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Area & Perimeter Calculator

Calculate area and perimeter for 2D geometric shapes.

Shape Configuration

Select a shape and enter the dimensions.

Rectangle

Circle

Square

Triangle

Area
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Perimeter
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Enter dimensions to compute area and perimeter.

About this topic

Rectangles & Squares Four-sided shapes with right angles and parallel opposite sides.

A rectangle is a quadrilateral with four right angles. A square is a special rectangle where all four sides are equal. Their area represents the 2D space they cover, while the perimeter is the total distance around them.

Key formulas & rules

  • •Opposite sides are equal and parallel
  • •All internal angles are exactly 90°
  • •Area = length × width
  • •Perimeter = 2(length + width)
  • •Square is a rectangle with equal sides
  • •Diagonals bisect each other

Examples

Input Output Note
Rectangle 10×5 Area = 50 10 × 5
Rectangle 10×5 Perimeter = 30 2(10+5)
Square side=6 Area = 36 6²
Square side=6 Perimeter = 24 4 × 6

Real-world uses

Flooring Fencing Screen dimensions
Circles Perfectly round shapes defined by a center and a radius.

A circle is the set of all points equidistant from a center point. The distance from the center to the edge is the radius (r). The perimeter of a circle is called the circumference. All circles are similar.

Key formulas & rules

  • •Area = πr²
  • •Circumference = 2πr
  • •Diameter = 2r
  • •π (Pi) ≈ 3.14159
  • •Ratio of circumference to diameter is always π
  • •Infinite lines of symmetry

Examples

Input Output Note
Radius = 7 Area ≈ 153.94 π × 7²
Radius = 7 Circum ≈ 43.98 2π × 7
Radius = 10 Area ≈ 314.16 π × 100
Radius = 10 Circum ≈ 62.83 2π × 10

Real-world uses

Wheels Pipes Circular tracks
Triangles Three-sided polygons where the angles sum to 180°.

A triangle is the simplest polygon. Its area is half the base times the height. The perimeter is the sum of its three sides. To form a valid triangle, the sum of any two sides must be greater than the third.

Key formulas & rules

  • •Area = ½ × base × height
  • •Perimeter = a + b + c
  • •Angles always sum to 180°
  • •Triangle Inequality Theorem applies
  • •Height must be perpendicular to base
  • •Can be acute, right, or obtuse

Examples

Input Output Note
Base=8, Height=6 Area = 24 ½ × 8 × 6
Sides 5, 6, 7 Perimeter = 18 5+6+7
Base=10, Height=5 Area = 25 ½ × 10 × 5
Sides 3, 4, 5 Perimeter = 12 3+4+5

Real-world uses

Bridges Roof trusses Surveying

Modes & formulas

1

Rectangle

• Calculates area and perimeter for a rectangle. • Enter the length and width. • The calculator multiplies length by width for area, and adds all four sides for perimeter.
Area = l × w | Perimeter = 2(l + w)

A rectangle has equal opposite sides, which is why the perimeter formula multiplies the sum of length and width by 2.

2

Circle

• Calculates area and circumference for a circle. • Enter the radius. • The calculator uses π (Pi) to determine the results.
Area = πr² | Circumference = 2πr

Pi (π) is the ratio of a circle's circumference to its diameter, approximately 3.14159. The radius is half the diameter.

3

Triangle

• Calculates area and perimeter for a triangle. • Enter the base, height, and side lengths. • The calculator multiplies base and height for area, and sums the sides for perimeter.
Area = ½ × b × h | Perimeter = a + b + c

The triangle must satisfy the Triangle Inequality Theorem (the sum of any two sides must be greater than the third side).

4

Square

• Calculates area and perimeter for a square. • Enter the length of one side. • The calculator squares the side for area, and multiplies by 4 for perimeter.
Area = s² | Perimeter = 4s

A square is a special rectangle where all four sides are exactly equal.

How to use it

Select the shape from the tabs, enter the required dimensions, and the calculator will instantly provide both the Area and Perimeter.

Frequently asked questions

Why is area measured in square units?
Because area is a two-dimensional measurement, representing how many unit squares can fit inside the shape.
What is the Triangle Inequality Theorem?
For any valid triangle, the sum of the lengths of any two sides must be strictly greater than the length of the third side.
What is the difference between area and perimeter?
Area is the amount of 2D space inside a shape (measured in square units). Perimeter is the total distance around the outside of the shape (measured in linear units).
How do you find the area of a triangle if you don’t know the height?
You can use Heron’s formula if you know all three sides, or use ½ab·sin(C) if you know two sides and the included angle.
What is Pi (π)?
Pi is the ratio of a circle’s circumference to its diameter. It is an irrational number approximately equal to 3.14159.
What is the radius vs. the diameter?
The radius is the distance from the center to the edge. The diameter is the distance across the circle passing through the center. Diameter = 2 × Radius.

Related calculators

Pythagorean Theorem Solve for side A, B, or hypotenuse C. Triangle Solver Solve triangles using SSS, SAS, or ASA inputs. Circle Calculator Calculate arc length, sector area, and chord length. Distance & Midpoint Find the distance between two points (x₁,y₁) and (x₂,y₂).
Read the full Area & Perimeter guide — examples & 18 FAQs