How To Find The Perimeter Of An Object

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

What is perimeter? Perimeter definition

Perimeter is the purlieus of a closed geometric effigy. It may also be defined every bit the outer edge of an area, simply the longest continuous line that surrounds a shape. The name itself comes from Greek perimetros: peri meaning "around" + metron, understood as "measure". Every bit information technology's the length of the shape'south outline, it's expressed in distance units - e.chiliad., meters, feet, inches or miles.

the same area for different shapes

How to discover perimeter - perimeter formulas

Unremarkably the most uncomplicated and straightforward approach is to find the sum of all of the sides of a shape. Withal, 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. Gyre down to next sections if you're curious most a specific shape, and wish to see an caption, derivation, and an epitome for each of the twelve shapes present in this calculator. Nosotros besides have tools dedicated to each shape - simply blazon the name of the shape in the search bar at the height 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 = two(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))
Circumvolve perimeter formula: P = 2πr
Circle sector perimeter formula: P = r(α + two) (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 expanse formula: P = due north * a

Perimeter of a square formula

A foursquare has four sides of equal length. To summate its perimeter, all you lot need to do is to multiply side length by 4:

Square Perimeter = a + a + a + a = 4a

Formula for the perimeter of a rectangle

The formula for the [perimeter of a rectangle](calc:749) is well-nigh equally piece of cake as the equation for the perimeter of a a square. The only difference is that we have two pairs of equal length sides:

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 triangle formula

The easiest formula for finding the perimeter of a triangle is - equally usual - by summing all sides:

Triangle Perimeter = a + b + c

Nevertheless, yous aren't e'er given three sides. What tin you lot do and so? Well, instead of fretting, y'all can use the law of cosines to find the missing side:

triangle, given two sides and the angle between them

c = √(a² + b² - 2ab * cos(γ))

This can be incorporated into the perimeter formula:

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

triangle, given two angles and a side between them

The other option is to use the police force of sines if you have one side and the two angles that are formed past that side:

b = sin(β) * a / sin(β + γ)

c = sin(γ) * a / sin(β + γ)

so the triangle perimeter may exist expressed as:

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

Perimeter of a circle formula (circumference formula)

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

Circumference = 2π*r

Have yous ever wondered how many times your bike cycle will rotate on a ten-mile trip? Well, that'south one of the cases where you lot'll need to utilize the circumference formula. Input the radius of your cycle (one-half of the wheel'south diameter), and divide 10 miles past the obtained circumference (only don't forget almost the catechumen the units of length!). If y'all want to be even more authentic, you tin can include the size of the wheel tire. If yous're cracking cyclist, don't forget to take a wait at our bike cadence and speed calculator and the gear calculator.

Non convinced? Need more examples? How about calculating the icing around your circular altogether cake, or y'all can discover how much lace you lot need to sew your circle skirt.

Perimeter of a circle sector formula

Calculating the perimeter of a circle sector may audio catchy - is it only the arc length or is it the arc length plus two radii? But keep in heed perimeter definition! The sector perimeter is the sum of the lengths of all its boundaries, so it's the latter:

Circle Sector Perimeter = r * (α + ii) where α is in radians.

Perimeter of an ellipse formula (ellipse circumference formula)

ellipse and semi-major and semi-minor axes

Although the formula for the area of an ellipse is really simple and like shooting fish in a barrel to remember, the perimeter of an ellipse formula is the most troublesome of all the equations listed here. We've called 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 than authentic Ramanujan approximation is:

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

At that place is also a simpler form, using an additional variable h:

h = (a - b)²/(a + b)²

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

Or you could just use our calculator!

Perimeter of a trapezoid formula

trapezoid with bases a and b and height h

If you want to summate the perimeter of an irregular trapezoid, there'south no special formula - just add all four sides:

Trapezoid perimeter = a + b + c + d

Maybe you lot've noticed, simply information technology's the formula for any quadrilateral perimeter.

There'southward besides an choice that that presents itself with certain special trapezoids - like an isosceles trapezoid, where you need a, b, and c sides. Another example is a right trapezoid, where the length of the bases and 1 leg are enough to detect the shape's perimeter (the last leg is calculated using Pythagoras' Theorem).

Perimeter of a parallelogram formula

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

The most straightforward 1, adding all sides together

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

parallelogram, given one side and diagonals

The perimeter of a parallelogram formula that requires ane side and diagonals

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

parallelogram, given base, height and any parallelogram angle

The perimeter given base, height and whatever parallelogram angle

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

Perimeter of a rhomb formula

The perimeter of a rhombus formula is non rocket science, and so let's make information technology curtailed - it's the aforementioned as the perimeter of a square formula!

Rhombus Perimeter = 4a

Another solution to finding the rhombus perimeter requires the diagonal lengths:

Rhombus Perimeter = 2 * √(east² + f²)

Try deriving the formula yourself. You know that the two diagonals of a rhombus are perpendicular to and bifurcate each other, and so you tin can divide the shape into iv coinciding right triangles. Each triangle has legs that are e/2 and f/2 long - all y'all need to practice is observe the triangle's hypotenuse which is, at the aforementioned time, the rhombus side. Then multiply the result by 4 to find the terminal perimeter of a rhombus formula.