Miscellaneous Questions #11

This section contains brief discussions of various ballistics and shooting related topics as requested by correspondents. If you have a question you have been trying to find an answer to (keep 'em ballistics and shooting related--see your minister for the mysteries of life) email me by clicking here and I'll do my best to find the answer for you and if it is of general interest, publish it here. If you can contribute additional input to one of the answers I'd would appreciate hearing from you too.

Check back frequently as new topics are always being added.

On this page:

What is +P and +P+ ammunition?
What are the current SAAMI pressure specifications for ammunition?
How are proof pressures determined?
What is the Hatcher Formula?

Q. What is +P and +P+ ammunition?

A. "Plus P" and "Plus P Plus" ammunition is simply ammunition loaded to higher than normal SAAMI (Sportings Arms & Ammunition Makers Institute) pressure specifications.  "Plus P-ing" was first done with law enforcement pistol ammunition in an effort to wring the last bit of power out of a cartridge. For most rounds the gain in performance is minimal and leads to increased wear and tear on the firearm.  The +P+ ammunition is loaded to even higher pressure levels than +P.  +P+ loadings are generally limited to "law enforcement sale only."  The SAAMI pressures for pistol ammunition are given below.  Note that there are no SAAMI specifications for +P+ loads, but by general industry agreement they are about 15 percent greater than +P.  Note that there are no SAAMI specifications for +P pistol loads other than those shown below.  (The .38 Super is frequently listed as "+P" but that is just to differentiate between the "Super" round and the original .38ACP round.)

+P headstamp (10k jpg)

The table below gives an idea of what some common +P  and +P+ loads do.  (Velocity data varies with manufacturer.  I have chosen to use the high end figures.) Pressures are given as PSI (piezo transducer).

  Standard Load +P Load +P+ Load (Not SAAMI) Proof Pressure
Approximate Velocity Pressure (PSI)
(Max Avg)
Approximate Velocity Pressure (PSI)
(Max Avg)
Approximate Velocity Pressure (PSI)
(Max Avg)
Allowable PSI
Allowable PSI
9 mm 115 gr
9 mm 125 gr
35,000 1280
38,500 1335
42,000 52,000 55,000
.38 SPL 125 gr
.38 SPL 158 gr
17,000 945
18,500 1000
22,000 25,000 27,500
.45 ACP 185 gr
.45 ACP 230 gr

21,000 1140

23,000 n/a n/a 31,000 33,000
257 Roberts 110 gr
257 Roberts 115 gr

54,000 2980

58,000 n/a n/a 77,500 83,000

Pressure data per SAAMI

Q. What are the current ANSI/SAAMI pressure specifications for ammunition?

A. The tables below give the current maximum average pressure specifications for common commercial cartridges.  Note that these specification may differ from previous ones because, unless specified otherwise, they are now based on Piezo transducer PSI measurements and not copper crusher (CUP) measurements.  Piezo measurements tend to read slightly higher than copper crusher measurements as they more accurately read pressure peaks.  The standards are set in the following SAAMI publications.  Not all specifications have been changed to piezo measurement.  The standards are available in printed format at the prices below.

#205 ANSI/SAAMI Centerfire Pistol & Revolver,  Z.299.3 1993 - $30.00
#206 ANSI/SAAMI Centerfire Rifle, Z.299.4 1992 - $35.00
#208 ANSI/SAAMI Rimfire, Z.299.1 1992 - $20.00
#209 ANSI/SAAMI Shotshell, Z.299.2 1992 - $25.00
#203 ANSI/SAAMI Ammunitions Standard CR-ROM - $90.00 (the complete set)

They can be ordered from

11 Mile High Rd
Newton, CT 06470
Contact Coleen Swayne and ask for the ANSI Ammunition Specification publications.

The tables below were excerpted from those publications.

Under ANSI/SAAMI procedures,  for bottlenecked cases the center of the transducer is located .175" behind the shoulder of the case for large diameter (.250") transducers and .150" for small diameter (.194") transducers. For straight cases the center of the transducer is located one-half of the transducer diameter plus .005" behind the base of the seated bullet.  Small transducers are used when the case diameter at the point of measurement is less than .35".

The rest of the world uses the Commission Internationale Permanete (CIP) standards for ammunition.  Under CIP standards a drilled case is used and the measuring device will be positioned at a distance of 25 mm from the breech face when the length of the cartridge case is between 30 and 40 mm, including limits. When the length of the cartridge case is less than 30 mm, pressure measurement will take place between 5 mm and 25 mm from the base of  the case depending on the size of the case. (6.35 mm for the Hornady 17 Mach 2, and 25 mm for most rifle cartridges)  The difference in the location of the pressure measurement gives different results than the SAAMI standard

I am currently working on putting together a table of CIP pressure specifications.

