Enter any two inputs and click on Calculate button
How to use this Rectangle Calculator 🤔
There are input fields for length \((l)\), width \((w)\), Area \((A)\), Perimeter \((P)\), and diagonal \((d)\). Enter any two inputs 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.
Rectangle Calculator
A rectangle is a quadrilateral with four right angles, which means each angle measures 90 degrees.
In geometry, rectangles are one of the most fundamental shapes, and they have a wide range of applications in both academic problems and real-world scenarios.
The properties of a rectangle are defined by its length, width, area, perimeter, and diagonal. Understanding these properties is crucial for solving various problems related to rectangles, whether you're designing a room, planning a garden, or working on a mathematical project.
One of the defining characteristics of a rectangle is that opposite sides are equal in length. This symmetry allows for straightforward calculations involving the rectangle's properties. For instance, if you know the length and width of a rectangle, you can easily calculate its area, perimeter, and diagonal. Similarly, knowing any two of these properties allows you to determine the remaining ones.
Let's look into the formulas used to calculate the various properties of a rectangle:
Area of a Rectangle
The area of a rectangle is the amount of space enclosed within its boundaries. It is calculated by multiplying the length by the width.
The formula is expressed as:
\(A = l \times w\)
Where:
l is the length of the rectangle.
w is the width of the rectangle.
Perimeter of a Rectangle
The perimeter of a rectangle is the total distance around the rectangle. It is calculated by adding twice the length and twice the width. The formula is:
\(P = 2(l + w)\)
Where:
l is the length of the rectangle.
w is the width of the rectangle.
Diagonal of a Rectangle
The diagonal of a rectangle 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 length and width as the other two sides. The formula is:
\(d = \sqrt{l^2 + w^2}\)
Where:
l is the length of the rectangle.
w is the width of the rectangle.
In many situations, you might only know two of these properties and need to calculate the others. This is where our Rectangle Calculator becomes incredibly useful. By inputting any two of the length, width, area, perimeter, or diagonal, the calculator can quickly determine the remaining three properties.
For example, if you know the length and the area, the calculator can find the width, perimeter, and diagonal. Similarly, if you know the perimeter and the diagonal, it can find the length, width, and area. This versatility makes the Rectangle Calculator an invaluable tool for anyone dealing with rectangular shapes, whether in an academic setting or in practical applications.
Below are the formulas used in this calculator for various combinations of inputs:
Simply enter any two known values into the Rectangle Calculator, and it will automatically compute the remaining properties, providing you with a comprehensive understanding of the rectangle in question.
{
"topic": "rectangle",
"input_types": [
"float",
"float",
"float",
"float",
"float"
],
"input_labels": [
"l",
"w",
"A",
"P",
"d"
],
"input_descriptions": [
"length",
"width",
"Area",
"Perimeter",
"diagonal"
],
"input_units": [
