Cube Calculator

Data Source & Methodology (Geometric Cube)

A cube is a regular hexahedron, one of the five Platonic solids. It is defined as a 3D solid with 6 square faces, 12 equal-length edges, and 8 vertices. All calculations are derived from these fundamental definitions.

• Authoritative Source: The formulas are based on foundational principles of **Euclidean Geometry** and the **Pythagorean Theorem**.
• Methodology: "Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte." All properties of a perfect cube can be derived from its single edge length, or side ($a$). This calculator can also reverse-engineer the side $a$ from other properties like volume or surface area.

The Formulas Explained (Geometric Cube)

All calculations are based on the side length $a$.

1. Calculations from Side ($a$)

Volume ($V$):

Surface Area ($SA$): A cube has 6 identical square faces, each with an area of $a^2$.

Face Diagonal ($f$): The diagonal of one square face. Found using Pythagoras' theorem ($a^2 + a^2 = f^2$).

Space Diagonal ($d$): The diagonal from one corner to the opposite, through the cube's center. Found using Pythagoras' theorem ($f^2 + a^2 = d^2$).

2. Reverse Formulas (Solving for $a$)

This calculator uses these formulas to find $a$ from other values.

Glossary of Geometric Variables

• Side ($a$): The length of any of the 12 equal edges.
• Volume ($V$): The total 3D space enclosed by the cube.
• Surface Area ($SA$): The total 2D area of all 6 faces combined.
• Face Diagonal ($f$): The diagonal distance across one of the square faces.
• Space Diagonal ($d$): The longest possible diagonal, running from one vertex to the opposite vertex through the cube's interior.

How It Works: A Geometry Example

Let's find the properties of a cube that has a **Surface Area (SA) of 150 sq ft**.

1. Select the "Given" Value:

   In the calculator, choose "Surface Area (SA)" from the dropdown and enter "150". Select "ft" as the unit.

2. Step 1: Find Side ($a$) from Surface Area:

   The calculator first finds the side length using the reverse formula:

   $$ a = \sqrt{SA / 6} = \sqrt{150 / 6} = \sqrt{25} = 5 \text{ ft} $$
3. Step 2: Calculate Other Properties from Side ($a$):

   Now that $a = 5 \text{ ft}$, the calculator finds all other values.

   Volume ($V$):

   $$ V = a^3 = 5^3 = 125 \text{ ft}^3 $$

   Space Diagonal ($d$):

   $$ d = a\sqrt{3} = 5 \times 1.732... \approx 8.66 \text{ ft} $$

Result: A cube with a surface area of 150 ft² has a side of 5 ft and a volume of 125 ft³.

Data Source & Methodology (Shipping Volume)

This calculator determines the total cubic volume of a shipment, commonly used in logistics, freight, and mailing services. The calculation is based on standard geometric formulas for a rectangular prism (cuboid).

• Authoritative Source: The formulas are based on **standard international freight and logistics industry practices** for calculating dimensional weight and volume.
• Methodology: "Tutti i calcoli si basano rigorosamente sulle formule e sui dati forniti da questa fonte." The tool calculates the volume of a single item and multiplies it by the quantity. It also provides a conversion to Cubic Meters (CBM), the standard industry unit.

The Formulas Explained (Shipping Volume)

Calculations are based on the length, width, height, and quantity of the items.

1. Volume per Item

2. Total Volume

3. Cubic Meters (CBM) Conversion

CBM is the standard unit for international freight. The calculator converts your total volume to CBM automatically.

• 1 m³ = 1 CBM
• 1,000,000 cm³ = 1 CBM
• 35.3147 ft³ $\approx$ 1 CBM
• 61,023.7 in³ $\approx$ 1 CBM

Glossary of Shipping Variables

• Length (L), Width (W), Height (H): The three dimensions of a single shipping carton or item.
• Quantity (Q): The total number of identical items in the shipment.
• Volume per Item: The cubic volume of a single carton.
• Total Volume: The combined cubic volume of all items in the shipment.
• CBM (Cubic Meter): The industry-standard unit for freight volume, equal to 1m x 1m x 1m.

How It Works: A Shipping Example

Let's calculate the total volume for a shipment of **20 boxes**.

Item Dimensions: 50 cm (Length) x 40 cm (Width) x 30 cm (Height)

1. Enter Values:

   In the "Shipping Volume" mode, enter L=50, W=40, H=30, and Q=20. Select "cm" as the unit.

2. Step 1: Calculate Volume per Item:
   $$ V_{\text{item}} = 50 \times 40 \times 30 = 60,000 \text{ cm}^3 $$
3. Step 2: Calculate Total Volume:
   $$ V_{\text{total}} = 60,000 \text{ cm}^3 \times 20 = 1,200,000 \text{ cm}^3 $$
4. Step 3: Convert to CBM:
   $$ \text{CBM} = 1,200,000 / 1,000,000 = 1.2 \text{ CBM} $$

Result: The calculator will show a total volume of 1,200,000 cm³ and a total CBM of 1.2 m³.