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Weapon Rank determines the lower cap and upper cap of fSTR and fSTR2.
Weapon Rank is calculated: floor( Weapon Damage Rating / 9 )
For compound ranged weapon such as crossbow, gun, or bow, value for Weapon Damage Rating only accounts for the ranged weapon damage excluding the ammo.
For Hand-to-hand weapons, Weapon Rank is calculated: floor( (Weapon Damage Rating +3) / 9 ). Hand-to-hand skill is not calculated into weapon rank.

floor = truncate the decimal, or round down all the decimal points to 0.
Example: Valkyrie's Fork, DMG 95, 95 / 9 = 10.5 repeating. This would be just 10

Additional Notes

Some weapons such as Company Sword/Company Fleuret, Blau Dolch, Maneater and Mensur Epee have their base damage increased when the latent / hidden effect is activated. Due to this damage increase, the value of Weapon Base Damage / 9 is changed, but the weapon rank doesn't reflect this change. The weapon rank is still the same as when the items have their latent / hidden effect inactive.
However, weapons that have their base damage permanently changed by a latent effect, such as Dissector, Subduer, Gondo-Shizunori and Destroyers, (the 500 or more Weapon Skill Points weapons), will always have a weapon rank based on the latent effect base damage, even before the latent effect becomes active.

Regarding weapons augmented through Trial of the Magians: Weapons inflict accurate damage to their post-augment rating.

See also