Calculate the Number of Fields and Spaces Inside, Outside and Total

Calculator for two- and three-dimensional objects with integer length, width and height. If every dimension is longer as 2, then there are fields (2D) or spaces (3D) which lie inside, which have no outer borders and fields at the outside. Here the number of these fields and spaces can be calculated. It is a precondition that there are no empty fields or spaces, so that the separating lines are all within the object and don't go beyond. Please enter two or three positive integers.

The formula for the total number of fields is a * b. For the inside fields, the formula is (a−2) * (b−2) for a, b > 2
The formula for the total number of spaces is a * b * c. For the inside spaces, the formula is (a−2) * (b−2) * (c−2) for a, b, c > 2
The ratios inside/outside or outside/inside are determined by dividing one value by the other.

Fields inside and outside

Example: an area with the length 4 and the width 3 has 12 fields, 2 fields inside and 10 at the outside.

The difference between total fields and inner fields for a given dimension is 2 if there are two or more than two fields in total. This is because there are always two fields at the outer ends, depending on the dimension: left and right, top and bottom, or front and back. The ratio of inner to outer fields is particularly high when all three dimensions have high values. A high ratio of this kind means a small surface area per volume and can be conceptualized as a compact object.
Compact objects are often more stable, less sensitive, and better withstand weathering. Less compact objects tend to be more chemical reactive and lighter. Of course, the material and shape of these objects play a significant role here.

Length a:
Width b:
Height c:

Type:
Total:
Inside:
Outside:
Inside/outside:
Outside/inside: