Square Calculator

MiniWebtool’s Square Calculator derives a square’s measurements from one known value: side, area, perimeter, or diagonal. Formulas and a diagram show how the remaining quantities are connected.

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Help me understand MiniWebtool's Square Calculator: https://miniwebtool.com/square-calculator/. What can I use it for, what inputs or settings do I need, and how do I use it and understand the output? Walk me through one simple example. Use this page as your source and answer in English.

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One side gives everything: P = 4s, A = s², d = s√2

Enter the side, area, perimeter or diagonal below to get every other measurement, with the steps.

Try Quick Examples

s = 5 side A = 100 area P = 24 perimeter d = 10 diagonal

Input Type

Value

Decimal Precision

Embed Square Calculator Widget

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.

At a Glance

Square Calculator finds every measurement of a square from one known value: side, area, perimeter or diagonal. It shows the formulas used and a labeled diagram.

Square Calculator: features at a glance
Feature	What you get	Good for
Four starting points	Enter the side length, area, perimeter or diagonal and the other three are worked out.	Geometry problems that give any one measurement
Formulas	Uses A = s², P = 4s and d = s√2. Side from diagonal is s = d/√2.	Checking which formula applies
Circle radii	Also gives the inscribed circle radius r = s/2 and the circumscribed circle radius R = d/2.	Fitting a circle inside or around a square
Precision	Choose 2 to 12 decimal places.	Results to a set number of decimals
Step-by-step	Shows each formula with your numbers filled in.	Showing working in homework
Diagram	An interactive SVG diagram of the square.	Seeing how the side, diagonal and circles relate

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

Four equal sides of length s
Four right angles (90° each)
Two equal diagonals that bisect each other at right angles
Four lines of symmetry
Rotational symmetry of order 4 (90°, 180°, 270°, 360°)

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

Square Calculator: Side Length from Other Measurements
Given	Formula 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:

Inscribed circle (incircle): The largest circle that fits inside the square, touching all four sides. Radius: $r = \frac{s}{2}$
Circumscribed circle (circumcircle): The circle passing through all four vertices. Radius: $R = \frac{d}{2} = \frac{s\sqrt{2}}{2}$

How to Use This Calculator

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

Real-World Applications

Architecture: Designing square rooms, windows, tiles, and floor plans
Construction: Calculating material quantities for square surfaces
Landscaping: Planning square gardens, patios, and fencing
Art & Design: Creating balanced, symmetrical compositions
Engineering: Calculating cross-sectional areas of square beams

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

Rectangle Calculator - Calculate rectangle area, perimeter, and diagonal
Triangle Calculator - Calculate triangle properties
Circle Calculator - Calculate circle area, circumference, and diameter
Pythagorean Theorem Calculator - Calculate sides of right triangles

Additional Resources

Square - Wikipedia

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

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