The purpose of this thread is to show the formula to calculate the required twist rate for a particular bullet length.  I touched on a few other topics for explanation.

From:
www.z-hat.com/twistrate.htm
You can download a FREE program that calculates twist rate here.  I had to download the zip file in order to get it to work.

Several threads have been posted regarding which twist rate to use: 1:12, 1:9, 1:8, 1:7, etc.  It all depends on the bullet you are most likely to use.  From what I remember, the general consensus is that a 1/9 twist barrel will suit most of the AR shooters.  From the calculations below, it appears that that 1:9 twist rate will handle all bullets except the Sierra 80 grain and Hornady AMAX 75 grain.

Some barrels will stabilize bullets that are right on the calculated cusp of being stable.  In this area, I can think of two things that could make or break bullet stabilization.
1. The barrel may have an actual twist rate tighter than what is labeled on the barrel.  In mass produced barrels, it is not uncommon for barrel twists to be slightly off, but close enough to label it.  Mass produced barrels are NOT match barrels, thus some slack may enter the picture.
2.  The more the bullet's tip is yawed, or the bullet unbalanced, the less the bullet is apt to stabilize, similar to a thrown football.  A football may start out wobbling and then stabilize to no yaw; this is due to more than enough spin to remove the wobbling.  If the football does not have enough spin, the wobbling gets worse until the football points just about all over the place flying down the field.  Bullets pretty much do the same thing, only much faster.

AR15.com Ammo Oracle has a good description of how a bullet shoots.

Basically, this is the formula for calculating twist rate: Greenhill Twist Rate formula.
Twist = 150 X D/R
Where:
D = bullet diameter in inches;
L= bullet length in inches;
R = length of bullet divided by its diameter
150 = a constant.  Substitute 180 for the 150 value, for velocities exceeding 2800 fps, which is most AR loads.

Below are calculations using some of the more popular bullets, and the twist rate required to stabilize each.  The program rounds off the calculations to the nearest whole number.  I calculated using a calculator using the "180" constant.

The lower the number, the faster the twist rate.
9 is faster than 12.
9 is faster than 9.17.
12 is faster than 12.12.

M193, 55 grain, bullet length = 0.745”
Calculated twist rate = 1:12
When done by hand, twist rate = 1:12.12

M855, IMI, 63 grain, bullet length = 0.872”
Calculated twist rate = 1:10
When done by hand, twist rate = 1:10.36

SS109, 62 grain, bullet length = 0.866”
Calculated twist rate = 1:10
When done by hand, twist rate = 1:10.43

Hornady match, 68 grain, bullet length = 0.985”
Calculated twist rate = 1:9
When done by hand, twist rate = 1:9.17

Sierra match, 69 grain, bullet length = 0.898”
Calculated twist rate = 1:10
When done by hand, twist rate = 1:10.06

Hornady AMAX, 75 grain, bullet length = 1.070”
Calculated twist rate = 1:8
When done by hand, twist rate = 1:8.44

Sierra match, 77 grain, bullet length = 0.985”
Calculated twist rate = 1:9
When done by hand, twist rate = 1:9.17

Nosler HPBT, 77 grain, bullet length = 0.990”
Calculated twist rate = 1:9
When done by hand, twist rate = 1:9.12

Sierra match, 80 grain, bullet length = 1.090”
Calculated twist rate = 1:8
When done by hand, twist rate = 1:8.29

My first course gun had a 1 in 9" that would shoot the 75 amax but would NOT shoot the 77 SMK...go figure.

Hmm... so according to this, most people shouldn't get a 1:7? It seems like a 1:7 is just way to fast for most ammo, huh?

Quoted: Hmm... so according to this, most people shouldn't get a 1:7? It seems like a 1:7 is just way to fast for most ammo, huh?

You are not talented in reading comprehension.

Another fact to consider is that some barrels change twist rate in bore to either a faster twist or slower twist.  As indicated actual production may or may not be what is stamped on it.  A QA manager at a major arms firm told me they got to checking twist rates from a sub contractors barrels and the rates changed.

Another thing  that can happen is tight spots and loose spots.  I recently had a Marlin that a snug patch would all of a sudden jump free for about a inch and a  half and get snug again.  I contacted manufacturer and was basically told they did not do anything on a product over five years old or not owned by original owner.

Tight spots is a different ball game though.  It is well known in bullet swaging that you can make a bullet a larger diameter and do fine but you can't squeeze a bullet smaller and when the compression takes place the jacket springs back  losing contact with the core and now the core is free to rotate off the center line of it's axis.

This is a point of contention with me, you can have the best design and everything works on CAD perfectly but by the time the guerrillas on the factory floor get through with it there are dimensions on the pieces that would make a CAD program show major
interference problems.

