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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 90Ā°). 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 (90Ā°). 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 = sĀ². For example, if the side length is 5 units, the area is 5Ā² = 25 square units. You can also calculate area from the diagonal using A = dĀ²/2.

How do you find the diagonal of a square?

The diagonal of a square can be found using the formula d = sāˆš2, 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 āˆš2: s = d/āˆš2. This can also be written as s = d Ɨ āˆš2/2 or approximately s = d Ɨ 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 = sāˆš2/2.

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

Developer API available: Run this tool from your app, automation, or agent with one JSON HTTP request. View API docs

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

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