Area of a Square Calculator | Side, Diagonal, Perimeter

Q: What is the formula for the area of a square?

The standard formula is A = a^2 , where a is the side length. You can also use A = d^2 / 2 from the diagonal or A = P^2 / 16 from the perimeter.

Q: How do I calculate square area from the diagonal?

Use A = d^2 / 2 . For example, if the diagonal is 10 cm , the area is 100 / 2 = 50 cm^2 .

Q: How do I calculate square area from the perimeter?

Use A = P^2 / 16 . For example, if the perimeter is 40 cm , the area is 40^2 / 16 = 100 cm^2 .

Q: Can I find the side, diagonal, or perimeter from the area?

Yes. From the area, the side is a = sqrt(A) , the diagonal is d = sqrt(2A) , and the perimeter is P = 4sqrt(A) . The calculator handles those reverse steps automatically.

Area of a square calculator: find square area from side, diagonal, or perimeter, and reverse the formulas to get side length, diagonal, or perimeter from area.

Use this area of a square calculator to find square area from the side length, diagonal, or perimeter. It also works in reverse, so you can start with the area and calculate a missing square dimension.

The main formulas are A = a^2, A = d^2 / 2, and A = P^2 / 16. That makes the calculator useful for geometry homework, flooring and tile estimates, land measurements, and any square layout where one dimension is easier to measure than another.

Input

Area of a square formula

$$A= a^2$$

Side Diagonal Perimeter

Side (a)

Area (A)

2-dimensional shapes

3-dimensional shapes

Fig. 1 Square diagram

Area of a Square Calculator FAQs

What is the formula for the area of a square?
The standard formula is A = a^2, where a is the side length. You can also use A = d^2 / 2 from the diagonal or A = P^2 / 16 from the perimeter.

How do I calculate square area from the side length?
Multiply the side length by itself. For example, if the side is 10 cm, the area is 10 x 10 = 100 cm^2.

How do I calculate square area from the diagonal?
Use A = d^2 / 2. For example, if the diagonal is 10 cm, the area is 100 / 2 = 50 cm^2.

How do I calculate square area from the perimeter?
Use A = P^2 / 16. For example, if the perimeter is 40 cm, the area is 40^2 / 16 = 100 cm^2.

Can I find the side, diagonal, or perimeter from the area?
Yes. From the area, the side is a = sqrt(A), the diagonal is d = sqrt(2A), and the perimeter is P = 4sqrt(A). The calculator handles those reverse steps automatically.

What is this calculator useful for?
It is useful for geometry, flooring, tiling, square plots, layout planning, and quick measurement checks when you know the side, diagonal, perimeter, or area of a square.

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