"units",
"units",
"sq. units",
"units",
"units"
],
"input_values": [
"",
"",
"",
""
],
"input_pre_msg": "Enter any two inputs and click on Calculate button",
"type": "Calculate",
"title": "Rectangle Calculator",
"description": "Use our Rectangle Calculator to easily calculate length, width, area, permimeter, and lenght of diagonal easily, given only two of these parameters.",
"category": "Geometry",
"shape": "Rectangle",
"template": "mathematics_multiple_outputs",
"formulas": [
{
"parameters": [
"l",
"w"
],
"outputs": [
{
"label": "A",
"formula": " l * w ",
"formula_mathjax": "\\( l \\times w \\)"
},
{
"label": "P",
"formula": " 2 * ( l + w ) ",
"formula_mathjax": "\\( 2 * ( l + w ) \\)"
},
{
"label": "d",
"formula": " Math.sqrt( l * l + w * w ) ",
"formula_mathjax": "\\( \\sqrt{ l ^2 + w ^2 } \\)"
}
]
},
{
"parameters": [
"l",
"A"
],
"outputs": [
{
"label": "w",
"formula": " A / l ",
"formula_mathjax": "\\( A / l \\)"
},
{
"label": "P",
"formula": " 2 * ( l + w ) ",
"formula_mathjax": "\\( 2 * ( l + w ) \\)"
},
{
"label": "d",
"formula": " Math.sqrt( l * l + w * w ) ",
"formula_mathjax": "\\( \\sqrt{ l ^2 + w ^2 } \\)"
}
]
},
{
"parameters": [
"w",
"A"
],
"outputs": [
{
"label": "l",
"formula": " A / w ",
"formula_mathjax": "\\( A / w \\)"
},
{
"label": "P",
"formula": " 2 * ( l + w ) ",
"formula_mathjax": "\\( 2 * ( l + w ) \\)"
},
{
"label": "d",
"formula": " Math.sqrt( l * l + w * w ) ",
"formula_mathjax": "\\( \\sqrt{ l ^2 + w ^2 } \\)"
}
]
},
{
"parameters": [
"l",
"P"
],
"outputs": [
{
"label": "w",
"formula": " P / 2 - l ",
"formula_mathjax": "\\( \\frac{P}{2} - l \\)"
},
{
"label": "A",
"formula": " l * w ",
"formula_mathjax": "\\( l \\times w \\)"
},
{
"label": "d",
"formula": " Math.sqrt( l * l + w * w ) ",
"formula_mathjax": "\\( \\sqrt{ l ^2 + w ^2 } \\)"
}
]
},
{
"parameters": [
"w",
"P"
],
"outputs": [
{
"label": "l",
"formula": " P / 2 - w ",
"formula_mathjax": "\\( \\frac{P}{2} - w \\)"
},
{
"label": "A",
"formula": " l * w ",
"formula_mathjax": "\\( l \\times w \\)"
},
{
"label": "d",
"formula": " Math.sqrt( l * l + w * w ) ",
"formula_mathjax": "\\( \\sqrt{ l ^2 + w ^2 } \\)"
}
]
},
{
"parameters": [
"l",
"d"
],
"outputs": [
{
"label": "w",
"formula": " Math.sqrt( d * d - l * l ) ",
"formula_mathjax": "\\( \\sqrt{ d^2 - l^2 } \\)"
},
{
"label": "A",
"formula": " l * w ",
"formula_mathjax": "\\( l \\times w \\)"
},
{
"label": "P",
"formula": " 2 * ( l + w ) ",
"formula_mathjax": "\\( 2 * ( l + w ) \\)"
}
]
},
{
"parameters": [
"w",
"d"
],
"outputs": [
{
"label": "l",
"formula": " Math.sqrt( d * d - w * w ) ",
"formula_mathjax": "\\( \\sqrt{ d^2 - w^2 } \\)"
},
{
"label": "A",
"formula": " l * w ",
"formula_mathjax": "\\( l \\times w \\)"
},
{
"label": "P",
"formula": " 2 * ( l + w ) ",
"formula_mathjax": "\\( 2 * ( l + w ) \\)"
}
]
},
{
"parameters": [
"A",
"P"
],
"outputs": [
{
"label": "l",
"formula": " ( P + Math.sqrt( P * P - 16 * A ) ) / 4 ",
"formula_mathjax": "\\( \\frac{P + \\sqrt{P^2 - 16A}}{4} \\)"
},
{
"label": "w",
"formula": " A / l ",
"formula_mathjax": "\\( \\frac{ A }{ l } \\)"
},
{
"label": "d",
"formula": " Math.sqrt( ( ( P + Math.sqrt( P * P - 16 * A ) ) / 4 ) ** 2 + ( ( P - Math.sqrt( P * P - 16 * A ) ) / 4 ) ** 2 ) ",
"formula_mathjax": "\\( \\sqrt{ l ^2 + w ^2 } \\)"
}
]
},
{
"parameters": [
"A",
"d"
],
"outputs": [
{
"label": "l",
