Calculate Area and Volume with and without Margin

Name: Calculate Area and Volume with and without Margin
Author: Jürgen Kummer

Calculator for the size of two- and three-dimensional rectangular objects with margin. Those objects are rectangle and cuboid. The margin has the same thickness on each side. Please enter the margin thickness and two lengths for a rectangle or three length for a cuboid, each including the margin. The margin must be smaller than half the smallest length. The complete area or volume, that of the inside without margin and that of the margin will be calculated. If the length units are e.g. meters, then the area unit is square meters and the volume unit is cubic meters.

Example: a rectangle with length 9.7 cm, width 4.8 cm and margin 0.5 cm has an area of 46.56 cm², an inside of 33.06 cm² and a margin of 13.5 cm². If this now has a height of 3.7 cm, then the total volume is 172.27 cm³, the inside 89.26 cm³, and the margin 83.01 cm³.

Sometimes objects can only be measured at the outside. If you want to know their volume without the outer shell, you need to know the margin thickness or at least be able to estimate it accurately. Mathematically, this calculation is the volume or area of a solid minus that of a similar but smaller solid. In geometry, similarity means the exact same shape but different proportions (and a different location and orientation, but that is irrelevant here). If these solids are rectangles or cuboids, then this calculation is relatively simple. For more complex shapes, more complicated formulas are of course required for each object, but the principle remains the same. The object is calculated in two different sizes. For the smaller size, twice the edge width is subtracted in each dimension from the larger one. Then, the smaller value is subtracted from the larger value.

Length with margin:
Width with margin:
Height with margin:
Margin thickness:

Type:
Complete:
Inside:
Margin: