Enter the base side and height to get the total surface area, the lateral area (sides only), the base area and the volume.
Square Prism Surface Area Calculator
Total, lateral and base area of a right square prism from base side and height.
The Square Prism Surface Area Calculator calculates the total surface area of a prism with square ends by adding the two square bases to the four rectangular sides: A = 2a² + 4ah.
Formula
A = 2a² + 4ah
- Lateral area: L = 4ah
- Base area: B = a²
- Volume: V = a²h
Where:
- A = total surface area
- a = side of the square base
- h = height (length) of the prism
How the Calculation Works
Step 1: Find the area of one square base (a²) and double it for the top and bottom.
Step 2: Find the area of one side rectangle (a × h) and multiply by 4.
Step 3: Add the bases and sides together.
Variables Explained
| Variable | Meaning | Unit |
|---|---|---|
| a | Base side | cm, m, in, ft |
| h | Height | cm, m, in, ft |
| A | Total surface area | cm², m², in², ft² |
| V | Volume | cm³, m³, in³, ft³ |
Example Calculation
Given: base side = 5 cm, height = 10 cm
Formula: A = 2a² + 4ah
Calculation: A = 2 × 25 + 4 × 5 × 10 = 50 + 200
Result: A = 250 cm² (lateral area 200 cm², volume 250 cm³)
Example in feet
Given: a square column 1.5 ft wide and 9 ft tall, painted on four sides only
Result: lateral area = 4 × 1.5 × 9 = 54 ft²
Common Area Conversion Table
| Unit | Equivalent |
|---|---|
| 1 m² | 10,000 cm² |
| 1 ft² | 144 in² |
| 1 m² | 10.7639 ft² |
Shape Properties
A square prism (also called a square cuboid) has 6 faces: 2 squares and 4 identical rectangles, with 12 edges and 8 vertices. When the height equals the base side, it is a cube and A = 6a².
Dimensions Explained
The base side is the length of one edge of the square end. The height is the distance between the two square ends, whichever way the prism is standing.
Frequently Asked Questions
What is the formula for the surface area of a square prism?
A = 2a² + 4ah, where a is the base side and h is the height.
What is the lateral surface area of a square prism?
The four side faces only: L = 4ah.
Is a square prism the same as a cube?
Only when the height equals the base side. Otherwise it is a taller or shorter box with square ends.
How do you find the height of a square prism from its surface area?
Rearrange the formula: h = (A − 2a²) ÷ 4a.
What is the volume of a square prism?
V = a² × h. A 5 × 5 × 10 cm prism holds 250 cm³.