Area calculator | 16 popular shapes! (2023)

If you wonder how you can calculate the area of a basic form, you are in the right place.This area calculator answers all of your questions. Use our intuitive tool to choose from sixteen different forms, and calculate your area in no time at all, whether you are looking for an area definition or, for example, the area of a rhombus formula, we have covered you.Continue to read more to read more or simply play with our tool - you won't be disappointed!

What is the area in mathematics? Area definition

Simply said,The area is the size of a surface. With other words, it can be defined as the space that is occupied by a flat shape. To understand the concept, it is usually helpful to think about the area asThe amount of color required to cover the surface. Take a look at the picture below - all numbers have the same area, 12 square meters:

Area calculator | 16 popular shapes! (1)

There are many useful formulas to calculate the area of easier forms. In the following sections you will not only find the known formulas for triangles, rectangles and circles, but also other forms such as parallelograms, dragons or annuli.

We hope that, according to this explanation, you have no problems define what kind of area is in mathematics!

How do you calculate the area?

Well, of course itdepends on the shape! In the following you will find formulas for all sixteen forms that are presented in our area calculator. In addition to the reason of clarity, we will only list the equations - their images, explanations and derivations can be found in the following separate paragraphs (and also in tools that everyoneare devoted to certain form).

Are you ready? Here are the most important and useful area formulas for sixteen geometric forms:

  • SquareArea formula:A = a²
  • rectangleArea formula:A = a × b
  • triangleArea formulas:
    • A = B × H / 2or
    • A = 0,5 × A × B × sin (γ)or
    • A = 0,25 × √ ((a + b + c) × (-a + b + c) × (a - b + c) × (a + b - c)))or
    • A = a² × sin (b) × sin (c) / (2 × sin (b + c))
  • KreisArea formula:A = πr²
  • Circular sectorArea formula:A = R² × shop / 2
  • EllipseArea formula:A = a × b × p
  • trapezeArea formula:A = (a + b) × h / 2
  • ParallelogrammArea formulas:
    • A = a × hor
    • A = a × b × sin (Winkel)or
    • A = e × f × sin (store)
  • RhombusArea formulas:
    • A = a × hor
    • A = (e × f) / 2or
    • A = S² × Sin (store)
  • KiteArea formulas:
    • A = (e × f) / 2or
    • A = a × b × sin (γ)
  • PentagonArea formula:A = a² × √ (25 + 10√5) / 4
  • HexagonArea formula:A = 3/2 × √3 × a²
  • octagonArea formula:A = 2 × (1 + √2) × a²
  • AnnulusArea formula:A = π (R² - R²)
  • squareArea formula:A = e × f × sin (store)
  • Regular polygonArea formula:A = n × a² × cot (π / n) / 4

Would you like to change the area unit? Just click on the unit name and a dropdown list is displayed.

Square area formula

Area calculator | 16 popular shapes! (2)

Have you forgot how high the Square area is? Then you are in the right place. The area of a square is the product of the length of its pages:

  • Square surface = a × a = a², WoAIs a square side

This is the most basic and most common formula, although others also exist. For example, there are square surface formulas that use diagonal, scope, circradius or inradius.

Formula for rectangular area

Area calculator | 16 popular shapes! (3)

The formula for the rectangular area is also a child's play - it is simply the multiplication of the rectangular pages:

  • Rectangular area = a × b

The calculation of the rectangular area is extremely useful in everyday situations: from Baubau (estimate of the tiles, decks, siding or finding the roof area) to the decoration of your apartment (how much color or wallpaper do I need?) To calculate your yoursPeople are cake.

Triangular area formula

There are many different formulas for triangle areas, depending on what is given and which laws or theorems are used. In this area calculator we have implemented four of them:

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Area calculator | 16 popular shapes! (4)

1. Given base and height

  • Triangular area = W / 2
Area calculator | 16 popular shapes! (5)

2. Two pages and the angle between them (SAS)

  • Triangular surface = 0.5 × a × W × sin (γ)
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3. Three pages (SSS)(This triangle area formula meansHerons Formel)

  • Dreieckfläche = 0,25 × √ ((a + b + c) × (-a + b + c) × (a - b + c) × (a + b - c)))

You can discover more in theHerons Formel Rechner.

Area calculator | 16 popular shapes! (7)

4. Two angles and the side between them (ASA)

  • Triangular area = a² × sin (b) × sin (c) / (2 × sin (b + c))

There is a special type of triangle, the right triangle. In this case, the basis and the height are the two sides that form the right angle. Then the area of a right triangle can be expressed as:

Right triangle area = a × b / 2

District area formula

Area calculator | 16 popular shapes! (8)

The circle area formula is one of the best known formulas:

  • District area = πR², WoRIs the radius of the circle

In this calculator we only implemented this equation, but in ourDistrict computerYou can calculate the area from two different specified formulas:

  1. diameter
  • Circular area = πR² = π × (d / 2) ²
  1. Scope
  • District area = c² / 4π

In addition, the Circle Area formula is useful in everyday life -like the serious dilemma for which the pizza size must be chosen.

