Calculate Parts from Cutting

Name: Calculate Parts from Cutting
Author: Jürgen Kummer

Calculator for the number of parts, which are produced by cutting an object in length, width and height. If you cut an object once in length, you get two parts, cutting twice in length gives three parts and so on. If you cut once in length and once in width, four parts are produced. When cutting in each dimension, eight parts are made. It is required, that the object is not left during cutting and that any two cuts in different dimensions intersect exactly once, whereas two cuts in the same dimension do not intersect within the object.

The formula for the number of parts is (a+1) * (b+1) * (c+1)

Each dimension therefore has an additional multiplier added, which is increased by the number of cuts in that dimension. A single cut in a new dimension intersects all existing cuts and thus doubles the number of parts. If no value is entered for one dimension, then no division occurs in that dimension. Accordingly, if no value is entered at all, the number of parts is one.

Example: two cuts in length and one cut in width produce six parts. If another cut were made in height, the number of parts would double to 12, for two cuts in height, this value would triple to 18.

For the number of pieces it doesn't matter where the cuts are, as long as the cuts meet the conditions mentioned above. The cuts don't even need to be straight. For the size of the pieces, however, this would be relevant, but their size is neglected in this calculation anyway. Also in practice, cutting becomes increasingly difficult the more and the smaller these pieces become. This is also disregarded here. This consideration is therefore purely theoretical. It describes the mathematical procedure and not the actual cutting of objects.

Cuts in length a:
Cuts in width b:
Cuts in height c:

Number of parts: