There are input fields for side length \((s)\), Area \((A)\), Perimeter \((P)\), and diagonal \((d)\). Enter any one input and click on Calculate button.
The calculator uses the formula, substitues given values, and calcuates the missing value.
The missing value is calcuated and displayed in the input field. Also, the caculation is displayed under the input section.
Square Calculator
A square is a special type of rectangle where all four sides are of equal length and all angles are right angles (90 degrees). This symmetry makes the square a fundamental shape in geometry, with numerous applications in both theoretical and practical contexts. Understanding the properties of a square—such as its side length, area, perimeter, and diagonal—is essential in fields ranging from architecture to mathematics, design, and beyond.
Because a square has equal sides, knowing just one property allows you to calculate all the others. For example, if you know the side length, you can easily find the area, perimeter, and diagonal. Similarly, knowing the area, perimeter, or diagonal enables you to determine the side length and other properties. This inherent simplicity makes squares particularly useful in geometric calculations.
Let's explore the fundamental formulas used to calculate the various properties of a square:
Area of a Square
The area of a square is the space enclosed within its boundaries. Since all sides are equal, the area is simply the square of the side length. The formula is:
\(A = s^2\)
Where:
s is the side length of the square.
Perimeter of a Square
The perimeter of a square is the total distance around the square. Since all four sides are equal, the perimeter is four times the side length. The formula is:
\(P = 4s\)
Where:
s is the side length of the square.
Diagonal of a Square
The diagonal of a square is the straight line connecting opposite corners. It can be found using the Pythagorean theorem, as the diagonal forms the hypotenuse of a right triangle with the side length as both of the other two sides. The formula is:
\(d = s\sqrt{2}\)
Where:
s is the side length of the square.
In many cases, you might only know one of these properties and need to calculate the others. This is where our Square Calculator is extremely helpful. By inputting any one of the side length, area, perimeter, or diagonal, the calculator can quickly determine the remaining properties.
For example, if you know the area, the calculator can find the side length, perimeter, and diagonal. Similarly, if you know the diagonal, it can determine the side length, area, and perimeter. This versatility makes the Square Calculator an indispensable tool for anyone dealing with squares in geometry.
Below are the formulas used in this calculator for various combinations of inputs:
Formulas
1. Given Side Length (s):
Area: \(A = s^2\)
Perimeter: \(P = 4s\)
Diagonal: \(d = s\sqrt{2}\)
2. Given Area (A):
Side Length: \(s = \sqrt{A}\)
Perimeter: \(P = 4s\)
Diagonal: \(d = s\sqrt{2}\)
3. Given Perimeter (P):
Side Length: \(s = \frac{P}{4}\)
Area: \(A = s^2\)
Diagonal: \(d = s\sqrt{2}\)
4. Given Diagonal (d):
Side Length: \(s = \frac{d}{\sqrt{2}}\)
Area: \(A = s^2\)
Perimeter: \(P = 4s\)
Simply enter any one known value into the Square Calculator, and it will automatically compute the remaining properties, providing you with a comprehensive understanding of the square in question. This tool simplifies complex calculations and is perfect for anyone needing quick and accurate results.