"formula": " Math.sqrt( ( d * d + Math.sqrt( d * d * d * d - 4 * A * A ) ) / 2 ) ",
"formula_mathjax": "\\( \\sqrt{\\frac{d^2 + \\sqrt{d^4 - 4A^2}}{2}} \\)"
},
{
"label": "w",
"formula": " A / l ",
"formula_mathjax": "\\( \\frac{ A }{ l } \\)"
},
{
"label": "P",
"formula": " 2 * ( l + w ) ",
"formula_mathjax": "\\( 2 * ( l + w ) \\)"
}
]
},
{
"parameters": [
"P",
"d"
],
"outputs": [
{
"label": "l",
"formula": " ( P + Math.sqrt( 8 * d * d - P * P ) ) / 4 ",
"formula_mathjax": "\\( \\frac{ P + \\sqrt{ 8 d ^2 - P ^2}}{4} \\)"
},
{
"label": "w",
"formula": " P / 2 - l ",
"formula_mathjax": "\\( \\frac{ P }{ 2 } - l \\)"
},
{
"label": "A",
"formula": " l * w ",
"formula_mathjax": "\\( l \\times w \\)"
}
]
}
],
"content": "<h2>Rectangle Calculator</h2>\n<p>A rectangle is a quadrilateral with four right angles, which means each angle measures 90 degrees.</p> <img src=\"/images/mathematics/rectangle.png\" alt=\"Rectangle with 90 degree angles\" width=\"400\" height=\"250\" loading=\"lazy\"> <p>In geometry, rectangles are one of the most fundamental shapes, and they have a wide range of applications in both academic problems and real-world scenarios.</p><p>The properties of a rectangle are defined by its length, width, area, perimeter, and diagonal. Understanding these properties is crucial for solving various problems related to rectangles, whether you're designing a room, planning a garden, or working on a mathematical project.</p>\n\n<p>One of the defining characteristics of a rectangle is that opposite sides are equal in length. This symmetry allows for straightforward calculations involving the rectangle's properties. For instance, if you know the length and width of a rectangle, you can easily calculate its area, perimeter, and diagonal. Similarly, knowing any two of these properties allows you to determine the remaining ones.</p>\n\n<p>Let's look into the formulas used to calculate the various properties of a rectangle:</p>\n\n<h3>Area of a Rectangle</h3>\n<p>The area of a rectangle is the amount of space enclosed within its boundaries. It is calculated by multiplying the length by the width.</p> <img src=\"/images/calculators/rectangle-area.png\" alt=\"Rectangle with Length and Breadth\" width=\"420\" height=\"255\" loading=\"lazy\"> <p>The formula is expressed as:</p>\n<p class=\"tabspace\">\\(A = l \\times w\\)</p>\n<p>Where:</p>\n<ul><li><b>l</b> is the length of the rectangle.</li>\n<li><b>w</b> is the width of the rectangle.</li></ul>\n\n<h3>Perimeter of a Rectangle</h3>\n<p>The perimeter of a rectangle is the total distance around the rectangle. It is calculated by adding twice the length and twice the width. The formula is:</p>\n<p class=\"tabspace\">\\(P = 2(l + w)\\)</p>\n<p>Where:</p>\n<ul><li><b>l</b> is the length of the rectangle.</li>\n<li><b>w</b> is the width of the rectangle.</li></ul>\n\n<h3>Diagonal of a Rectangle</h3>\n<p>The diagonal of a rectangle is the straight line connecting opposite corners.</p> <img src=\"/images/calculators/rectangle-diagonal-length.png\" alt=\"Rectangle with Length and Breadth\" width=\"405\" height=\"255\" loading=\"lazy\"> <p>It can be found using the Pythagorean theorem, as the diagonal forms the hypotenuse of a right triangle with the length and width as the other two sides. The formula is:</p>\n<p class=\"tabspace\">\\(d = \\sqrt{l^2 + w^2}\\)</p>\n<p>Where:</p>\n<ul><li><b>l</b> is the length of the rectangle.