Quick answer
The area of a square is A = s². A side of 5 gives an area of 25.
Enter the side length. The calculator returns the area.
Related tools: Area Calculator: Area of common two-dimensional shapes. Area of a Circle Calculator: Area of a circle from its radius, diameter or circumference. Area of a Trapezoid Calculator: Area of a trapezoid from its parallel sides and height.
How to use the Square Area Calculator
- Enter side (above 0).
- Press Calculate to see the result, and use Reset to start again.
| Input | What to enter | Allowed values |
|---|---|---|
| Side | A number | > 0 |
Formula and method
Formula
A = s²
IEEE-754 double precision; shown to at most 6 decimal places.
Direct formula.
Worked examples
These examples are verified: each one is an automated test case that the live calculator must reproduce exactly.
Example 1
Inputs: Side = 5.
| Result | Value |
|---|---|
| Square Area | 25 |
Example 2
Inputs: Side = 1.5.
| Result | Value |
|---|---|
| Square Area | 2.25 |
The first line is the headline result (square Area). IEEE-754 double precision; shown to at most 6 decimal places.
Scaling
Doubling the side quadruples the area: s = 10 gives 100. Perimeter is 4s, so a side of 5 has perimeter 20, and diagonal 5√2 = 7.07.
From area back to side
Take the square root: an area of 49 means a side of 7. For flooring, a 12 ft square room has 144 ft² and needs about 158 ft² with 10% waste.
Units and scaling
Area is measured in square units: a 5 m side gives 25 m². Doubling the side quadruples the area (a 10 m side gives 100 m²), because both length and width double.
To cover a floor, convert units before comparing. A room 12 ft on a side is 144 ft², which is 144 ÷ 9 = 16 square yards.
How the result changes with side
Holding every other input at the first worked example, this table changes only side. It shows how sensitive the answer is to that one value; each row was produced by running this calculator.
| Side | Square Area |
|---|---|
| 2.5 | 6.25 |
| 5 | 25 |
| 10 | 100 |
| 20 | 400 |
What happens with invalid input
These messages are produced by the calculator itself, so you know what to fix.
- Side: entering "0" shows "Side must be greater than 0." beside that field and no result.
Choosing between the Square Area Calculator and similar calculators
Each row shows what a related calculator on this site asks for and what it returns, so you can pick the one that matches your question.
| Calculator | You enter | It returns |
|---|---|---|
| [Area Calculator](/math/area-calculator/) | shape and a | Area |
| [Area of a Circle Calculator](/math/area-of-a-circle/) | i know the and value | Area |
| [Area of a Trapezoid Calculator](/math/area-of-a-trapezoid/) | base a, base b and height | Area |
| [Surface Area Calculator](/math/surface-area-calculator/) | shape and a | Surface area |
| [Triangle Area Calculator](/math/triangle-area-calculator/) | base and height | Area |
Background: geometry measurements
Geometry results carry units that depend on the quantity: a perimeter or length is in linear units such as cm, an area or surface area is in square units (cm²) and a volume is in cubic units (cm³). Use one length unit for every input, because the calculator multiplies the numbers as given.
Flat (2D) shapes have an area and a perimeter; solids (3D) have a surface area and a volume. Two familiar checks: a circle of radius r has area πr² and circumference 2πr, and a sphere has volume (4/3)πr³ and surface area 4πr².
Assumptions and limitations
- Positive value
If a required value is empty, not a number, or outside its allowed range, the form marks that field with a message and shows no result instead of a misleading number. The automated checks deliberately try invalid entries for side to confirm this.
Frequently asked questions
What is the area of a square with side 3.5?
3.5² = 12.25 square units.
How is a square's area related to its diagonal?
A = d² ÷ 2, so a diagonal of 10 gives 50.
What units does the area have?
Squared units of the side, such as m² or ft².
Why does doubling the side quadruple the area?
Area is side × side, so doubling the side multiplies the area by 2 × 2 = 4.
How do I convert square feet to square yards?
Divide by 9, because one square yard is 3 ft × 3 ft = 9 ft².
What does the Square Area Calculator calculate?
Area of a square. It returns Square Area.
What formula does the Square Area Calculator use?
A = s². Direct formula.
What do I need to enter in the square Area Calculator?
You enter Side.
How is the result rounded or limited?
IEEE-754 double precision; shown to at most 6 decimal places. Positive value.
What is an example of a square Area result?
With side 5, the square Area is 25.
Related calculators
- Area Calculator — Area of common two-dimensional shapes.
- Area of a Circle Calculator — Area of a circle from its radius, diameter or circumference.
- Area of a Trapezoid Calculator — Area of a trapezoid from its parallel sides and height.
- Surface Area Calculator — Surface area of a sphere, cube, cylinder, cone or box.
- Triangle Area Calculator — Area of a triangle from base and height.
- Sector Area Calculator — Area and arc length of a circular sector.
Sources
- OpenStax, Prealgebra 2e (Rice University): perimeter, area, volume, circumference and the Pythagorean theorem
Content last reviewed 2026-11-04. Formulas and worked examples are checked by automated tests against independently computed values.