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"title": "Square Calculator",
"description": "Use our Square Calculator to easily calculate side length, area, permimeter, and length of diagonal easily, given only one of these parameters.",
"category": "Geometry",
"shape": "Square",
"template": "mathematics_multiple_outputs",
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"parameters": [
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"outputs": [
{
"label": "A",
"formula": " s * s ",
"formula_mathjax": "\\( s ^2 \\)"
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"formula": " 4 * s ",
"formula_mathjax": "\\( 4 * s \\)"
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{
"label": "d",
"formula": " Math.sqrt( 2 ) * s ",
"formula_mathjax": "\\( s \\sqrt{ 2 } \\)"
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"label": "s",
"formula": " Math.sqrt( A ) ",
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"content": "<h2>Square Calculator</h2>\n<p>A square is a special type of rectangle where all four sides are of equal length and all angles are right angles (90 degrees). This symmetry makes the square a fundamental shape in geometry, with numerous applications in both theoretical and practical contexts. Understanding the properties of a square—such as its side length, area, perimeter, and diagonal—is essential in fields ranging from architecture to mathematics, design, and beyond.</p>\n\n<p>Because a square has equal sides, knowing just one property allows you to calculate all the others. For example, if you know the side length, you can easily find the area, perimeter, and diagonal. Similarly, knowing the area, perimeter, or diagonal enables you to determine the side length and other properties. This inherent simplicity makes squares particularly useful in geometric calculations.</p>\n\n<p>Let's explore the fundamental formulas used to calculate the various properties of a square:</p>\n\n<h3>Area of a Square</h3>\n<p>The area of a square is the space enclosed within its boundaries. Since all sides are equal, the area is simply the square of the side length. The formula is:</p>\n<p class=\"tabspace\">\\(A = s^2\\)</p>\n<p>Where:</p>\n<ul><li><b>s</b> is the side length of the square.</li></ul>\n\n<h3>Perimeter of a Square</h3>\n<p>The perimeter of a square is the total distance around the square. Since all four sides are equal, the perimeter is four times the side length. The formula is:</p>\n<p class=\"tabspace\">\\(P = 4s\\)</p>\n<p>Where:</p>\n<ul><li><b>s</b> is the side length of the square.</li></ul>\n\n<h3>Diagonal of a Square</h3>\n<p>The diagonal of a square is the straight line connecting opposite corners. It can be found using the Pythagorean theorem, as the diagonal forms the hypotenuse of a right triangle with the side length as both of the other two sides. The formula is:</p>\n<p class=\"tabspace\">\\(d = s\\sqrt{2}\\)</p>\n<p>Where:</p>\n<ul><li><b>s</b> is the side length of the square.</li></ul>\n\n<p>In many cases, you might only know one of these properties and need to calculate the others. This is where our Square Calculator is extremely helpful. By inputting any one of the side length, area, perimeter, or diagonal, the calculator can quickly determine the remaining properties.</p>\n\n<p>For example, if you know the area, the calculator can find the side length, perimeter, and diagonal. Similarly, if you know the diagonal, it can determine the side length, area, and perimeter. This versatility makes the Square Calculator an indispensable tool for anyone dealing with squares in geometry.</p>\n\n<p>Below are the formulas used in this calculator for various combinations of inputs:</p>\n\n<h3>Formulas</h3>\n<p><b>1. Given Side Length (s):</b></p>\n<ul>\n<li><b>Area:</b> \\(A = s^2\\)</li>\n<li><b>Perimeter:</b> \\(P = 4s\\)</li>\n<li><b>Diagonal:</b> \\(d = s\\sqrt{2}\\)</li>\n</ul>\n\n<p><b>2. Given Area (A):</b></p>\n<ul>\n<li><b>Side Length:</b> \\(s = \\sqrt{A}\\)</li>\n<li><b>Perimeter:</b> \\(P = 4s\\)</li>\n<li><b>Diagonal:</b> \\(d = s\\sqrt{2}\\)</li>\n</ul>\n\n<p><b>3. Given Perimeter (P):</b></p>\n<ul>\n<li><b>Side Length:</b> \\(s = \\frac{P}{4}\\)</li>\n<li><b>Area:</b> \\(A = s^2\\)</li>\n<li><b>Diagonal:</b> \\(d = s\\sqrt{2}\\)</li>\n</ul>\n\n<p><b>4. Given Diagonal (d):</b></p>\n<ul>\n<li><b>Side Length:</b> \\(s = \\frac{d}{\\sqrt{2}}\\)</li>\n<li><b>Area:</b> \\(A = s^2\\)</li>\n<li><b>Perimeter:</b> \\(P = 4s\\)</li>\n</ul>\n\n<p>Simply enter any one known value into the Square Calculator, and it will automatically compute the remaining properties, providing you with a comprehensive understanding of the square in question. This tool simplifies complex calculations and is perfect for anyone needing quick and accurate results.</p>",
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