What is the perimeter of a rectangle?

The perimeter of a rectangle is twice the sum of its length and width: P = 2 times (length + width). The area is length times width. For a rectangle 6 units long and 4 units wide, the perimeter is 2 times (6 + 4) = 20 units and the area is 6 times 4 = 24 square units.

What is the perimeter of a circle?

The perimeter of a circle is called its circumference. It equals 2 times pi times the radius, or equivalently pi times the diameter. For a circle of radius 5, the circumference is 2 times pi times 5 = approximately 31.42 units and the area is pi times 25 = approximately 78.54 square units.

How do you find the perimeter of a regular polygon?

A regular polygon has n sides of equal length s. Its perimeter is simply n times s. The area is (n times s squared) divided by (4 times tan(pi divided by n)). For example, a regular hexagon with side length 4 has a perimeter of 24 and an area of approximately 41.57 square units.

Perimeter Calculator

This calculator finds the perimeter and area of five common two-dimensional shapes: square, rectangle, triangle, circle and regular polygon. The perimeter of a shape is the total length of its outer boundary: add up all the side lengths for polygons, or use the formula 2 pi r for a circle (where the perimeter is called the circumference). Area is the amount of flat space enclosed inside the boundary. For a square with side s, perimeter is 4s and area is s squared. For a rectangle with length l and width w, perimeter is 2 times (l plus w) and area is l times w. For a triangle where you know all three sides a, b and c, perimeter is a plus b plus c and area uses Heron's formula: first compute the semi-perimeter s equal to half the sum of all three sides, then area equals the square root of s times (s minus a) times (s minus b) times (s minus c). For a circle with radius r, circumference is 2 pi r and area is pi r squared. For a regular polygon with n sides each of length s, perimeter is n times s and area is (n times s squared) divided by (4 times tan(pi divided by n)). You select the shape, enter the required dimensions, and the results appear instantly. The tool is useful for students at all levels of school geometry, tradespeople estimating materials such as fencing or carpet, and designers working out boundary lengths and surface areas. All inputs must be positive; triangle sides must satisfy the triangle inequality (no single side longer than the sum of the other two).

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Shape

Length

Width

Side length

Side a

Side b

Side c

Radius

Number of sides

Side length

20.00

perimeter

Area24.00

ShapeRectangle

How it works

Square: P = 4s; A = s². Rectangle: P = 2(l + w); A = l × w. Triangle: P = a + b + c; area via Heron's formula: s = P/2, A = sqrt(s(s−a)(s−b)(s−c)). The triangle must satisfy the triangle inequality. Circle: P (circumference) = 2πr; A = πr². Regular polygon: P = n × s; A = (n × s²) / (4 × tan(π/n)). All inputs must be positive. For the regular polygon the number of sides must be 3 or more.

Worked example

Select Rectangle, enter length = 6 and width = 4. Perimeter = 2 × (6 + 4) = 20. Area = 6 × 4 = 24. These match the default values pre-filled in the calculator above. To verify with a square: set side = 5, perimeter = 20, area = 25. For a circle of radius 5: circumference = 2 × π × 5 = 31.42, area = π × 25 = 78.54.

Related calculators

Arc Length and Sector Area Calculator: find the arc and area of a circular sector rather than the full circle.
Law of Cosines Calculator: find an unknown triangle side before calculating its perimeter.
Triangle Angle Calculator: find the missing angle in the triangle you are measuring.
Percentage Calculator: express one shape's perimeter as a percentage of another's.

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