ANSI/SAAMI Rifle Pressure Specifications (Maximum Average pressure)
All Piezo measurements unless specified)

5 mm RFM 37,000

.30-30 Winchester   


.17 Rem 52,000 cup

.30-06 Springfield   


.22RF  Short 


.30-30 Winchester   (Saboted)


.22RF Long & LR 24,000

.300 Savage   


.22WRF 19,000

.300 Weatherby Magnum   




.300 H&H Mag 54,000 cup

.22 Hornet   

43,000 cup   

.300 Win Mag   


.218 Bee 40,000 cup

.303 British   


.22-250 Remington   


.307 Win 52,000 cup
220 Swift 54,000cup

.308 Winchester   


.222 Remington   


.308 Winchester   (Saboted)


.222 Rem Mag 50,000 cup

.32 Win Special   


.223 Remington   


.32 Rem 37,000 cup

.243 Winchester   


.32-20 16,000 cup

.25-06 Remington   


.32-40 30,000 cup
.250 Savage 45,000 cup

8mm Mauser   


.256 Win 43,000 cup

8mm Rem Magnum   


.257 Roberts   


.338 Win Mag   


.257 Roberts  +P  58,000 .348 Win 40,000 cup

.264 Win Mag   


.35 Remington   


.270 Winchester   


.351 Win SL 45,000 cup

.280 Remington   


.35 Whelan 52,000 cup

.284 Winchester   


.350 Rem Mag 56,200 cup

6mm Remington   


.356 Win 52,000 cup
6 mm BR-REM 52,000 cup .358 Win 52,000 cup


46,000 cup 

.375 H&H   


6.5 Rem Mag 56,200 cup .375 Win 52,000 cup

7mm BR   Rem

52,000 cup   

.38-40 Win 14,000 cup

7mm Mauser   


.38-55 Win 30,000 cup

7mm Rem Magnum   


.416 Remington Magnum   


7mm Weatherby Mag   


.444 Marlin   

44,000 cup



.45-70 Government   


7-30 Waters    45,000

.458 Winchester Magnum   

53,000 cup



.470 NE 35,000 cup

.30 Carbine   


.30-40 Krag 40,000 cup


ANSI/SAAMI Pistol Pressure Specifications (Maximum Average pressure)
All Piezo measurements unless specified)

Cartridge Pressure (Max Avg) Cartridge Pressure (Max Avg)
.221 Rem Fireball 52,000 cup .38 Colt 12,000 cup
.22 Jet 40,000 cup .357 Magnum 35,000
.25 ACP 25,000 cup  .357 Maximum 40,000
.30 Luger 28,000 cup .40 S&W 35,000
.32 ACP 20,500 10 mm 37,500
.32 S&W Long 15,000 .41 AE 35,000
.32  H&R Mag 21,000 cup .41 Magnum 36,000
.380 ACP 21,500 .44 Special 15,500
9 mm Luger 35,000 .44-40 13,000 cup
9.mm Luger +P 38,500 .44 Magnum 36,000
9 mm Win Mag 45,000 cup .45 Auto Rim 15,000 cup
.38 Auto 26,500 .45 ACP 21,000
.38 S&W 14,500 .45 ACP +P 23,000
.38 Special 17,000 .45 Colt 14,000
.38 Special +P 18,500 .45 Colt (Ruger) 25,000 cup
.38-40 14,000 cup .45 Win Mag 40,000 cup
.38 Super +P 36,500 .454 Casull 50,000 cup
.38 S&W 13,000 cup .50 AE 35,000


ANSI/SAAMI Shotgun Pressure Specifications (Maximum Average Pressure in PSI)
All Piezo measurements unless specified)

Cartridge Maximum Average pressure
10 gauge 11,000 (all)
12 gauge 11,5000 (all but 3 1/2" mag)
12 gauge 3 1/2" mag 14,000
16 gauge (11,500 (all)
20 Gauge 12,000 (all)
28 gauge 12,500 (all)
.410 Bore 2 1/2" 12,500
.410 Bore 3" 13,500

New statistical data analysis suggests that for most cartridges ANSI/SAAMI Maximum Average Piezo (PSI) and Maximum Average copper crusher (CUP) can be related by the following formula which has an R2 value (a statistical measurement of certainty) of .927.  

(1.51586 * CUP) - 17902.0 = PSI

While the relationship is generally within 3Kpsi (it assumes that the CUP was determined using ANSI/ SAAMI standards) one should not rely on this conversion for absolute maximum loads. This conversion is only applicable to rifle ammunition.

Comparison of Pressure Specifications Between
Copper Crusher and Piezo ANSI/ SAAMI Specifications for .308 Win.

