What Does 3-9x40 Mean on a Scope? Numbers Decoded

The name is a spec sheet in shorthand

Scope names look like a code because they are one. "3-9x40" packs two of the most important numbers about a scope into five characters. Once you know how to read it, you can glance at a wall of scopes and immediately know which are for close work, which are for long range and roughly how big each one will be.

Breaking down 3-9x40

The magnification range (3-9). At 3x, a target looks three times closer than it does to your naked eye. At 9x, nine times closer. The hyphen tells you this is a variable scope. A fixed scope has one number, like "4x32."

A useful shorthand is the zoom ratio: the high number divided by the low number. 3-9 is a 3x zoom ratio. A 1-6 LPVO is 6x, and a 1-10 is 10x. Higher zoom ratios are harder to design and often bring more weight or a tighter eyebox.

The objective (40). The objective is the big front lens. A 40mm objective is a middle size for hunting scopes. Larger objectives can gather more light into a larger exit pupil, but make the scope bigger and heavier, and may require taller rings to clear the barrel.

The hidden number: exit pupil

You can work out one more important figure from the name alone. Divide the objective diameter by the magnification, and you get the exit pupil in millimeters. That is the diameter of the beam of light leaving the eyepiece, the small bright circle you see if you hold the scope at arm's length.

For a 3-9x40:

• At 3x: 40 ÷ 3 = about 13.3mm
• At 9x: 40 ÷ 9 = about 4.4mm

Those numbers match the published figures. Ammunition Depot's listing for the Sig Sauer Buckmasters 3-9x40 gives an exit pupil of 13.30mm to 4.40mm.

Why it matters: the pupil of your eye opens wider in low light. If the exit pupil is smaller than your own pupil, the image you see can look dimmer. That is why many hunters turn the magnification down at dawn and dusk. A lower power means a larger exit pupil and an easier, brighter-looking view.

What the name does not tell you

The three numbers leave out a lot. Before buying, check the spec sheet for:

• Tube diameter. Usually 1 inch or 30mm on hunting scopes, and 30mm or 34mm on many LPVOs. Rings must match. The Sig Buckmasters 3-9x40 is listed with a 1-inch tube.
• Focal plane. First focal plane reticles change size with magnification; second focal plane reticles do not. Many 3-9x40 hunting scopes are second focal plane.
• Reticle. Duplex, BDC (bullet drop compensating), mil or MOA hash marks, illuminated or not.
• Eye relief. The distance your eye needs to be behind the eyepiece. The Sig Buckmasters is listed at 4.17 to 4.40 inches.
• Field of view. How wide a view you see at 100 yards. The same Buckmasters is listed at 24.10 ft at 3x and 11.35 ft at 9x.
• Click value. How far each turret click moves the point of impact, often 1/4 MOA on hunting scopes. The Buckmasters is listed at 0.25 MOA.
• Parallax setting or side focus. Many hunting scopes have fixed parallax at 100 yards. The site's parallax explainer covers why that matters.

Reading other common scope names

The exit pupil math is a simple division, but at very low power, the eyepiece design often limits the real exit pupil. Primary Arms, for example, lists its SLx 1-6x24 Gen IV with an exit pupil of 10.6mm at low power, not the 24mm that simple division would suggest. Use the maker's figure when it is published.

Worked example: reading a spec line

Here is how the name and the spec sheet fit together, using the published figures for the Sig Sauer Buckmasters 3-9x40 from Ammunition Depot's listing:

• Name: 3-9x40. You know it zooms from 3x to 9x and has a 40mm objective.
• Exit pupil: listed at 13.30mm to 4.40mm, which matches 40 ÷ 3 and 40 ÷ 9.
• Field of view: listed at 24.10 ft at 3x and 11.35 ft at 9x at 100 yards. Notice how the view narrows as magnification rises. Tripling the power cuts the field of view by roughly half here. Field of view depends on the eyepiece design, so you cannot calculate it from the name.
• Eye relief: listed at 4.17 to 4.40 inches. Eye relief often changes slightly through the zoom range.
• Tube: 1 inch, so it needs 1-inch rings.
• Reticle: a BDC with holdover dots.
• Clicks: 0.25 MOA per click.

From just five characters in the name you could predict two of those lines. The rest you get from the spec sheet. That is the right way to use a scope name: as a quick filter, not as the whole story.

Why bigger is not always better

It is tempting to assume a bigger objective or a higher top magnification means a better scope. Not necessarily.

A bigger objective adds weight and height. It may need taller rings, which raises the scope above the bore and can make a solid cheek weld harder. On a light hunting rifle, a 32mm or 40mm objective is often a better balance than a 50mm.

More magnification narrows your field of view and makes every wobble more visible. It also reduces exit pupil, which can make the image look dimmer in poor light. Many hunters find they rarely use the top of a very wide zoom range.

A wider zoom ratio is harder to make well. At the same price, a scope with a modest range may offer better glass than one that tries to cover everything.

Letters you might see

Scope names often carry letters too, and these vary a lot by brand:

• FFP or SFP: first or second focal plane.
• IR or "illuminated": an illuminated reticle.
• AO or SF: adjustable objective or side focus, both ways of adjusting parallax.
• BDC: a bullet-drop-compensating reticle with holdover marks.
• MOA or MIL/MRAD: the unit of the reticle and turret adjustments.

Is 3-9x40 the right size for you?

The 3-9x40 became a classic hunting configuration because it covers a lot of ground. At 3x you have a wide view for a deer stepping out of cover close by. At 9x you have enough detail for a longer shot across a field. It is also compact enough to sit low on most bolt-action rifles.

It is not right for everything. On an AR-15 carbine for close and mid-range use, a 1-6x24 or 1-8x24 LPVO that goes all the way down to 1x is usually a better fit. For long-range target work, a higher top end, like 4-16x or 5-25x, makes small targets easier to see.

If you are shopping, Ammunition Depot's rifle scope category lets you filter by maximum magnification, and the site's rifle scope and LPVO guide and hunting scope setup guide go deeper into choosing one.

Quick reference

• First number: lowest magnification.
• Second number: highest magnification.
• After the x: objective lens diameter in millimeters.
• Objective ÷ magnification: exit pupil in millimeters, at least roughly.
• Not in the name: tube size, focal plane, reticle, eye relief, field of view, click value and parallax. Check the spec sheet.

Editorial note: This is an independent editorial overview built from manufacturer specifications, retailer listings and published sources. We have not performed hands-on testing of the products discussed, and nothing here is a performance guarantee. Verify specifications, compatibility and the law where you live.

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