Volume of a Rectangular Prism Calculator
Calculate rectangular prism volume, surface area, and diagonals using multiple input methods
Calculate Rectangular Prism Volume
Longest dimension of the prism
Width dimension of the prism
Height dimension of the prism
Calculation Results
Formula Used
Volume Formula: V = l × w × h
Where: l = 0.0000 cm, w = 0.0000 cm, h = 0.0000 cm
Calculation: V = 0.0000 × 0.0000 × 0.0000 = 0.0000 cm³
Example Calculation
Problem
Find the volume of a rectangular shipping box with dimensions: length = 30 inches, width = 19 inches, height = 11 inches.
Solution
Given: Length (l) = 30 in, Width (w) = 19 in, Height (h) = 11 in
Formula: V = l × w × h
Calculation: V = 30 × 19 × 11 = 6,270 in³
Answer: Volume = 6,270 cubic inches
Rectangular Prism Properties
6 rectangular faces (including squares)
12 edges of varying lengths
8 vertices (corners)
All angles are 90 degrees
Also called a cuboid or box
Key Formulas
Volume:
V = l × w × h
Surface Area:
SA = 2(lw + lh + wh)
Face Diagonals:
d₁ = √(l² + w²)
d₂ = √(l² + h²)
d₃ = √(w² + h²)
Space Diagonal:
d = √(l² + w² + h²)
Quick Tips
A cube is a special rectangular prism where l = w = h
Volume represents the space inside the prism
Surface area is the total area of all 6 faces
Face diagonals are on the flat surfaces
Space diagonal goes through the 3D interior
Understanding Rectangular Prisms
What is a Rectangular Prism?
A rectangular prism (also called a cuboid or box) is a three-dimensional shape with six rectangular faces. Each face is a rectangle, and opposite faces are identical and parallel. It's one of the most common 3D shapes in everyday life, found in boxes, buildings, books, and containers.
Real-World Applications
- •Shipping: Calculate box capacity and shipping costs
- •Construction: Determine concrete or material volumes
- •Storage: Optimize warehouse and storage space
- •Aquariums: Calculate water volume for fish tanks
- •Gardening: Determine soil volume for raised beds
Why is the Volume Formula V = l × w × h?
The volume formula comes from the principle of counting unit cubes that fit inside the prism:
V = Length × Width × Height
Think of it as stacking layers: each layer has an area of l × w, and you stack h layers high.
V = (Area of base) × Height
Diagonal Calculations
Face Diagonals: Diagonals across rectangular faces
d₁ = √(l² + w²) (length-width face)
d₂ = √(l² + h²) (length-height face)
d₃ = √(w² + h²) (width-height face)
Space Diagonal: 3D diagonal through the interior
d = √(l² + w² + h²)