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Math • Rectangular Prism & Cube Volume Calculator

Rectangular Prism & Cube Volume Calculator

Calculate the volume, surface area, and space diagonal of a rectangular prism (or cube) from its length, width, and height.

Volume (V = l × w × h)
192.00
Surface Area (2(lw+lh+wh))
208.00
Space Diagonal (d)
10.77
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Calculation Guide & Reference

Rectangular Prism & Cube Volume Mathematics

Rectangular prism calculator computes volume, surface area, and space diagonal from length, width, and height — also works for cubes.

Standardized Mathematical Formula
V = L × W × H | Diagonal = √(L² + W² + H²)

A rectangular prism's volume is simply the product of its three dimensions. Its space diagonal — the longest straight line that fits inside the box, corner to corner — extends the Pythagorean theorem into three dimensions.

Variables:
L:Length
W:Width
H:Height
How It Works (Step-by-Step)
  • 1Enter the length, width, and height of the box (use equal values for a cube).
  • 2View the volume, total surface area, and the space diagonal.
Real-World Numerical Example
A Box 6 × 4 × 8

A shipping box measures 6 units long, 4 units wide, and 8 units tall.

•Volume: 6 × 4 × 8 = 192 cubic units.
•Surface area: 2 × (6×4 + 6×8 + 4×8) = 2 × (24+48+32) = 2 × 104 = 208 square units.
•Space diagonal: √(6² + 4² + 8²) = √(36+16+64) = √116 ≈ 10.77 units.
Result: The box has a volume of 192 cubic units, a surface area of 208 square units, and a space diagonal of about 10.77 units.
Calculation Best Practices & Tips
Examine the discriminant (b² - 4ac) before solving quadratics to instantly know if roots are real, distinct, repeated, or complex.
In statistical analysis, always check both the mean and median to identify if data distribution is skewed by outliers.
When calculating percentage changes, ensure you divide by the original starting baseline value: ((New - Old) / Old) * 100.

Frequently Asked Questions (FAQ)

V = Length × Width × Height — multiply all three dimensions together.

The space diagonal is the longest straight line that fits inside a 3D box, running from one corner to the opposite corner — found with the 3D Pythagorean theorem: √(L²+W²+H²).

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