</li>\n<li><b>w</b> is the width of the rectangle.</li></ul>\n\n<p>In many situations, you might only know two of these properties and need to calculate the others. This is where our Rectangle Calculator becomes incredibly useful. By inputting any two of the length, width, area, perimeter, or diagonal, the calculator can quickly determine the remaining three properties.</p>\n\n<p>For example, if you know the length and the area, the calculator can find the width, perimeter, and diagonal. Similarly, if you know the perimeter and the diagonal, it can find the length, width, and area. This versatility makes the Rectangle Calculator an invaluable tool for anyone dealing with rectangular shapes, whether in an academic setting or in practical applications.</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 Length (l) and Width (w):</b></p>\n<ul>\n<li><b>Area:</b> \\(A = l \\times w\\)</li>\n<li><b>Perimeter:</b> \\(P = 2(l + w)\\)</li>\n<li><b>Diagonal:</b> \\(d = \\sqrt{l^2 + w^2}\\)</li>\n</ul>\n\n<p><b>2. Given Length (l) and Area (A):</b></p>\n<ul>\n<li><b>Width:</b> \\(w = \\dfrac{A}{l}\\)</li>\n<li><b>Perimeter:</b> \\(P = 2(l + w)\\)</li>\n<li><b>Diagonal:</b> \\(d = \\sqrt{l^2 + w^2}\\)</li>\n</ul>\n\n<p><b>3. Given Width (w) and Area (A):</b></p>\n<ul>\n<li><b>Length:</b> \\(l = \\dfrac{A}{w}\\)</li>\n<li><b>Perimeter:</b> \\(P = 2(l + w)\\)</li>\n<li><b>Diagonal:</b> \\(d = \\sqrt{l^2 + w^2}\\)</li>\n</ul>\n\n<p><b>4. Given Length (l) and Perimeter (P):</b></p>\n<ul>\n<li><b>Width:</b> \\(w = \\dfrac{P}{2} - l\\)</li>\n<li><b>Area:</b> \\(A = l \\times w\\)</li>\n<li><b>Diagonal:</b> \\(d = \\sqrt{l^2 + w^2}\\)</li>\n</ul>\n\n<p><b>5. Given Width (w) and Perimeter (P):</b></p>\n<ul>\n<li><b>Length:</b> \\(l = \\dfrac{P}{2} - w\\)</li>\n<li><b>Area:</b> \\(A = l \\times w\\)</li>\n<li><b>Diagonal:</b> \\(d = \\sqrt{l^2 + w^2}\\)</li>\n</ul>\n\n<p><b>6. Given Length (l) and Diagonal (d):</b></p>\n<ul>\n<li><b>Width:</b> \\(w = \\sqrt{d^2 - l^2}\\)</li>\n<li><b>Area:</b> \\(A = l \\times w\\)</li>\n<li><b>Perimeter:</b> \\(P = 2(l + w)\\)</li>\n</ul>\n\n<p><b>7. Given Width (w) and Diagonal (d):</b></p>\n<ul>\n<li><b>Length:</b> \\(l = \\sqrt{d^2 - w^2}\\)</li>\n<li><b>Area:</b> \\(A = l \\times w\\)</li>\n<li><b>Perimeter:</b> \\(P = 2(l + w)\\)</li>\n</ul>\n\n<p><b>8. Given Area (A) and Perimeter (P):</b></p>\n<ul>\n<li><b>Length:</b> \\(l = \\dfrac{P + \\sqrt{P^2 - 16A}}{4}\\)</li>\n<li><b>Width:</b> \\(w = \\dfrac{A}{l}\\)</li>\n<li><b>Diagonal:</b> \\(d = \\sqrt{l^2 + w^2}\\)</li>\n</ul>\n\n<p><b>9. Given Area (A) and Diagonal (d):</b></p>\n<ul>\n<li><b>Length:</b> \\(l = \\sqrt{\\dfrac{d^2 + \\sqrt{d^4 - 4A^2}}{2}}\\)</li>\n<li><b>Width:</b> \\(w = \\dfrac{A}{l}\\)</li>\n<li><b>Perimeter:</b> \\(P = 2(l + w)\\)</li>\n</ul>\n\n<p><b>10. Given Perimeter (P) and Diagonal (d):</b></p>\n<ul>\n<li><b>Length:</b> \\(l = \\dfrac{P + \\sqrt{8d^2 - P^2}}{4}\\)</li>\n<li><b>Width:</b> \\(w = \\dfrac{P}{2} - l\\)</li>\n<li><b>Area:</b> \\(A = l \\times w\\)</li>\n</ul>\n\n<p>Simply enter any two known values into the Rectangle Calculator, and it will automatically compute the remaining properties, providing you with a comprehensive understanding of the rectangle in question.</p>"
}
ConvertOnline
