Rectangular Prism Calculator
Calculate volume, surface area, and other properties of a rectangular prism (cuboid)
Calculation Results
Enter rectangular prism measurements to calculate all properties.
Length (l): units
Width (w): units
Height (h): units
Base Area (B): square units
Volume (V): cubic units
Lateral Area (L): square units
Surface Area (S): square units
Base Perimeter (P): units
Space Diagonal (d): units
Rectangular Prism Diagram
Rectangular Prism Formulas
Key Properties
- Length (l): Longest side of the base
- Width (w): Shortest side of the base
- Height (h): Distance between the two rectangular bases
- Base Area (B): Area of the rectangular base
- Volume (V): Space contained within the prism
- Lateral Area (L): Area of the four rectangular faces
- Surface Area (S): Total area including both rectangular bases
- Base Perimeter (P): Perimeter of the rectangular base
- Space Diagonal (d): Diagonal through the 3D space of the prism
Calculation Formulas
- Base Area (B): B = l × w
- Volume (V): V = l × w × h
- Lateral Area (L): L = 2h(l + w)
- Surface Area (S): S = 2(lw + lh + wh)
- Base Perimeter (P): P = 2(l + w)
- Space Diagonal (d): d = √(l² + w² + h²)
Where: l = length, w = width, h = height
Example Calculation
For a rectangular prism with:
Length (l) = 6 units, Width (w) = 4 units, Height (h) = 5 units.Calculations:
- Base Area = 6 × 4 = 24 units²
- Base Perimeter = 2 × (6 + 4) = 20 units
- Volume = 6 × 4 × 5 = 120 units³
- Lateral Area = 2 × 5 × (6 + 4) = 100 units²
- Surface Area = 2 × (6×4 + 6×5 + 4×5) = 148 units²
- Space Diagonal = √(6² + 4² + 5²) ≈ 8.77 units
About Rectangular Prisms
A rectangular prism (also called a cuboid) is a three-dimensional shape with six rectangular faces, where all angles are right angles and opposite faces are equal. It has 6 faces, 12 edges, and 8 vertices. When all sides are equal, it becomes a cube.
Real-World Applications
- Packaging: Most boxes and containers are rectangular prisms
- Construction: Bricks, rooms, and buildings often use this shape
- Furniture: Tables, cabinets, and shelves frequently have this form
- Electronics: TVs, monitors, and smartphones often fit this shape
Special Cases
- Cube: When length = width = height
- Square Prism: When length = width ≠ height
- Rectangular Column: When height is much greater than length/width
- Rectangular Slab: When height is much smaller than length/width
Rectangular Prism Components
Base Area (B)
B = l × w
Prism Height (h)
Lateral Area (L)
L = 2h(l + w)
Surface Area (S)
S = 2(lw + lh + wh)
Space Diagonal (d)
d = √(l² + w² + h²)
Volume (V)
V = l × w × h
How to Use the Rectangular Prism Calculator
The Rectangular Prism Calculator helps compute various properties based on input values. Here's how to use it:
1. Select Calculation Method
Choose what measurements you know:
- Length, Width & Height - Enter all three dimensions
- Base Area & Height - When you know the base area
- Volume & Height - To find the base dimensions
- Lateral Area & Height - To find the base perimeter
2. Enter Your Values
Input positive numbers in the appropriate fields:
Example 1: Length = 6, Width = 4, Height = 5
Example 2: Base Area = 24, Height = 5
3. Get Results
The calculator will compute all properties:
- Length (l)
- Width (w)
- Height (h)
- Base Area (B)
- Volume (V)
- Lateral Area (L)
- Surface Area (S)
- Base Perimeter (P)
- Space Diagonal (d)
Practical Applications
- Calculate material needed for rectangular structures
- Determine paint required for rectangular prism-shaped objects
- Find storage capacity of rectangular containers
- Calculate shipping costs based on box dimensions
- Determine if an object will fit through a doorway
Frequently Asked Questions
A cube is a special case of rectangular prism where all sides are equal (length = width = height). All cubes are rectangular prisms, but not all rectangular prisms are cubes.
A rectangular prism has 6 rectangular faces - three pairs of identical opposite faces.
Use the formula: d = √(l² + w² + h²) where l is length, w is width, and h is height.