Perimeter Calculator

With this perimeter calculator, you don't need to worry about perimeter calculations anymore. Below you'll find the perimeter formulas for twelve different shapes as well as a quick reminder about what a perimeter is and a perimeter definition. Read on, give it a try, or check this calculators twin brother - our comprehensive area calculator.

How to find perimeter - perimeter formulas

Usually the most simple and straightforward approach is to find the sum of all of the sides of a shape. However, there are cases where there are no sides (such as an ellipse, circle, etc), or one or more sides are unknown. In this paragraph, we'll list all of the equations used in this perimeter calculator. Scroll down to next sections if you're curious about a specific shape, and wish to see an explanation, derivation, and an image for each of the twelve shapes present in this calculator. We also have tools dedicated to each shape - just type the name of the shape in the search bar at the top of this webpage.

Here are the perimeter formulas for the twelve geometric shapes in this calculator:

• Square perimeter formula: P = 4a
• Rectangle perimeter formula: P = 2(a + b)
• Triangle perimeter formulas:
  • P = a + b + c or
  • P = a + b + √(a² + b² - 2ab * cos(γ)) or
  • P = a + (a / sin(β + γ)) * (sin(β) + sin(γ))
• Circle perimeter formula: P = 2πr
• Circle sector perimeter formula: P = r(α + 2) (α is in radians)
• Ellipse perimeter formula: P = π(3(a + b) - √((3a + b) * (a + 3b)))
• Quadrilateral / Trapezoid perimeter formula: P = a + b + c + d
• Parallelogram perimeter formulas:
  • P = 2(a + b) or
  • P = 2a² + √(2e² + 2f² - 4a²) or
  • P = 2(b + h/sin(α))
• Rhombus perimeter formulas:
  • P = 4a or
  • P = 2√(e² + f²)
• Kite perimeter formula: P = 2(a + b)
• Annulus perimeter formula: P = 2π(R + r)
• Regular polygon area formula: P = n * a

Formula for the perimeter of a rectangle

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

Calculating the perimeter of a rectangle is useful in all sorts of everyday situations, like, e.g., if you want to fence your plot or garden.

Perimeter of a circle formula (circumference formula)

A perimeter of a circle has a special name - it's also known as the circumference. The most well-known perimeter of a circle formula uses only one variable - circle radius:

Circumference = 2π*r

Have you ever wondered how many times your bike wheel will rotate on a ten-mile trip? Well, that's one of the cases where you'll need to use the circumference formula. Input the radius of your wheel (half of the wheel's diameter), and divide 10 miles by the obtained circumference (but don't forget about the convert the units of length!). If you want to be even more accurate, you can include the size of the bike tire. If you're keen cyclist, don't forget to have a look at our bike cadence and speed calculator and the gear calculator.

Not convinced? Need more examples? How about calculating the icing around your circular birthday cake, or you can find how much lace you need to sew your circle skirt.

Perimeter of an ellipse formula (ellipse circumference formula)

Although the formula for the area of an ellipse is really simple and easy to remember, the perimeter of an ellipse formula is the most troublesome of all the equations listed here. We've chosen to implement one of the Ramanujan approximations in this perimeter calculator:

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

Where a is the shortest possible radius and b in the longest possible radius of an ellipse. The other, more accurate Ramanujan approximation is:

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

There is also a simpler form, using an additional variable h:

h = (a - b)²/(a + b)²

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

Or you could just use our calculator!

Perimeter of a parallelogram formula

In this perimeter calculator you'll find three formulas for the perimeter of a parallelogram:

1. The most straightforward one, adding all sides together

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

2. The perimeter of a parallelogram formula that requires one side and diagonals

Parallelogram Perimeter = 2a² + √(2e² + 2f² - 4a²)

3. The perimeter given base, height and any parallelogram angle

Parallelogram Perimeter = 2 * (b + h / sin(α))

Perimeter of a kite formula

Formula for the perimeter of a kite is pretty straight forward - just sum up all of the sides:

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

Perimeter of a polygon formula (regular pentagon, hexagon, octagon, etc.)

In our perimeter calculator we've also implemented a simple formula for regular polygon perimeter:

Polygon Perimeter = n * a

where n is the number of polygon sides. So, for example, you can calculate the perimeter of a pentagon, hexagon, or octagon.

Additionally, for polygons up to 12 sides, the polygon name will appear in the tool. Awesome!

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

Polygon Perimeter = Σ aᵢ

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

Σ is the sum symbol (from i = 1 to n)

Or use the vertices coordinates:

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

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