Understanding national differences is extremely important to understand when evaluating "penetration" across countries.

The easiest way to show why this is so important was done by Carl Hamilton in a Quora Thread (LINK), where he made this very excellent graph showing the results of national differences in penetration measurement:

(Click for full size image)

You can see from the above image that the same gun(s), with the same ammunition gives wildly different results, depending on who is doing the evaluations.

• 8.8 cm KWK 43 (L/71) (Tiger II): 205~ mm (German) vs 138~ mm (Russian)
• 8.8 cm KWK 36 (L/56) (Tiger I): 170~ mm (German) vs 100~ mm (Russian)
• 7.5 cm KWK 42 (L/70) (Panther): 190~ mm (German) vs 110~ mm (Russian)
• 7.5 cm KWK 40 (L/48) (Panzer IV): 138~ mm (German) vs 82~ mm (Russian)

Steve Lorenz over at Panzer War (panzer-war.com - Alt) has done yeoman work in collating the national differences for his wargame series Panzer War, and I'm indebted to him for digging up many of these penetration measurement tidbits.

American Penetration Standards

Basic References
Penetration of Armour Plate, US Ordnance Board, Aberdeen Proving Ground, March 1950 (5.9~ MB PDF)

Early in the war, armor angled at 0 degrees was used and the basic penetration criteria was that 50% of all shots fired must penetrate that armor thickness (V⁵⁰).

The US Army used 50% of shell mass passing through the armor as a complete penetration.

There were a few specific interservice differences within the USA as listed below:

Obliquity was poorly understood, with obliquity effects taken into account via mathematical adjustments applied to 0 degree penetration numbers. This is what led to the infamous "76mm Scandal" in 1944, where Eisenhower remarked "Ordnance told me this 76mm would take care of anything the Germans had. Now I find you can't knock out a damn thing with it."

Once it became known how important obliquity effects were, angled plates were added to "proof testing" for guns and ammunition by the US, rather than relying on mathematical equations to estimate obliquity effects.

German Penetration Standards

There's a lot of contradictory information out there about German Penetration Criteria; but the "gold standard" is the 137-page German Steel Armour Piercing Projectiles and Theory of Penetration (BIOS Final Report No. 1343 ADM 213/951) (19.9~ MB ZIP) which has been referenced many times as "BIOS Report" across many secondary sources.

German design policy (with the exception of very small calibers) was to produce a projectile that penetrated the armor plate whole and depended on an internal explosive charge (AP-HE) for the majority of lethal effect. Thus, Germany defined a successful penetration as one in which a shell passed through the armor plate and was in a condition to explode after pass-thru.

As you might guess, under German criteria, a penetrating hit under other nations' standards would count as a non penetration under German standards if it failed to explode after pass-thru.

German Test Values were:

G_S (Complete Protection): This was defined as the maximum velocity at which the plate gave complete protection. There should be no cracks and no plate material removed from the back of the plate. "The human eye must be safe behind the plate."

G_D: This was defined as the velocity at which the projectile will just penetrate the plate with no remaining velocity.

German firing tests for penetration curves had some specific criteria, namely:

1.) Rather than using randomly sampled shell lots as in other nations; the Germans determined a projectile weight and checked the weight of all projectiles involved in the trials.

2.) They were first calibrated via firing a single round whose striking velocity was just under that deemed necessary for complete penetration. This was determined via comparison with previous firing and inter/extrapolation or by calculations.

3.) The target plate was angled at 30°. Later in the war; 45° and 60° angles were added for testing. By the end of the war, tests were conducted at 15° intervals from 0 to 75°. (NOTE: These are British Inclinations, not German).

4.) A certain number of rounds had to penetrate to obtain a satisfactory limit value. The number varied by caliber, being:

20mm to 37mm: 10 rounds.
75mm to 105mm: 5 rounds.
210mm: 3 rounds.

Russian Penetration Standards

The Russians defined "penetration" as being achieved when 75% of the mass of a shell passed through the armor. (This meant that shell fragments/splinters could still count towards success).

They then broke down penetration into categories:

Certified Penetration (CP): 80% of all hits result in penetration.

Initial Penetration (IP): 20% of all hits result in penetration.