Square Prism Calculator
Calculate volume, surface area, and other properties of a square prism (cube if sides are equal)
Calculation Results
Enter square prism measurements to calculate all properties.
Side Length (a): units
Base Area (B): square units
Height (h): units
Volume (V): cubic units
Lateral Area (L): square units
Surface Area (S): square units
Base Perimeter (P): units
Square Prism Diagram
Square Prism Formulas
Key Properties
- Side Length (a): Length of one side of the square base
- Base Area (B): Area of the square base
- Height (h): Distance between the two square bases
- Volume (V): Space contained within the prism
- Lateral Area (L): Area of the four rectangular faces
- Surface Area (S): Total area including both square bases
- Base Perimeter (P): Perimeter of the square base
Calculation Formulas
- Base Area (B): B = a²
- Volume (V): V = B × h = a² × h
- Lateral Area (L): L = P × h = 4a × h
- Surface Area (S): S = L + 2B = 4ah + 2a²
- Base Perimeter (P): P = 4a
Where: a = side length of square base, h = height of prism
Example Calculation
For a square prism with:
Side length (a) = 5 units, Prism height (h) = 8 units.Calculations:
- Base Area = 5² = 25 units²
- Base Perimeter = 4 × 5 = 20 units
- Volume = 25 × 8 = 200 units³
- Lateral Area = 20 × 8 = 160 units²
- Surface Area = 160 + (2 × 25) = 210 units²
About Square Prisms
A square prism is a three-dimensional shape with two identical square bases connected by four rectangular lateral faces. When all sides are equal (a = h), it becomes a cube. Square prisms have 6 faces, 12 edges, and 8 vertices.
Real-World Applications
- Architecture: Many buildings use square prism shapes for simplicity
- Packaging: Boxes and containers often use square prism shapes
- Storage: Shelving units and cabinets frequently have this shape
- Construction: Concrete blocks and bricks are often square prisms
Special Cases
- Cube: When side length equals height (a = h)
- Square Column: When height is much greater than side length
- Square Tile: When height is much smaller than side length
Square Prism Components
Base Area (B)
B = a²
Prism Height (h)
Lateral Area (L)
L = 4ah
Surface Area (S)
S = 2a² + 4ah
Base Perimeter (P)
P = 4a
Volume (V)
V = a²h
How to Use the Square Prism Calculator
The Square 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:
- Side Length & Height - Enter the square side and prism height
- Base Area & Height - When you know the base area
- Volume & Height - To find the side length
- Lateral Area & Height - To find the side length
2. Enter Your Values
Input positive numbers in the appropriate fields:
Example 1: Side Length = 5, Prism Height = 8
Example 2: Base Area = 25, Prism Height = 8
3. Get Results
The calculator will compute all properties:
- Side Length (a)
- Base Area (B)
- Prism Height (h)
- Volume (V)
- Lateral Area (L)
- Surface Area (S)
- Base Perimeter (P)
Practical Applications
- Calculate material needed for square column construction
- Determine paint required for square prism-shaped objects
- Find storage capacity of square containers
- Solve geometry problems involving square prisms
Frequently Asked Questions
A square prism becomes a cube when all sides are equal (side length = height). All cubes are square prisms, but not all square prisms are cubes.
A square prism has 6 faces - two square bases and four rectangular lateral faces.
Use the formula: a = √(V / h) where V is volume and h is height.