Volume of Rectangular Prism Calculator 2025: Complete Guide (1000+ Words)
A rectangular prism (cuboid) is a 3D shape with six rectangular faces. Our 2025 Volume of Rectangular Prism Calculator computes volume, surface area, space diagonal, and face diagonals from length, width, height with full step-by-step explanations and live 3D visualization.
What is a Rectangular Prism?
Also called a cuboid. Has 6 faces, 12 edges, 8 vertices. Opposite faces are equal.
- Length (l), Width (w), Height (h)
- Volume (V): Space inside
- Surface Area (SA): Total face area
- Space Diagonal: From one vertex to opposite
Core Formulas
Volume: V = l × w × h
Surface Area: SA = 2(lw + lh + wh)
Space Diagonal: d = √(l² + w² + h²)
Face Diagonals: √(l² + w²), √(l² + h²), √(w² + h²)
Surface Area: SA = 2(lw + lh + wh)
Space Diagonal: d = √(l² + w² + h²)
Face Diagonals: √(l² + w²), √(l² + h²), √(w² + h²)
Example: l=10, w=5, h=3 cm
V = 10 × 5 × 3 = 150 cm³
SA = 2(50 + 30 + 15) = 190 cm²
Space diagonal = √(100 + 25 + 9) = √134 approximately 11.576 cm
SA = 2(50 + 30 + 15) = 190 cm²
Space diagonal = √(100 + 25 + 9) = √134 approximately 11.576 cm
Applications
- Packaging: Boxes, containers, shipping
- Construction: Rooms, bricks, tanks
- Engineering: Beams, reservoirs
- Everyday: Refrigerators, books
Step-by-Step: l=8, w=6, h=4 m
V = 8 × 6 × 4 = 192 m³
SA = 2(48 + 32 + 24) = 208 m²
Space diagonal = √(64 + 36 + 16) = √116 approximately 10.770 m
Common Mistakes
- Using only two dimensions for volume
- Forgetting factor of 2 in surface area
- Confusing face and space diagonal
Advanced: In Coordinate Geometry
Vertices from (0,0,0) to (l,w,h)
Related Tools
FAQs
Is a cube a rectangular prism? Yes, when l = w = h.
Can volume be negative? No, dimensions must be positive.
Conclusion
Rectangular prisms are essential in real-world design. Our 2025 Volume of Rectangular Prism Calculator delivers instant precision with crystal-clear steps and interactive 3D graphics. Master 3D geometry today!
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