  Max Average Pressure Max Probable
Lot Mean
Max Probable
 Sample Mean
Copper Units of pressure (CUP) 52,000 53,300 55,300
PSI (Piezo) 62,000 63,600 66,000
PSI Converted from CUP 60,922 - -

Interestingly the correlation between the European CIP CUP measurements and Piezo measurements has an even better correlation with an R2 of .997.  The formula for the CIP conversion is

(1.20911 * CIPCUP) - 2806.88

The same warning about using this conversion for maximum load work and its being applicable to rifle ammunition only applies to this formula. too

For a detailed analysis of the origin of these formulas see the article "Correlating CUP and PSI" on  RSI's Tech Information Page at www.shootingsoftware.com.

Q. How are proof pressures determined?

A. US commercial proof pressures are set by SAAMI specifications while Europe uses the CIP standards.  The current standards for proof pressures are shown below.  Military proof load standards are set by the arsenals and government specification and may or may not be the same as SAAMI.


Multiply Max Probable Lot Mean Pressure by*

Multiply Max Average Pressure by

Cartridge Class Minimum Proof* Maximum Proof** Proof





Centerfire   Rifle



Centerfire Pistol 15,000 psi  or less 1.40    1.55 1.30

Centerfire Pistol 15,100 - 18,000 psi   




Centerfire Pistol 18,100 - 21,000 psi   




Centerfire Pistol  21,100 psi or greater   







* Max Probable Lot Mean is calculated by adding two standard errors to the Max Average pressure.  The "standard error is calculated by the standard deviation of the sample by the square root of the size of the sample.  For all intents and purposed just use the Max Avg Pressure.
* Min Proof values rounded UP to nearest 500 psi.
** Max Proof values rounded DOWN to nearest 500 psi.

Q. What is the Hatcher Formula?

A. The Hatcher Formula is a mathematical formula use to evaluate the approximate effectiveness of pistol ammunition in incapacitating a person shot with it.  It was developed by Gen. Julian Hatcher in the 1930s and uses the bullet momentum, bullet frontal area, velocity, and a form or shape factor. It  was derived from his observations of the effects of pistol ammunition on cadavers and steers.  While it does not take into consideration bullet penetration or expansion and is basically an approximation, it is still a good formula to use to give one an idea of how a given round will stack up as a fight stopper.

The original formula was somewhat cumbersome to use and the formula was:

RSP = MB * A * F  


RSP = Relative Stopping Power Index
B = Momentum of the bullet in pound feet -  (WB/450240) * V
(If you know the kinetic energy and the velocity you can divide the KE by the velocity to get the momentum.)
A = Area of the bullet in in2
F = Form factor derived from the chart below.

Note:  In the text of Textbook of Pistols and Revolvers the original formula given in the text contained an error in math (he used 240,125 or 1/2 the correct number as the divisor and thus if the text is followed you will get values double the correct ones.  The table for the momentum calculations is, however, correct in the book.

A more convenient variation of the original formula which eliminate working with big numbers is:

RSP = (WB * V * A * F) / 1000


RSP = Relative Stopping Power Index
B = the bullet weight in grains
A = Area of the bullet in in2
V = the bullet velocity in feet per second (f/s)
F = Form factor derived from the chart below.

In the form factor table below the entries in red are recent approximations for bullet types not originally listed by Hatcher.  For Hatcher's original formula the numbers below should be multiplied by 1000 before using.

Bullet Type


Bullet Type

Fully Jacketed Pointed .7   Lead Flat Point (Large Flat) 1.1 - 1.2
Fully Jacketed Round Nose .9   Jacketed Softpoint 
1 - 1.1
Fully Jacketed Flat Point 1.05   Jacketed Softpoint
Fully Jacketed Flat Point (Large flat) 1.1    Lead Semi-wadcutter 1.25
Lead Round Nose 1   Hollow Point
Lead Flat Point 1.05   Hollow Point

Note that the results obtained by this "short form" are not numerically equal to the original formula (they are about half the old formula numbers) but the the comparisons between different cartridges are still valid.  With this short form a value of about 14 is considered barely adequate and about 25 or greater highly desirable.  With the original formula a value of 30 was considered barely adequate and 50 or greater highly desirable.

There are several "modern" variations of this formula floating around.  One variation sometimes seen is to multiple the results by 0.9  if penetration in test media is less than 10" and by 1.1 if penetration is greater than 10".  Another one uses the average area of the "expanded" bullet (area of minimum expanded diameter + area of maximum expanded diameter) / 2, as the bullet diameter and no form factor is used.

For your enjoyment the table below lists the frontal area of common pistol calibers.

Bullet Caliber Area (in2)
.22 .039
.25 .052
.30 .074
.32 .076
9 mm .099
.38 / .357 .101
.40 / 10 mm .125
.41 .132
.44 .146
.45 ACP .160
.45 Colt .161

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As far as I know all the information presented above is correct and I have attempted to ensure that it is. However, I am not responsible for any errors, omissions, or damages resulting from the use or misuse of this information, nor for you doing something stupid with it. (Don't you hate these disclaimers? So do I, but there are people out there who refuse to be responsible for their own actions and who will sue anybody to make a buck.)

Updated 2013-10-23