Sometimes we are asked by out customers, "How sharp is this blade?" When we hear this we are always a little confused as to how to respond. "Sharpness" is not an easy concept to define as there are many factors to consider. 
We will now look at some of the issues. 
The angle of the cutting edge 
Usually, we think of a thin cutting edge like a razor as very sharp and a thick cutting edge like an axe as not so sharp. 
This is true. A razor can shave a moustache, but an axe can not. 
Therefor we can say that a small angled cutting edge is sharper than a large angled cutting edge. 
By this definition Japanese swords are not very sharp. 
Usually their blades are bevel ground with full "meat" on the cutting surface, so the angle of cutting edge is large. 
The angle of cutting edge is different on each of these tools. They are designed for a specific purposes. 
A razor is very sharp, but can't cut down a tree. Japanese swords are not very sharp, because the object being cut is not always a straw man.  
How sharp is the edge 
A newly purchased razor cuts a moustache well. 
If you use the razor everyday, the quality of the cut will decline and it will need to be sharpened to bring back the edge. The cutting angle of the razor hasn't change yet, it won't cut well. Irrespective of the cutting angle, a sharp edge will always out perform a dull one. 
On Japanese swords, the cutting edge has to be well sharpened by a polisher, even though the cutting surface is bevelled and full of meat.
The hardness of the cutting edge 
A sharp edge of a piece of paper can accidentally cut your finger, and however sharp a razor is, it can't cut glass. 
The cutting edge has to be harder than the object being cut. 
Edge hardness is a very important factor when it comes to sharpness. What we can say is that a hard cutting edge can be made sharper than a mild edge. 
A Japanese sword is not a tool for wood carving. A sword is used on the battle field. Its blade has to attack every part of the enemy's body including armour and helmets. Therefore toughness in the edge is as important as hardness. 
Hardness can mean brittleness. A cutting edge that is too hard can sometimes break. A slightly milder cutting edge is tougher but again, too mild and the edge is weak. 
Therefore the hardness of the cutting edge is very important for a blade. It depends with the quality of the steel and the hardening work (heat treatment). 
A Japanese sword can't cut a stone. The cutting edge is not so hard as a diamond. 
The shape and the curvature 
Most Japanese swords have a curvature and are used with a swinging action. That is all blades except for tanto and tsurugi. 
On such swords, sharpness is not only a matter of the cutting edge. The shape of the blade also relates to sharpness. 
In cases where cutting is by a swinging action, a heavily curved blade is sharper than a straight blade. 
A battle field is not a stage for cutting performances. In battle a sword is used to parry and to thrust as well as to cut. Because of this, we can't simply say a deeper curvature makes a better blade. 
In the end, we can't give you a simple answer to explain "sharpness". 
Having a sharp edge is one of the many attributes of a good blade. Sharpness is one of the elements that makes up the cutting power of a blade. 
Therefore, what does "sharp" mean? 

If we want to know the cutting qualities of a blade without testing it, we carefully study the blade. Examining swords isn't just for pleasure. We are also judging its quality. To carefully examine a blade is to understand a blade.