Calculations at a grid. Here, a grid is a rectangle with regular square holes and equally thick bars between. Enter the number of holes in length and width, as well as their edge length and the bar thickness. Choose the number of decimal places and click Calculate.
Formulas:
Lengths, width, thickness and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter). Numbers of holes have no unit. Perimeter refers to inner and outer boundary lines.
The term grid is used here colloquially to describe this specific shape. Strictly speaking, in geometry, a grid describes the subdivision of space using lines. This is not what is meant here. In the context of a geometric grid, the lines possess no width, so they are one-dimensional, and they do not necessarily maintain equal spacing from one another. In the case of the grid shape described here, much like physical grids as tangible objects, the bars situated between the holes do possess width. Furthermore, in this context, as is also common with real, world grids, these bars are arranged in a regular pattern.
Such a grid is composed of various rectangles. These rectangles may be conceptualized as either overlapping or non-overlapping. In the case of overlapping rectangles, fewer, albeit larger rectangles are required to construct the grid. The holes in this specific grid are square in shape. Also squares can also be identified within the bars situated between any four adjacent holes simply by connecting their respective adjacent corners.
The total number of holes is, of course, the product of the number of holes along the length multiplied by the number along the width. Sometimes the number of holes situated at the outside and the number of holes within needs to be known. For this purpose, please refer to the calculator for the number of inner and outer fields. To calculate the number of fields, bars, and nodes within a two- or three-dimensional grid, without taking the thickness of the bars into account, see another grid calculator.
The grid described here is a planar surface with holes. If the specific shape of these holes is deemed irrelevant, then such objects fall within the domain of topology, a distinct and entirely different branch of mathematics.