Cuboid Calculator
Calculate volume, surface area, and diagonal of a cuboid (rectangular prism)
Calculate Cuboid Properties
Cuboid Calculation Results
Formulas Used:
Volume: V = l × w × h = 0 × 0 × 0 = 0.00 cm³
Surface Area: SA = 2(lw + wh + lh) = 2(0×0 + 0×0 + 0×0) = 0.00 cm²
Diagonal: d = √(l² + w² + h²) = √(0² + 0² + 0²) = 0.00 cm
Cuboid Properties
Example Calculation
Rectangular Box Example
Dimensions: Length = 12 cm, Width = 9 cm, Height = 10 cm
Volume: V = l × w × h = 12 × 9 × 10 = 1,080 cm³
Surface Area: SA = 2(lw + wh + lh) = 2(108 + 90 + 120) = 636 cm²
Diagonal: d = √(12² + 9² + 10²) = √(144 + 81 + 100) = √325 ≈ 18.03 cm
Step-by-Step Process
1. Measure length, width, and height
2. Apply volume formula: V = l × w × h
3. Apply surface area formula: SA = 2(lw + wh + lh)
4. Apply diagonal formula: d = √(l² + w² + h²)
Cuboid vs Cube
Cuboid
• Length ≠ Width ≠ Height
• 6 rectangular faces
• Also called rectangular prism
Cube
• Length = Width = Height
• 6 square faces
• Special case of cuboid
Common Applications
Packaging and shipping boxes
Room volume calculations
Storage capacity planning
Construction material estimation
Quick Tips
Ensure all dimensions are in the same unit
Volume unit is always cubed (³)
Surface area unit is always squared (²)
Diagonal is the longest distance inside the cuboid
Understanding Cuboids
What is a Cuboid?
A cuboid is a three-dimensional geometric shape with six rectangular faces. It has length, width, and height that are typically different measurements. Cuboids are also known as rectangular prisms and are one of the most common 3D shapes in everyday life.
Key Properties
- •6 faces: All faces are rectangles
- •8 vertices: Corner points where edges meet
- •12 edges: 4 edges of each dimension
- •Right angles: All corners form 90° angles
Mathematical Formulas
Volume Formula
V = l × w × h
Where l = length, w = width, h = height
Surface Area Formula
SA = 2(lw + wh + lh)
Sum of all 6 rectangular face areas
Diagonal Formula
d = √(l² + w² + h²)
Space diagonal using 3D Pythagorean theorem