import { create, all } from 'mathjs'

Perimeter Calculator

Handy Perimeter Calculator gives the perimeter of all geometric shapes. You have to choose the shape semicircle or ellipse or annulus (ring) and fill the input fields to get the output as perimeter in a short span of time.

Perimeter Calculator: This calculator tool helps the one who are solving the geometric problems. Here, you can see the complete details of geometric shapes perimeter and what is meant by perimeter. Get simple formulas and procedure to compute the perimeter of annulus, ellipse or semicircle. Go through the following sections to calculate the perimeter.

What is meant by Perimeter?

Perimeter is defined as the length of the outline of the geometrical shape. To calculate the perimeter of two dimensional shapes, you must have the lengths of sides of that particular shape. There are different formulas to compute the perimeter and we have given all of them in the below sections.

Formulas To Calculate Perimeter

Calculating the perimeter is totally depends upon the shape and we have covered many shapes. Check out the formulas for each shape along with the step by step explanation and derivations that are required.

The formula to find perimeter of square P = 4*a

Rectangle Perimeter P = 2(l + b)

Triangle Perimeter Formulas are

  • P = a + b + c
  • P = a + b + √(a² + b² - 2ab * cos(γ))
  • P = a + (a / sin(β + γ)) * (sin(β) + sin(γ))

Circle Perimeter Formula is P = 2π * r

Semicircle Perimeter Formula is P = (π + 2) * r

Ellipse Perimeter formulas are

  • P = π * [3(a + b) - √((3a + b) * (a + 3b))]
  • P = π * (a + b) * [1 + 3(a - b)²/(a + b)²] / [10 + √(4 - 3(a - b)²/(a + b)²)]
  • P = π * (a + b) * [1 + 3 * h] / [10 + √(4 - 3 * h)]

Annulus ring Perimeter Formula is P = 2π(R + r)

Perimeter of a Circle Sector Formula is P = r(α + 2)

Quadrilateral/ trapezoid Perimeter formula is P = a + b + c + d

Parallelogram Perimeter formulas are

  • P = 2(a + b)
  • P = 2a² + √(2e² + 2f² - 4a²)
  • P = 2 * (b + h / sin(α))

Perimeter of a kite formula is P = 2(a + b)

Rhombus Perimeter Formulas are

  • P = 4a
  • P = 2 * √(e² + f²)

Regular Polygon Perimeter Formulas are

  • P = n * a
  • P = Σ aᵢ
  • P = Σ √[(xᵢ₊₁ - xᵢ)² + (yᵢ₊₁ - yᵢ)²]

Perimeter of a Square Formula

Square have four equal sides. So add those four sides length to get the square perimeter.

Let's take a is the side length of a square, then

Square perimeter = a + a + a + a = 4*a

This is the basic way to find square perimeter using side. Other ways can be with diagonals.

Perimeter of a Rectangle Formula

A rectangle also has 4 sides, but opposite sides have equal length. Here also, add the sides of a rectangle to find its perimeter.

Take l, b as the two different sides of a rectangle.

Rectangle Perimeter = l + b + l + b = 2l + 2b = 2(l + b)

Perimeter of a Triangle Formula

The simple way to calculate the triangle perimeter is add all sides.

If a, b , c are the different sides of a rectangle,

Perimeter = a + b + c

If you have, two sides and angle between them, the other side will become c = √(a² + b² - 2ab * cos(γ))

Triangle Perimeter = a + b + √(a² + b² - 2ab * cos(γ))

If you have two angles and side length between those angles, then missing sides are

b = sin(β) * a / sin(β + γ)

c = sin(γ) * a / sin(β + γ)

So, Perimeter of Triangle = a + (a / sin(β + γ)) * (sin(β) + sin(γ))

Perimeter of a Circle Formula

Perimeter of circle is also called as circumference. It uses only one variable i.e radius r.

Circumference = 2π*r

Perimeter of a Semicircle Formula

Semicircle perimeter is half of the circumference of a circle and diameter of a semicircle. Its formula is

Perimeter = π * r + d = π * r + 2 * r = (π + 2) * r

Where, r is the radius of semicircle and d is the diameter of a circle.

Ellipse Perimeter Formula

Perimeter of an ellipse can be calculated by using different formulas. The most basic formula uses shortest possible radius a and longest possible radius b.

Ellipse perimeter ≈ π * [3(a + b) - √((3a + b) * (a + 3b))]

Ellipse perimeter ≈ π * (a + b) * [1 + 3(a - b)²/(a + b)²] / [10 + √(4 - 3(a - b)²/(a + b)²)]

When we have, shortest & longest radius a, b and height h

Where h = (a - b)²/(a + b)²

Ellipse perimeter ≈ π * (a + b) * [1 + 3 * h] / [10 + √(4 - 3 * h)]

Perimeter of an Annulus Formula

Add circumference of both concentric circles to get its perimeter.

Annulus Perimeter = 2π * R + 2π * r = 2π * (R + r)

Where, r is the inner circle radius, R is the outer circle radius

Circle Sector Perimeter Formula

Get angle and radius of the circle section to find its perimeter.

Let us say r is the radius of the sector and α is triangle.

Perimeter of Circle sector P = r * (α + 2)

Perimeter of a Trapezoid Formula

Calculate the perimeter of a irregular trapezoid by adding all their sides.

Trapezoid perimeter = a + b + c + d

where, a, b, c, d are the sides of a trapezoid

Perimeter of a Parallelogram

There are various ways to compute the parallelogram perimeter based on the things you know.

1. Adding all sides

Perimeter = a + b + a + b = 2(a + b)

Where, a, b are the sides lengths of parallelogram

2. If you know side length and diagonals,

Perimeter = 2a² + √(2e² + 2f² - 4a²)

Where, a is the length of side of a parallelogram, e and f are the diagonals.

3. If you have base, height and one angle,

Perimeter = 2 * (b + h / sin(α))

Where, b is the base, h is the height and α is the angle

Perimeter of a Kite Formula

Add all sides of a kite to get its perimeter.

Kite Perimeter = a + b + a + b = 2(a + b)

Where, a, b are the sides of a rhombus

Perimeter of a Rhombus Formula

Rhombus have all sides pf equal length. The two simple formulas to find the rhombus perimeter is using sides and using diagonals.

1. Using sides

Perimeter = 4a

Where, a is the side length of rhombus

2. Using Diagonals

Perimeter = 2 * √(e² + f²)

Where, e, f are the lengths of diagonals

Perimeter of a Regular Polygon Formula

The simple formula is

Polygon Perimeter = n * a

Where, n is the number of sides of polygon, a is the length of side.

Other ways is Perimeter = Σ aᵢ

where a₁, a₂, ..., aₙ are sides lengths

Or using vertices coordinates

Regular Polygon Perimeter = Σ √[(xᵢ₊₁ - xᵢ)² + (yᵢ₊₁ - yᵢ)²]

with x(n+1) = x(1) and y(n+1) = y(1)

Procedure to Calculate Perimeter

  • Make a note of the information given in the question.
  • As per your requirement make use of these formulas
  • Substitute the values and do further calculations.

Keep on visiting our website to get the data related to area, volume, perimeter, etc of all geometric shapes.

Annulus(Ring) Capsule Circle Circumference Cone Conical Frustum Cube Cylinder Equilateral Triangle Hemisphere Isosceles Triangle Parallelogram Perimeter Polygon Pyramid Rectangle Rectangular Prism Rhombus Sphere Square Stadium Surface Area Triangle Calculator Right Triangular Prism Tube Volume Orthocenter Moment of Inertia Golden Rectangle Centroid