Cuboid Volume Calculator

Length \( l \):

Width \( w \):

Height \( h \):

Volume

Volume (cm³): Volume (in³): Volume (ft³): Volume (m³): Volume (L):

Diagonal

Diagonal (cm): Diagonal (in): Diagonal (ft): Diagonal (m):

1. What is a Cuboid Volume Calculator?

Definition: This calculator computes the volume and diagonal of a cuboid (rectangular prism) based on its length (\( l \)), width (\( w \)), and height (\( h \)).

Purpose: Useful in geometry, engineering, and everyday applications for determining the volume and diagonal of cuboid-shaped objects (e.g., boxes, rooms).

2. How Does the Calculator Work?

The calculations are based on the following formulas:

\[ V = l \times w \times h \] \[ d = \sqrt{l^2 + w^2 + h^2} \]

Unit Conversions:

Input (Length): mm (×0.1), cm (×1), m (×100), in (×2.54), ft (×30.48) to cm
Output (Length): cm (direct), in (×0.393701), ft (×0.0328084), m (×0.01)
Volume: cm³ (direct), in³ (×0.0610237), ft³ (×0.0000353147), m³ (×0.000001), L (×0.001)

Explanation: All dimensions are converted to cm, the volume and diagonal are calculated in cm³ and cm, respectively, and then converted to other units.

3. Importance of Cuboid Volume Calculation

Details: Calculating the volume of a cuboid is essential in packaging, construction, and storage for determining capacity and dimensions of rectangular objects.

4. Using the Calculator

Tips: Enter the length \( l \), width \( w \), and height \( h \) in mm, cm, m, in, or ft (all must be >0). The result shows the volume in cm³, in³, ft³, m³, and L, and the diagonal in cm, in, ft, and m.

5. Example

Given: Length \( l = 9 \, \text{cm} \), width \( w = 7 \, \text{cm} \), height \( h = 8 \, \text{cm} \).
Volume Calculation: \( V = 9 \times 7 \times 8 = 504 \, \text{cm}^3 \).
Diagonal Calculation: \( d = \sqrt{9^2 + 7^2 + 8^2} = \sqrt{81 + 49 + 64} = \sqrt{194} \approx 13.928 \, \text{cm} \).

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