Square Calculator
Calculate area, perimeter, diagonal, and circle radii from any known value
Square Calculator
How to Use the Square Calculator
- Select Input Type: Choose whether you want to calculate from side length, area, perimeter, or diagonal
- Enter Value: Input the known value in the text field
- View Results: All square properties are calculated automatically and displayed instantly
- Copy Values: Click the copy button next to any result to copy it to your clipboard
Understanding Square Properties
A square is a regular quadrilateral with four equal sides and four right angles (90°). It is both a special type of rectangle (with equal sides) and a special type of rhombus (with right angles).
Key Properties:
- All sides are equal: If one side is s, all sides are s
- All angles are 90°: Each internal angle is a right angle
- Diagonals are equal: Both diagonals have the same length (d = s√2)
- Diagonals bisect each other at 90°: They cross at right angles at the center
- Diagonals bisect the angles: Each diagonal creates two 45° angles
- Four-fold symmetry: A square has 4 lines of symmetry and 90° rotational symmetry
Square Formulas
Basic Formulas
Circle Relationships
Practical Applications
Construction & Architecture
- Floor tile calculations
- Room area measurements
- Window and door sizing
- Foundation planning
Arts & Crafts
- Canvas and frame sizing
- Quilting and fabric cutting
- Paper crafts and origami
- Photography composition
Gardening & Landscaping
- Garden bed dimensions
- Patio and deck planning
- Planting grid calculations
- Mulch and soil coverage
Technology & Design
- Icon and avatar sizing
- Social media image dimensions
- QR code sizing
- UI element proportions
Frequently Asked Questions
How do I find the area of a square?
The area of a square is calculated by squaring the side length: A = s². If you know the diagonal, use A = d²/2. If you know the perimeter, first find the side (s = P/4), then calculate the area.
What is the formula for the diagonal of a square?
The diagonal of a square is calculated as d = s√2, where s is the side length. This comes from the Pythagorean theorem applied to the right triangle formed by two sides and the diagonal.
How do I find the side length from the area?
To find the side length from the area, take the square root of the area: s = √A. For example, if the area is 25 square units, the side length is √25 = 5 units.
What is the inscribed circle radius of a square?
The inscribed circle (incircle) of a square has a radius equal to half the side length: r = s/2. This is the largest circle that fits completely inside the square, touching all four sides.
What is the circumscribed circle radius of a square?
The circumscribed circle (circumcircle) of a square has a radius equal to half the diagonal: R = d/2 = s√2/2. This is the smallest circle that completely contains the square, passing through all four corners.
What is the relationship between a square and its circles?
The ratio of the circumscribed circle radius to the inscribed circle radius is always √2 (approximately 1.414). The inscribed circle has area πs²/4, while the circumscribed circle has area πs²/2.