Geometry
Rectangular Prism Volume Calculator
Volume and surface area of any box or cuboid. Enter length, width, and height to compute volume, total surface area, and diagonal of a rectangular prism.
Live Vector System
Core Dimensions
Analytic Metrics
Surface Area
78.54
Perimeter
31.416
Mathematical Verification
Our engine utilizes double-precision floating-point arithmetic for geometric derivations. For triangles, we implement Heron's Theorem with strict validation to ensure the triangle inequality principle is maintained.
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Solution Methodology
01
Enter Dimensions
Provide length l, width w, and height h in consistent units.
02
Compute Volume
Apply V = l × w × h.
03
Compute SA & Diagonal
Calculate SA = 2(lw + lh + wh) and d = √(l²+w²+h²).
Common Questions
How do you calculate the volume of a rectangular prism?
Multiply length × width × height: V = lwh. This is equivalent to computing the area of the base (l×w) and then extending it through the height — the same logic as stacking identical rectangular layers.
What is the space diagonal of a rectangular prism?
The space diagonal connects two opposite corners through the interior of the prism. Its length is d = √(l²+w²+h²), derived by applying the Pythagorean theorem twice — first across the base, then up through the height.