Area of a square calculator
If you’re unsure how to calculate the area of a square, you’ve come to the perfect place! This srea of a square calculator is a straightforward and reliable tool designed to make the process easy for you. Whether you need to quickly find the area using the length of a square's side or simply refresh your knowledge, this tool is here to assist.
Area of a square
How does the calculator work?
- Inputting the side length:
- The user enters the length of the square's side in the text field.
- The user can choose the unit of measurement (meters, centimeters, millimeters, etc.).
- Calculating the area:
- The calculator automatically converts the side length to meters.
- It calculates the area using the formula: Area = side2
- Converting the result:
- The calculated area in square meters is converted to the selected output unit (e.g., square meters, square centimeters, square feet).
- Displaying the result:
- The result is continuously updated and displayed in the text field in real-time as the user changes the input or unit selections
Formulas for the area of a square
The area of a square is the total two-dimensional space enclosed within its four equal sides. Since a square has all sides of equal length and forms right angles at every corner, its area can be calculated using various formulas depending on the available data. Below, we outline all possibilities for calculating the area of a square, provide definitions, and explain each formula in detail with examples.
1. Using the side length
Definition: This formula calculates the area by squaring the length of one side (s), as all sides of a square are equal in length.
Explanation: Squaring the side length accounts for the two-dimensional nature of the area, as the square’s area is derived by multiplying one side by itself.
Example:
If the side length is s = 5 units, the area is:
A = 52 = 25 square units.
2. Using the diagonal
Definition: This formula uses the length of the diagonal (d), which connects two opposite corners of the square.
Explanation: In a square, the diagonal divides the shape into two congruent right triangles. Using the Pythagorean theorem, the relationship between the side and diagonal is derived, leading to the formula.
Example:
If the diagonal is d = 8 units, the area is:
A = 82 / 2 = 64 / 2 = 32 square units.
3. Using the perimeter
Definition: This formula calculates the area based on the perimeter (P), which is the total length of all four sides.
Explanation: Since the perimeter of a square is P = 4s, the formula is derived by isolating the side length (s = P / 4) and substituting it into the standard area formula (A = s2).
Example:
If the perimeter is P = 20 units, the area is:
A = 202 / 16 = 400 / 16 = 25 square units.
