Rectangular Prism Calculator
Calculate volume, surface area, and diagonal of a rectangular prism (cuboid)
Enter Rectangular Prism Dimensions
The longest side of the prism
The horizontal dimension
The vertical dimension
Rectangular Prism Properties
Rectangular Prism Properties
Example Calculation
Cardboard Box Example
Dimensions:
Length = 18 inches
Width = 12 inches
Height = 15 inches
Calculations
Volume: 18 × 12 × 15 = 3,240 in³
Surface Area: 2(18×12 + 18×15 + 12×15) = 2(216 + 270 + 180) = 1,332 in²
Diagonal: √(18² + 12² + 15²) = √(324 + 144 + 225) = √693 ≈ 26.32 in
Key Formulas
Volume
V = l × w × h
Cubic units (length³)
Surface Area
SA = 2(lw + lh + wh)
Square units (length²)
Space Diagonal
d = √(l² + w² + h²)
Linear units (length)
Common Applications
Packaging and shipping calculations
Construction material estimation
Gift wrapping paper requirements
Aquarium water volume
Storage space planning
Understanding Rectangular Prisms
What is a Rectangular Prism?
A rectangular prism, also called a cuboid or rectangular box, is a three-dimensional solid with six rectangular faces. It has three pairs of parallel rectangular faces, with opposite faces being congruent (identical in size and shape).
Key Properties
- •6 faces: All faces are rectangles
- •8 vertices: Corner points where edges meet
- •12 edges: Line segments where faces meet
- •Right angles: All angles are 90 degrees
Formula Explanations
Volume Formula
V = l × w × h
Volume represents the amount of space inside the prism. It's calculated by multiplying all three dimensions together.
Surface Area Formula
SA = 2(lw + lh + wh)
Surface area is the total area of all six faces. Each pair of opposite faces has the same area, so we calculate three different face areas and multiply by 2.
Diagonal Formula
d = √(l² + w² + h²)
The space diagonal connects two opposite vertices through the interior of the prism. This formula is a 3D extension of the Pythagorean theorem.