To really make matters worse I had a long talk with a former master machinest who retired from a major arms manufacturer a couple nights ago.  We have been friends about 26 years and he was also a highpower shooter.

He related to me that they (firm's name withheld to protect the guilty) were having problems with making a certain model do what it had been doing with ease but recent production was not performing to original production quality.

The chief engineer decided to investigate what the problem was and assigned my master machinest friend to go to  production line and obtain the thread gages.  When he got  to the line he asked the foreman for the thread gages and the foreman did not know where they were.  Thread gages do several things such as they tell you if thread is too tight, too loose, not deep enough and most importantly are cut at exact right angles to the bore line and whether the front of the receiver is also at right angles to the bore line.  These three things are critical to obtain accuracy initially.  During this investigation he learned that they receiver stock was placed in a fixture and chopped off with a a saw then chucked in a lathe and the center line drilled and reamed followed by the threading, lug recess cuts and lug ways broached.  Then the other cuts were made in other departments.  

OK back up a minute, what was missed?  Well just a few minor things.

1. After cutting with chop saw and placing in a lathe the first thing that should have been done was face the front of the receiver off so it would be at right angles to the bore line.  This was not done.

2. After the threading was done the thread gages should have been screwed in to determine fit and alignment with bore center line.  This was not done.

3. After the locking lug surfaces were cut they too should have been gage to make sure they were cut to the same level.  Best I can figure about 95% of the guns made will not have good solid contact on both lugs.  On a two lug receiver one lug not contacting can cause horizontal dispersion.

4. The bolt should also be indicated and turned to make sure the bearing surfaces are at right angles to the bore line and the bolt face is at right angles.

We aren't through yet folks, there are more things to be considered.  Next is the barrel.
Let us assume the barrel has no tight spots and no loose spots.  The questions one needs to ask here would be is the barrel bored straight?  I got a new Remington 40X that would not shoot.  It had a large oversize chamber that caused excessive swelling of the case base.  The barrel was cut off and rethreaded/chambered twice until I got a chamber I could live with.  It started shooting better, nothing outstanding but better.
I noted two things.  First was the iron sight zeroed way off center and secondly the recoil was "strange".  You could not call a shot standing with it.  You could call it at say
a 9 at 10:00 and you could wind up a X at 4:00.  Next you could call dead center and bullet hole comes up a 9 at 4:00.

I did a much closer examination and found the outside of the barrel was straight but the the inside of the barrel shows a definent offset to the left.  I finally pulled it off and it is waiting for a hunting rifle which it will be outstanding for.  I will just reorient the barrel to where the curvature faces toward 12:00 and hope it will work.

Other barrel problems are caused in production.  Barrel threads that are cut with a die and subject to being out of square with the bore line.  That is why when you get a bolt action rifle rebarreled you can wind up with a much more accurate rifle as the threads were cut on a lathe.

Now we are not quite through with the barrel.  Let's just PRETEND we have a nice square receiver with square threads, square bolt lugs, the bore is straight and the barrel threads are straight......... You will win your state lottery before this occurs.......... that doesn't mean it will shoot.  Case in point I once walked in a gun show and very first table I walked up to I was looking and hadn't really got on frequency good and I heard a guy say he wanted $200.00 for a Remington 700 Varmint ((20+ years ago) and by the time that computed the guy had paid him 200.00.  He offered it to me for 250.00.  I thought something is wrong with this rifle and gave it a once over.  Bolt face indicated maybe 50 rounds on it.  Bore was good and appeared straight and I continued to look and finally spotted it, the crown was messed up.  It has a very slight ding  on the crown so I paid the guy 250.00 and left.

Got home, loaded up three different loads and went to the range. 1.5" at 100 with handloads was best I had.  I pulled it out, chucked it in lathe and recrowned the muzzle with 11 deg crown and went back to range  and shot the same loads and I could not get it to shoot larger than 5/8"  One was 3/8".  That was a keeper then.

To make matters worse my friend said he just talked to one of the senior engineers who had left the firm in 90s and he was thinking about getting a new rifle and he called a production foreman at the factory he used to work at and asked him what was looking good these days and what he should buy.

The foreman's reply, "Anything that doesn't have our name on it."

To give you an idea of what is involved in making it right take a look at www.bryantcustom.com/articles/true.htm for detailed pictures of just what is involved in making it right.

A member of the Army Small Cal Lab once made a very prophetic statement, "When you buy a new rifle you have bought a kit that could make a good rifle if after you rebuild it."   Many have heard the term "blueprinting".  This is it, make it to the drawings and it "might just work".

