Grid Calculator

Name: Grid Calculator
Author: Jürgen Kummer

Calculate the number of fields or spaces, bars and knots of a two- and of a three-dimensional grid. A two-dimensional grid contains fields, a three-dimensional grid contains spaces, each of them surrounded by bars. The number of fields easily calculates as m=a*b, the rooms as m=a*b*c.
Please enter at least a and b, c is optional.

A bar here is a straight line between two crossings. The calculation of the number of grid bars is more complicated. The formula is:
for 2D: n = (2a+1)*b+a
for 3D: n = [(2a+1)*b+a]*(c+1)+(a+1)*(b+1)*c

A knot is at the crossing of bars. The formula is:
for 2D: k = (a+1)*(b+1)
for 3D: k = (a+1)*(b+1)*(c+1)

Example: a three-dimensional grid with 6 spaces in length, 5 spaces in height and one space in depth has 30 spaces, 184 grid bars and 84 knots.

The length of each direction is calculated as the number of fields multiplied by the according size of each, assuming the fields are all the same size. This is for an idealized grid, meaning it has no inherent size, or at least none that is significant. This grid would be a one-dimensional structure. If the grid bars are to have thicknesses, these can be added to the grid cell size. However, it is important to note that inner grid bars should only be calculated with half their thickness, as they are divided between two cells. This does not apply to outer grid bars, which must be calculated with their full thickness. The number of inner grid bars per dimension is the number of cells minus two. There are two outer grid bars per dimension. Working with thicknesses of course makes such calculations somewhat more complicated and less straightforward.
An example of a grid without dimensions is a stack of identical cuboids without gaps. The boundaries between these cuboids can be considered a virtual grid.

Fields, spaces in length a:
Fields, spaces in height b:
Fields, spaces in depth c:
Number of fields, spaces m:
Number of bars n:
Number of knots k: