Size of the weapon actually has no impact on combat stats apart from its weight - it represents the total volume of the weapon in cubic centimetres. Weapons in DF do not technically have any shape; all combat stats are based on the attack stats, specifically contact area and penetration size.
I'm not sure if there's a straightforward formula that gets the physical size and shape of the attack from its stats. Contact area appears to correspond to the width x height of the part of the weapon that penetrates the target (and therefore the amount of potential damage inflicted on the target, but also the chance of the weapon being stopped before it penetrates to deeper layers), while penetration size is how deep that part tries to go.
DF's large dagger is 200cc in volume. 200cc of steel is about 1.5 kg.
This is a dagger that weighs about 1.5 kg. The blade is about 40 cm long and 0.1 cm wide. DF's dagger stab penetration, and slash contact area, are both 1000. So let's guess that each unit represents about 0.005 square cm.
So that means that DF's short sword, with a contact area of 20000, is about 100 square cm. A short sword often has a width of around 2 cm, so that means DF's short sword is around 50 cm long, I guess, with a slash that penetrates 20 cm.
While the long sword, with a contact area of 60000, is about 300 square cm. So it might be anywhere from 75 cm with a thick, 4 cm blade, to 150 cm with a thinner, 2 cm one. And its slash penetrates about 30 cm deep.
Let's see...pike penetrating 60 cm, spear penetrating 50...
Yeah, so these figures sounds about right-ish. This is what I will assume is the correct calculation unless someone figures out a better one.
Each unit of contact area represents 0.005 square cm, while each unit of penetration depth represents 0.005 cm deep.