Will this stop a .223/556 55gr bullet or a 9mm FMJ round?
My cousin has a farm and can get a couple 4'x4' sheets of steel plates 3/16" thick (Not diamond plate steel) to use as a back stop. I don't think anything larger than a .357 round will be shot at the steel plates. I wish I had more info about the steel but he said it's very heavy and thought it might be a good back stop.

A 3/16" steel plate, even set at 45 degrees, will probably not stop a .223/5.56 round, especially if FMJ.... assuming that the plate is mild steel (as opposed to a hardened alloy). As to the 9mm or .357 magnum, I would believe that the situation might be marginal. With cast (unjacketed) bullets, you might well get reliable stops. I'm not so sure about FMJ's, though.

If you use a full 1/2" plate, especially if hardened steel and/or set at an angle, then it should stop any of the three you mentioned. TWO 3/16" plates, stacked together, might work OK.

I would be careful about using an angled plate as a backstop. You COULD have ricochet problems. That is, it is possible that a round ricocheting from the plate could end up somewhere you don't want. So, angling the plate should be done with that in mind.

It's not likely this is hardened steel, since in a 4 x 4 foot size, it likely has been machine-sheared from a 4 x 8 foot or larger size product, and shears don't like hardened or abrasion-resistant (AR) steel.

Most likely it is a "mild" steel, and K-framer's answer is a good one -- including his admonishment about the inherent dangers of ricochet by placing the plates at an angle.

IMHO, I would be surprised if a .223 round penetrated a 3/16" mild steel plate set at an angle to the shooter, unless it was one of the "green tip" military-type projectiles, but I'm no expert on that. On the other hand, a .223 round quite capably could penetrate sheet metal such as what's typically used in vehicle bodies. As you know, though, most of that stuff is less than 16 gauge (1/16") thick. More like 18 to 22 gauge.

Your friend's 3/16" plate weighs about 7.5 pounds per square foot, so I wouldn't be toting it too far to set it up, if you don't think it will do the job!

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Ukraine -- now more than ever

We use lower grade hardened 3/16 steel for our pistol plates, and .223 ball goes right throught it, even when it is a falling plate, shot at up to 30 degrees off angle.
We know because they shoot at it despite the NO RIFLES sign.

Using mild steel is unsafe with rifles, and not the best idea with FMJ pistol.

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Science plus Art

We have designed and built more than a few bullet traps. For handgun rounds, 3/8 inch steel plate angled 45 degrees to deflect bullet fragments downward works and that bullet trap has 80,000 rounds without damage. 160 sq ft of plate steel made a trap 6 feet high and 10 feet wide.

Hardened steel can be used to make a centerfire rifle trap, but repeated direct hits will chew through the trap dirt berms remain the cost effective way to stop rifle bullets.

Interesting stuff! I'm surprised, and impressed with that .223 round. Thanks for the authoritative answer.

That low-grade hardened steel must be the standard AR (abrasion resistant) plate used in stuff like liners for dump trucks. I think it rates somewhere in the 225 Brinell hardness range. There's a higher grade, 400 Brinell, but sounds like in 3/16 thick even it wouldn't stand up to rifles. Might be interesting to try it if you ever need to replace your plates, just to see.

All of the AR plates can be torch- or plasma-cut to shape.

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Ukraine -- now more than ever

For rifle rounds, 3/16 is just too thin. My 556 green tips zip right thru 3/16 A.R. 450 at 75 yards. I am currently shooting 514 AR, and it is 3/8" thick. Set at an angle to deflect downward, it shows all kinds of scars, but no gouges. The 3/16 pistol plates we were using had gouges and scars in them with hunting rounds when shot at an angle. But set straight up, the hunting ammo went thru, and made a gory ripped up hole. Now, the FMJ ammo punched a pretty clean hole at 75 yards.
The material simply has to be thicker to take the hits that rifle ammo delivers.