**Math Calculators** ▶ Perimeter Calculator

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An online perimeter calculator helps you to determine the perimeter for several geometrical shapes with different parameters. Well, how to find perimeter of different shapes is no more complex with our free online perimeter to area calculator. Let’s start with some basics.

In mathematics, the perimeter of a shape is defined as the total distance around the shape. Basically, it is the length of any shape, as long as it is expanded linearly. The range of various shapes can be the same in length according to their size.

For example, if a circle is made of a metal wire of length L, then we can use the same metal wire to construct a square with the same side length.

Usually, the simplest and most straightforward method is to sum all sides of the shape. However, sometimes there are no edges (such as ellipses, circles, etc.) or one or more edges are unknown. Below are some perimeter equations used with the perimeter calculator to determine the perimeter.

Our perimeter calculator uses a simple formula for regular polygon perimeter:

Polygon Perimeter = x * n

Where,

n = number of polygon sides

If you want to find the perimeter of any polygon, then take the sum of the lengths of all its sides:

Polygon Perimeter = Σ x

where x₁, x₂, …, xₙ are sides lengths and “Σ” is the sum (from i = 1 to n)

Or use the vertices coordinates:

Polygon Perimeter = Σ \sqrt { (aᵢ₊₁ – aᵢ)^2 + (bᵢ₊₁ – bᵢ)^2 }

with a(n+1) = a(1) and b(n+1) = b(1)

However, an Online Sine Calculator will determine the sine trignometric values for the given angle in degree, radian, or the π radians.

Although the formula for the area of an ellipse is very simple and easy to remember, the formula for the circumference of an ellipse is the most complicated. So, we decided to implement an approximation of Ramanujan in this ellipse circumference calculator:

Ellipse circumference ≈ π * [3(x + y) – \sqrt {((3x + y) * (x + 3y)} ]

Where,

A = shortest possible radius

B = longest possible radius

So, accurate Ramanujan approximation is:

Ellipse perimeter ≈ π * (x + y) * [1 + 3(x – y)^2/(x + y)^2] / [10 + \sqrt {(4 – 3(x – y)^2/(x + y)^2)}]

There is also a simpler form of perimeter formula with an additional variable h:

h = (x – y)^2/(x + y)^2

Ellipse perimeter ≈ π * (x + y) * [1 + 3 * h] / [10 + \sqrt {(4 – 3 * h)}]

To compute the perimeter of an irregular trapezoid, there is no specific formula – just add all sides:

Trapezoid perimeter = m + n + o + p

In this perimeter calculator, there are three formulas for the perimeter of the parallelogram:

**Adding all sides:**

Parallelogram Perimeter = x + y + x + y = 2(x + y)

**One side and diagonals:**

The parallelogram perimeter formula that requires one side and diagonals

Parallelogram Perimeter = 2x^2 + \sqrt {(2m^2 + 2n^2 – 4x^2)}

**Height and any angle of Parallelogram:**

The perimeter formula for height and any angle of parallelogram

Parallelogram Perimeter = 2 * (x + m / sin(α))

The perimeter of the rhombus is the same as the perimeter of the square formula!

Rhombus Perimeter = 4x

Rhombus, given diagonals

Another method: finding the rhombus perimeter with the diagonal lengths:

Rhombus Perimeter = 2 * \sqrt{ (m^2 + n^2)}

However, an Online Cosine Calculator helps in calculating the cosine value of the given angle in degrees, radians, mili-radians, and π radians.

The perimeter of a kite formula is very simple – just add all of the sides together:

Kite Perimeter = x + x + y + y = 2(x + y)

The annulus requires to add the perimeter of both concentric circles:

= 2π * r + 2π * R

= 2π * (R + r)

Calculating the perimeter of a sector of a circle seems difficult: Is it just the length of the arc or the length of the arc plus two radii? Think about the definition of the perimeter! The perimeter of a sector is the sum of the lengths of all its borders, so the last one:

Circle Sector Perimeter = r * (α + 2)

Where,

α is in radians.

A square has four equal-length sides. To find its perimeter, you need to multiply the side length by 4:

Square Perimeter = x + x + x + x = 4x

The perimeter of a rectangle formula is easy as the equation for the perimeter of the square. The only difference is that we just have two pairs of equal-length sides:

Rectangle Perimeter = x + y + x + y = 2x + 2y = 2(x + y)

The formula for determining the perimeter of a triangle is adding all sides together:

Triangle Perimeter = x + y + z

However, you aren’t always given all sides of the triangle. So, you can use the law of cosines to determine the missing side:

**Two sides and the angle:**

c = \sqrt{ (x^2 + y^2 – 2xy * cos(γ))}

This can be changed into the perimeter formula:

Triangle Perimeter = x + y + \sqrt{ (x^2 + y^2 – 2xy * cos(γ))}

**Two angles and a side:**

If you have one side and the two angles, then use the law of sines:

y = sin(β) * x / sin(γ + β)

z = sin(γ) * x / sin(γ + β)

So, the triangle perimeter can be represented as:

Triangle Perimeter = x + (x / (sin(β) + sin(γ) * sin(β + γ)))

A perimeter of a circle is also known as the circumference. The perimeter of the circle formula uses one variable:

Circumference/perimeter = 2π*r

Where,

r = circle radius

**Example:**

**Calculate perimeter and area of the circle with 21cm radius. **

**Solution:**

Radius = 9 cm

Area = π × r^2

A = 22/7 × 9 × 9

A = 1782 sq.cm.

**Finding perimeter of circle:**

Circumference = 2πr

C = 2 x 22/7 x 9 = 57 cm

An online perimeter to area calculator finds the perimeter of a particular shape by following these steps:

- First, select the geometric shape from the drop-down list.
- Now, the calculator displays the shape of the selected body.
- Then, substitute the values in the relevant fields.
- Hit the calculate button to see the results.

- The perimeter solver provides the perimeters for square, rectangle, triangle, circle, semicircle, ellipse, circle sector, trapezoid, parallelogram, rhombus, kite, annulus, and regular polygon instantly.

The area is the region that is surrounding by a figure or shape, and the perimeter is the distance covered by the outer edge of the shape.

The area unit is expressed in a square, and the perimeter unit is the same as the measurement unit.

The circle circumference is equal to the length of its outer boundary. It means that the circumference of a circle is equal to its perimeter.

A circle is a curved shape, and its area and circumference are defined by a radius.

- The area of the circle is πr2
- The circumference of the circle is 2πr.

Use this online perimeter calculator for determining the perimeters and dimensions of geometrical shapes. The perimeter defines the distance of the boundary of the shape, and the free online calculator explains the missing perimeters of common bodies.