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Area & Perimeter Calculator

Calculate area and perimeter for 8 common 2D shapes instantly.

Shape & Dimensions
Area
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Enter dimensions above

Area & Perimeter Formulas

ShapeAreaPerimeter / CircumferenceNotes
SquareA = s²P = 4ss = side length
RectangleA = l × wP = 2(l + w)diagonal = √(l²+w²)
TriangleA = ½bh or Heron'sP = a + b + cHeron: s=(a+b+c)/2; A=√(s(s-a)(s-b)(s-c))
CircleA = πr²C = 2πrd = 2r
TrapezoidA = ½(a+b)hP = a+b+c+da, b = parallel sides
ParallelogramA = b × hP = 2(a+b)h = perpendicular height
EllipseA = πabC ≈ π[3(a+b)−√((3a+b)(a+3b))]Ramanujan approximation
SectorA = ½r²θArc = rθθ in radians; perimeter = 2r + arc
Area Converter
Converted Area
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Enter a value to convert
Result
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Reverse
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How to Use This Calculator

1

Select the Shape

Choose rectangle or square as the shape you want to calculate.

2

Enter the Dimensions

Type the width and height (for rectangles) or side length (for squares).

3

View Area and Perimeter

Both the area and perimeter are computed and displayed with the step-by-step solution.

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Formula & Methodology

Rectangle Area
A = W × H
Multiply the width by the height to find the area of a rectangle.
Rectangle Perimeter
P = 2(W + H)
Add the width and height, then multiply by two to get the total perimeter.
Square Area
A = s²
The area of a square is the side length squared; its perimeter is 4s.

About this calculation · Accuracy & Methodology

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Rectangle vs. Square Properties

PropertyRectangleSquare
SidesTwo pairs of equal sidesAll four sides equal
Area formulaW × Hs²
Perimeter formula2(W + H)4s
DiagonalsEqual in lengthEqual and perpendicular
AnglesAll 90°All 90°
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Key Terms

Area The amount of two-dimensional space enclosed within a shape, measured in square units.
Perimeter The total length of the boundary around a two-dimensional shape.
Width (W) The horizontal measurement of a rectangle.
Height (H) The vertical measurement of a rectangle; also called length in some contexts.
Square A special rectangle where all four sides are equal in length.
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Real-World Examples

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Living Room Floor

Input: W = 15 ft, H = 20 ft

Result
Area = 300 ft², Perimeter = 70 ft

Area = 300 ft², Perimeter = 70 ft — useful for flooring and baseboard estimates

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Area and Perimeter in Everyday Problem Solving

Practical Applications

Area calculations determine how much paint covers a wall, how many tiles fill a floor, or how much sod a lawn requires. Perimeter is used to calculate fencing, trim, or border material. These two measurements are the foundation of virtually every construction, landscaping, and interior-design estimate.

Maximizing Area for a Given Perimeter

Among all rectangles with the same perimeter, the square encloses the maximum area. This principle, known as the isoperimetric property for rectangles, has practical implications—if you have a fixed length of fencing, building a square pen gives your animals the most space.

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Frequently Asked Questions

What shapes does this calculator support?+

This calculator handles all common geometric shapes including rectangles, squares, triangles, circles, trapezoids, parallelograms, ellipses, and regular polygons. Select your shape and enter the required dimensions for instant results.

How is area different from perimeter?+

Area measures the surface enclosed by a shape (in square units), while perimeter measures the total length around its boundary (in linear units). For example, a 5x3 rectangle has an area of 15 square units and a perimeter of 16 units.

Can I use this for real-world projects like flooring or fencing?+

Absolutely. Use the area calculation for materials that cover surfaces (paint, flooring, sod) and the perimeter calculation for materials that go around edges (fencing, baseboards, trim). Just make sure all measurements use the same unit.

How do I calculate the area of an irregular shape?+

Break irregular shapes into simpler geometric components (rectangles, triangles, circles), calculate each area separately, then add them together. For areas with curved or complex boundaries, you may need calculus-based methods.

What units does this calculator use?+

The calculator works with whatever units you provide. Enter measurements in feet, meters, inches, or centimeters, and the result will be in the corresponding square units for area or linear units for perimeter.