle 6–7 for suburban and Bortle 3–4 for dark.

One focal length, 1200 mm. Seven eyepieces. The 203 mm column and the 152 mm column share every power. Power ignores aperture.

The 32 mm row is the low end of a 1.25 in set. You get 37.5x. The beam on 203 mm is 5.41 mm, from 203 ÷ 37.5.

The 52° shortcut gives 1.39°. The 27 mm stop gives 1.29°. On this 1200 mm tube, keep 1.29° for a 1.25 in barrel.

The 10 mm row is the middle of three. You are at 120x, with a 1.69 mm beam and a 0.43° field. A 0.52° Moon no longer fits whole.

The 6 mm row is the high one. You get 200x, a 1.02 mm beam, and a 0.26° field. That circle covers 0.26 ÷ 0.52 = 0.50 of the Moon's width.

The 3 mm row is 400x and 0.51 mm. You are on the 0.5 mm line, just under the 406x ceiling.

On the 152 mm column, powers match the 203 mm column. Focal length is still 1200 mm. Beams shrink. At 48x you get 3.17 mm, from 152 ÷ 48.

The 152 mm ceiling is 304x, from 2 × 152. A 4 mm eyepiece at 300x is on that line, with a 0.51 mm beam. The 6-inch page uses this aperture.

Same 48x, same 1.08° field, two beams. That is why the calculator asks for aperture.

Area scales with the square of field diameter. A 2.20° stop against a 1.29° stop is 1.71 across. Square that and the sky area is about 2.9 times.

The 102 mm f/6.5 refractor is the 663 mm row. A 25 mm eyepiece gives 26.5x, from 663 ÷ 25. The beam is 3.85 mm. The 52° field is 1.96°.

Its 46 mm stop opens 3.98°, from 57.3 × 46 ÷ 663. That clears a 3° target. The 27 mm stop stops at 2.33°.

The 127 mm Mak at 1500 mm goes the other way. A 25 mm eyepiece gives 60x and 0.87°, and its 1.25 in back holds the field near the 1.03° stop cap.

The 130 mm f/5 at 650 mm is the wide fast case. At 25 mm you get 26x, a 5.00 mm beam, and 2.00°. The 46 mm stop reaches 4.06°.

Swap to a 10 mm eyepiece and the tubes split. On 663 mm you get 66.3x, a 1.54 mm beam, and 0.78°.

On 1500 mm that same 10 mm eyepiece gives 150x, a 0.85 mm beam, and 0.35°. Focal length did the splitting.

Suburban sky and dark sky

From a Bortle 6–7 yard the Moon and planets carry the night. At 48x the 0.52° disk fills 0.48 of the 1.08° circle.

Planets want about 20x to 30x per inch of aperture. On an 8 in tube that band is 160x to 240x. Sky & Telescope gives that range for planetary work.

On 1200 mm, 160x needs a 7.5 mm eyepiece, and 240x needs 5 mm. At 160x the beam is 1.27 mm and a 52° field is 0.33°.

At 240x the beam is 0.85 mm and the field is 0.22°. A 40″ Jupiter at 240x looks about 2.7° wide, roughly 1/20 of the 52° view.

A Bortle 3–4 sky does not widen the optic. Andromeda's length is six Moon diameters, or 3°, in the NASA note.

The 2.20° stop on the 1200 mm tube covers 2.20 ÷ 3 = 73% of that length. The 1.08° field covers 1.08 ÷ 3 = 36%.

The 3.98° field on the 663 mm tube covers that 3° length and still has margin. You want the whole galaxy, so you shorten the focal length.

Five misses

Carton power first. A 60 mm box says 675x. On that lens, 675x is unusable, about 5.6 times past the 120x ceiling.

Apparent field second. That angle is at the glass. Divide by magnification before you name a sky patch.

Barrel third. A 1.25 in eyepiece on a 1200 mm tube tops out at 1.29°. A printed 82° still has to pass that 27 mm stop.

Fourth miss: adding a 2× Barlow and keeping the old field. The 1.08° patch becomes 0.54°. The 4.23 mm beam becomes 2.11 mm.

Fifth miss: eye relief. If you keep glasses on for astigmatism, Tele Vue suggests at least 15–20 mm of eye relief (checked Oct 17, 2026). A 21 mm Baader Hyperion lists 20 mm, the top of that range. Below it, the field edge starts to vignette.

The calculator does not compute eye relief. Compare the printed millimeters after the power and field match. The eyepiece guide sorts the surviving focal lengths into a low, mid, and high set.