You have to remember the design guys generally want it to be perfect.  The production foreman sometimes wants it to meet spec. The guys on the production floor just want a paycheck for the most part and don't give a rat's about what it does.  I once asked a guy at Colt what he was making.  I knew what it was but I just wanted to see if he knew. He didn't know what he was making or what it did.

So now you have an appreciation of why folks like Iron Brigade Armory get big bucks for sniper rifles.  If you consider all that is involved it can be a deal.  Think about it I think machine shop time is 65.00 an hour these days.  Just to rework (blueprint) an action I would estimate 8 ot 10 hours.  Doing it like the site above on one lathe may be two days work depending on how bad the case is.    Then you buy a new barrel, get it chambered and threaded/crowned etc and installed you are looking at another three to four hours not to mention 275.00 for the barrel.

Then bedding, a nice McMillan stock, a high grade Leupold scope, nice trigger job...... yep you are looking at several days work and a pile just for the goodies to help the job along.

Then again if you specify the wrong twist rate for the bullet you are going to load ..................  So basically guys if you have a rifle that shoots you have the makings for the WWII song "Praise the Lord -And Pass the Ammunition".

Want to know a neat little trick of just how bad a problem you are looking at?  Well if you are thinking about a used rifle look at the firing pin hit on a fired primer.  Most 30 cal striker noses are about .060 to .065 diameter and the production "recommendation is not more than 1/2 offset the diameter of the striker.  OK lets say you have a .060 firing pin, the offset can be .030" and still meet spec.

Ask any machinest how much tolerance is to be expected from a piece of dialed in round stock center drilled on a lathe.  If the lathe is right no more than .001" offset for hole location.  I you have a round receiver, a round barrel and a round bolt, with a round chamber centered on a round hole and everything is off .001 you can have a maximum offset condition of maybe .006" and the factory production standards are .030"????????  Like my friend's quote, you have a "kit" that needs to be reassembled.  It just kind of depends on what you can live with.

Quoted:He related to me that they (firm's name withheld to protect the guilty) were having problems with making a certain model do what it had been doing with ease but recent production was not performing to original production quality. The chief engineer decided to investigate what the problem was and assigned my master machinest friend to go to  production line and obtain the thread gages.  When he got  to the line he asked the foreman for the thread gages and the foreman did not know where they were...During this investigation he learned that they receiver stock was placed in a fixture and chopped off with a a saw then chucked in a lathe and the center line drilled and reamed followed by the threading, lug recess cuts and lug ways broached.  Then the other cuts were made in other departments.

This is the EXACT same problems I had with a Remington 700 VS-SF, in .223 Rem.  I had to have the reciever and bolt trued, and barrel chopped and rechambered.  It shot better, but not good.  I then sent it to Blackstar for electro-polishing and tapering.  It got down to a MOA only rifle.  That thing was a POS!  For all the work that is involved, IF I ever have another bolt gun accurized, I am starting with a matching numbers Yugo Mauser.  Hell, it will require the same amount of time a new factory rilfe will, may as well spend less initially, and have the same shooting rifle when its all done.

Quoted: Quoted: Hmm... so according to this, most people shouldn't get a 1:7? It seems like a 1:7 is just way to fast for most ammo, huh? You are not talented in reading comprehension.

I got the same thing as bigez.  Basically a 1/9 bbl will stabilize everything up to 75gr.  However, that is just not the case in short barrels.  I have seen a 10.5" 1/9 barrel keyhole a 68gr bullet at 25 yards.  It might stabilize it in a 20" barrel, but not in a 10.5" barrel.

Quoted: Quoted: Quoted: Hmm... so according to this, most people shouldn't get a 1:7? It seems like a 1:7 is just way to fast for most ammo, huh? You are not talented in reading comprehension. I got the same thing as bigez.  Basically a 1/9 bbl will stabilize everything up to 75gr.  However, that is just not the case in short barrels.  I have seen a 10.5" 1/9 barrel keyhole a 68gr bullet at 25 yards.  It might stabilize it in a 20" barrel, but not in a 10.5" barrel.

The stabilization equations are based upon velocity, but the author of the thread does not address it here. The faster the bullet is traveling the less twist for a given bullet length is necessary for stabilzation. Therefore shorter barrells typically require more twist for a given bullet length and longer barrells require less twist for the same bullet.

Also the least amount of twist necessary for stabilization typically the more accurate the barrel for a given bullet. This is one of the reasons you see very slow twists comparitively in bench rest rifles. The faster the twist rate, the more dwell time is necessary for the bullet to go to sleep and not wobble.

Thanks Baldmonk and Forest, the original post was very vague.