Square Cube Law Calculator

How to find the new area or volume of an object when its size changes? Answer is here, The Square Cube Law Calculator. It uses the square-cube law to calculate new dimensions. But what exactly is the square-cube law?

Enter the initial area (e.g., 25 square meters) to calculate the final area.

Enter the initial volume (e.g., 50 cubic meters) to calculate the final volume.

Enter the initial length (e.g., 5 meters).

Enter the final length (e.g., 10 meters) to calculate the final area and volume.

The calculated final area will be displayed here.

The calculated final volume will be displayed here.

What is the Square Cube Law?

The square-cube law explains how the volume and surface area of an object change with its size. When an object’s size changes, its surface area and volume do not change proportionally. This law is important in fields like biology, physics, and engineering.

Square Cube Law Calculation tool

How to Use the Tool?

Input Fields

Enter Initial Area: To find the new area, input the initial area into the calculator.
Enter Initial Volume: To determine the new volume, input the initial volume.
Enter Initial Length: This is the original length of the object.
Enter Final Length: This is the new length of the object.

Example Values

Let’s say you have an object with an initial area of 20 square units, an initial volume of 40 cubic units, an initial length of 5 units, and a final length of 10 units.

Formula

The formulas used in the calculator are:

 $A 2 = A 1 \times {(\frac{L 2}{L 1})}^{2}$

Variable	Description
$A 1$	Initial Area
$V 1$	Initial Volume
$L 1$	Initial Length
$L 2$	Final Length
$A 2$	Final Area
$V 2$	Final Volume

Calculation Examples

Example 1

Initial Area (A1): 20
Initial Volume (V1): 40
Initial Length (L1): 5
Final Length (L2): 10

Calculation:

1. Calculate the new area:

 $A 2 = 20 \times {(\frac{10}{5})}^{2} = 20 \times 4 = 80$

2. Calculate the new volume:

 $V 2 = 40 \times {(\frac{10}{5})}^{3} = 40 \times 8 = 320$

Result: The new area is 80 square units, and the new volume is 320 cubic units.

Example 2

Initial Area (A1): 15
Initial Volume (V1): 30
Initial Length (L1): 3
Final Length (L2): 6

Calculation:

1. Calculate the new area:

 $A 2 = 15 \times {(\frac{6}{3})}^{2} = 15 \times 4 = 60$

2. Calculate the new volume:

 $V 2 = 30 \times {(\frac{6}{3})}^{3} = 30 \times 8 = 240$

Result: The new area is 60 square units, and the new volume is 240 cubic units.

I hope you liked the Square Cube Law Calculator. How was your experience? If you encounter any errors, please report them on our “Report an Error” page.

Square Cube Law Calculator