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Square Calculator

Calculate all properties of a square instantly. Enter side length, area, perimeter, or diagonal to find all other measurements with step-by-step formulas and interactive visualization.

Square Calculator
Try Quick Examples
s = 5 side A = 100 area P = 24 perimeter d = 10 diagonal

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About Square Calculator

Welcome to the Square Calculator, a comprehensive geometry tool that calculates all properties of a square from any single measurement. Whether you know the side length, area, perimeter, or diagonal, this calculator instantly computes all other measurements with step-by-step formulas and an interactive visualization.

What is a Square?

A square is a regular quadrilateral, meaning it has four equal sides and four equal angles (each 90°). It is both a special case of a rectangle (all angles equal) and a rhombus (all sides equal). Squares are fundamental shapes in geometry, architecture, design, and everyday life.

Key Properties of a Square

Square Formulas

Area of a Square

Area Formula
$$A = s^2$$

The area equals the side length squared. If you know the diagonal, you can also use: $A = \frac{d^2}{2}$

Perimeter of a Square

Perimeter Formula
$$P = 4s$$

The perimeter is four times the side length, representing the total distance around the square.

Diagonal of a Square

Diagonal Formula
$$d = s\sqrt{2}$$

This formula comes from the Pythagorean theorem. The diagonal forms the hypotenuse of a right triangle with two sides of the square.

Side Length from Other Measurements

GivenFormula for Side Length
Area (A)$s = \sqrt{A}$
Perimeter (P)$s = \frac{P}{4}$
Diagonal (d)$s = \frac{d}{\sqrt{2}} = \frac{d\sqrt{2}}{2}$

Inscribed and Circumscribed Circles

Every square has two special circles associated with it:

How to Use This Calculator

  1. Select input type: Choose whether you know the side length, area, perimeter, or diagonal.
  2. Enter your value: Input the known measurement. The calculator accepts various formats including decimals.
  3. Set precision: Choose decimal places for results (2-12).
  4. Calculate: Click "Calculate Square" to see all properties with step-by-step formulas.

Real-World Applications

Frequently Asked Questions

What is a square?

A square is a regular quadrilateral with four equal sides and four right angles (90°). It is a special case of both a rectangle (equal angles) and a rhombus (equal sides). All squares have two diagonals of equal length that bisect each other at right angles.

How do you calculate the area of a square?

The area of a square is calculated by squaring the side length: A = s². For example, if the side length is 5 units, the area is 5² = 25 square units. You can also calculate area from the diagonal using A = d²/2.

How do you find the diagonal of a square?

The diagonal of a square can be found using the formula d = s√2, where s is the side length. This comes from the Pythagorean theorem, since the diagonal forms a right triangle with two sides of the square.

What is the relationship between a square's perimeter and side length?

The perimeter of a square is four times the side length: P = 4s. Conversely, if you know the perimeter, you can find the side length by dividing by 4: s = P/4.

How do you find the side length from the diagonal?

To find the side length from the diagonal, divide the diagonal by √2: s = d/√2. This can also be written as s = d × √2/2 or approximately s = d × 0.7071.

What are the inscribed and circumscribed circles of a square?

The inscribed circle (incircle) is the largest circle that fits inside the square, touching all four sides. Its radius equals half the side length: r = s/2. The circumscribed circle (circumcircle) passes through all four vertices, with radius equal to half the diagonal: R = d/2 = s√2/2.

Related Geometry Tools

Additional Resources

Reference this content, page, or tool as:

"Square Calculator" at https://MiniWebtool.com/square-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Feb 01, 2026

You can also try our AI Math Solver GPT to solve your math problems through natural language question and answer.

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