Sector area formula

Area calculator | 16 popular shapes! (9)

The sector area formula can be accepted by taking a circle. The area of the sector is proportional to its corner.Therefore we can write that:

α / 360 ° = sector area / district area

Angle conversion tells us that360 ° = 2p

A / 2p = sector surface / pr²


  • Sector surface = R² × α / 2

Ellipse area formula

Area calculator | 16 popular shapes! (10)

To find an ellipse area formula, first remember the formula for the area of a circle:πr²For an ellipse you have no value for the radius, but two different values:AAndB. The only difference between the circle and the formula of the ellip surface is the substitution ofThrough the product of the semi-major and semi-minor axes,a × b:

  • Ellipsisfish of space = π × A × B
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Area calculator | 16 popular shapes! (11)

The area of a trapezoid can be found according to the following formula:

  • Trapeze area = (a + b) × h / 2, WoAAndBAre the lengths of the parallel sides andHIs the height

In addition, the formula of the trapezoidal area can be expressed as:

Trapeze area = M × H, WoMIs the arithmetic mean of the lengths of the two parallel sides

Area of a parallelogram formula

Regardless of whether you want to calculate the area with the base and height, sides and angles or diagonals of a parallelogram and the angle between you, you are at the right place. In our tool you will find three formulas for the area of a parallelogram:

Area calculator | 16 popular shapes! (12)

1. Base and height

  • Parallelogrammbereich = a × h
Area calculator | 16 popular shapes! (13)

2. pages and an angle between them

  • Parallelogram surface = a × b × sin (a)
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3. Diagonal and an angle between them

  • Parallelogram surface = e × f × sin (θ)

Area of a rhombus formula

We have implemented three useful formulas for calculating the area of a rhombus.

Area calculator | 16 popular shapes! (15)

1. Page and height

  • Rhombusbereich = a × h
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2. diagonal

  • Rhombus surface = (E × F) / 2
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3rd page and every angle, e.g.B. α

  • Rhombus area = a² × sin (a)

Area of a dragon formula

Area calculator | 16 popular shapes! (18)

To calculate the area of a kite, two equations can be used, depending on what is known:

1. area of a kite formula with kite diagonal

  • Dragon area = (E × F) / 2
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2. area of a kite formula, in two non-controlling side lengths and the angle between these two sides

  • Kite area = a × b × sin (α)
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Pentagon Area Formel

Area calculator | 16 popular shapes! (20)

The area of a pentagon can be calculated from the formula:

  • Pentagon area = a² × √ (25 + 10ond) / 4, WoAis a side of a normal pentagon

Take a look at our committed onesPentagon calculator, where other essential properties of a regular pentagon are provided: page, diagonal, height and scope as well as the radius of the meter and the Incircle.

Area of a hexagon formula

Area calculator | 16 popular shapes! (21)

The basic formula for the area of a hexagon is:

  • Six canteen = 3/2 × √3 × a²where A is the regular hexagon side

Where does the formula come from? You can imagine a regular hexagon as the collection of six congruent triangles. To find the hexagon area, we only have to find the area of a triangle and multiply it. The formula for a regular triangle area corresponds to the square areaSide of the square root of 3 divided by 4:

Equal triangular area = (a² × √3) / 4

Six canteen = 6 × equilateral triangular range = 6 × (a² × √3) / 4 = 3/2 √3 × a²

Area of an Octagon formula

Area calculator | 16 popular shapes! (22)

To find the Octagon area, all you have to do is know the side length and the following formula:

  • Oktagon surface = 2 × (1 + √2) * a²

The Octagon area can also be calculated from:

Oktagon surface = perimeter × apothem / 2

A radius in the Octagon case is easy8 × a. And what is an apothem? An apothem is a distance from the middle of the polygon to the center of a side. At the same time it is the height of a triangle that takes a line from the corner points of the octagon to its center. This triangle - one of eightCongruent - is an Iszelic triangle, so its height can be calculated from the formula using Pythagoras' theorem:

H = (1 + √2) × a / 4

Finally we get the first equation:

Actagon surface = circumference * apothem / 2 = (8 × a × (1 + √2) × a / 4) / 2 = 2 × (1 + √2) × a²

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Area of an annulus formula

Area calculator | 16 popular shapes! (23)

A annulus is a ring-shaped object-ES is a region that is limited by two concentric circles of different radii. Finding the area of an annulus formula is an easy task if you remember the formula of the district area.Annulus area is a difference in the areas of the larger radius -R circle and the smaller radius r:

  • Annulus area = Pr² - Pr² = π (R² - R²)

Area of a square formula

Area calculator | 16 popular shapes! (24)

The square formula, which implemented this area, uses two given diagonal and the angle between them.

  • Square area = e × f × sin (α), WoeAndFare diagonals.

We can use two angles if we calculate your sinus. If we know that two neighboring angles are complementary, we can say thatSin (angle) = sin (180 ° - angle).

If you are looking for other formulas for the area of a square, you will see our committed onesSquare calculatorwhere you can find the formula of Bretschneider (with four sides and two opposite angles) and a formula that Bimedians uses and the angle between them.

Regular polygon area formula

Area calculator | 16 popular shapes! (25)

The formula for the regular polygon range looks like this:

  • Regular polygon surface = n × a² × cot (π / n) / 4

Where n is the number of pages and a the side length.

There are other equations and use z.B. parameters such as circrad radius or scope. They can find these formulas in a special paragraph from ourPolygon surface calculator.

If you have to do with an irregular polygon, remember that you always in simpler figures, e.g.B. triangles, can simply be divided. Simply calculate the area of each of them and summarize them at the end.


Which square has the largest area?

For a certain area, the square with the maximum area will always be aSquare.

What is the shape of the largest area that has given a scope?

For a given area, the closed number with the maximum area A isKreis.

How do I calculate the area of an irregular shape?

Calculation of the area of an irregular form:

  1. Share the shape into several subhapes, for which you can easily carry out the surface calculations, such as triangles, rectangles, trapezoids, (half) circles, etc.
  2. Calculate the area of each of these subhapes.
  3. Summarize the areas of the undercuts to achieve the end result.

How do I calculate the area under a curve?

In order to find the area under a curve via an interval, you must calculate the certain integral of the function that describes this curve between the two points that correspond to the endpoints of the interval in question.


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