Area Calculator

This area calculator helps you find the area of a wide range of geometric shapes, including squares, rectangles, triangles, circles, trapezoids, and more. Each result displays the formula used, step-by-step calculations, and flexible unit options (cm, m, ft, in, etc.), making it ideal for students, engineers, and professionals working with geometry. It is designed to provide fast and accurate results while giving you a clear understanding of how each area is calculated.

How to Use the Area Calculator?

Follow these steps:

Step 1: Select Shape

Choose the geometric shape from the drop-down menu for which you want to find the area.

Step 2: Enter Dimensions & Choose Units

Input the dimensions of the selected shape (such as length, width, radius, or height) and choose the units for these measurements (mm, cm, m, ft, in, etc.).

Step 3: Click Calculate

Click on the Calculate button to get the area. The calculator will also show the step-by-step calculation and the formula used.

Supported Shapes & Formulas:

Square
Rectangle
Triangle
Circle
Semicircle
Sector
Ellipse
Trapezoid
Parallelogram
Rhombus
Kite
Regular Pentagon
Regular Hexagon
Annulus (Ring)
Irregular Quadrilateral
Regular Polygon

What Is The Area in Mathematics?

Area is the measurement of a space enclosed by a two-dimensional shape. It shows the actual size of the shape and indicates the surface it covers. For three-dimensional shapes, you can use our surface area calculator.

Unit of Area:

In the International System of Units (SI), the area is expressed in square meters (m²). Other units are also commonly used:

Small objects: square millimeters (mm²) or square centimeters (cm²)
Rooms, furniture, or indoor spaces: square meters (m²) or square feet (ft²)
Land plots, gardens, or large areas: square kilometers (km²)

Why Understanding Units Matters?

To define the scale of measurement correctly
To avoid confusion
To get accurate results
To maintain consistency

How To Find Area?

Square:

A square has equal length and width. Insert the values in the formula:

Square Area = a × a = a²

a = Length of the square side

Rectangle:

area of rectangle

The area of a rectangle can be calculated using the formula:

Area of a Rectangle = length × width = a × b

Triangle:

area of triangle

The formula depends on the parameters provided:

When Height and Base are Provided:

Triangle Area = (b × h) / 2

When Two Sides and Included Angle are Given (SAS):

Triangle Area = 1/2 × a × b × sin(γ)

When Three Sides are Given (Heron's Formula):

Area = √[s(s − a)(s − b)(s − c)]

where s = (a + b + c) / 2

If Two Angles and the Side Touching Them are Provided:

Triangle Area = a² × sin(β) × sin(γ) (2 × sin(β + γ))

Using these formulas, you can easily calculate the area of a triangle based on the information you have. If these formulas look difficult to remember, simply use our triangle area calculator. It supports all these formulas, allowing you to calculate the area of a triangle accurately and instantly.

Circle:

area of circle

This is one of the most common and widely used figures in geometry. You can calculate the area of a circle using the formula:

Circle Area = π × r²

If you are working with a circular shape and want to analyze its area and properties, then our circle area calculator is the perfect tool for you.

Semicircle:

area of semicircle

The formula to find the area of a semicircle is:

Area of a Semicircle = (π × r²) / 2

Sector:

sector

A sector is a measurement of a specific part of a circle. And if you wish to calculate its area, then you can follow up the formula given as:

Area of a Sector = r² * ? / 2

You can also employ the area of a sector calculator to determine the area and other crucial parameters of a circle sector.

Ellipse:

ellipse

Now as you better know that both circle and ellipse are identical in shape. But when you encounter area calculation for ellipse, then you must consider the length of the major and minor axis instead of radius. This is given as:

Area of an Ellipse = π ∗ a ∗ b

Trapezoid:

trapezoid

To find the area of a trapezoid, you need to recall the equation as:

Area of a Trapezoid = (a∗b) * h/2

Parallelogram:

parallelogram

Now here arise three different cases like that of triangle and are given as follows:

If height and Bass are Provided:

Area of a Parallelogram = a * h

If Two Sides and Angle Between them are Provided:

Area of a Parallelogram = a * b * sin (?)

If Diagonals and Mutual Angle Is Given:

Area of a Parallelogram = a * b * sin (θ)

Moreover, you can also explore a parallelogram by using the online parallelogram calculator.

Rhombus:

rhombus

Get going through the area formulas to find the area of the rhombus as follows:

If Side and Height are Given:

Area of Rhombus = a * b

If Diagonals are Given:

Area of a Rhombus = (a * b) / 2

If One Side and Any Angle Is Given:

Area of a Rhombus = a^2 * sin (?)

Kite:

kite

Here we have a couple of formulas that are used in certain condition where you are given with different parameters for area calculations:

If Diagonals are Given:

Area of a kite = (a * b) / 2

If Two Sides and their Mutual Angle Is Given:

Area of a Kite = a * b * sin (?)

Regular Pentagon:

Regular Pentagon

The following expression lets you calculate area of any pentagon:

\( Area of a Pentagon = a^2 * \frac {\sqrt {(25 + 10 \sqrt (5))}}{4} \)

Where;

a represents the side length

Regular Hexagon:

Regular Hexagon

Go by considering the equation mentioned as under to calculate area of a regular hexagon:

Area of a Hexagon = 3/2 * √3 * a^2

Where;

a is the length of a hexagon side.

However, we recommend you utilise our free area of shaded region calculator to determine the area of a hexagon.

Annulus (Ring):

Annulus (Ring)

As you know annulus is a ring shaped figure. And in this kind of figure, we have a couple of circles, one having radius R and other having radius as r. Now you can calculate area of a shape like an annulus by subtracting the area of the smaller circle from that of the bigger one.

Area of an Annulus = pi R² - pi r²

Area of an Annulus = π (R² - r²)

Irregular Quadrilateral:

Irregular Quadrilateral

Like triangle area, the area calculation for quadrilateral can also be performed by using the various formulas. Among these, the most effective and handy is given as follows:

Area of a Quadrilateral = a * b * sin (?)

Where;

a and b represent any two sides of the quadrilateral and alpha is the angle made in between them.

Regular Polygon:

Regular Polygon

Get going to explore the area of a polygon by considering the equation:

\( Area of a Regular Polygon = n * a^2 * \frac{cot \left( \frac{\pi}{n} \right)}{4} \)

Also, we have developed the polygon calculator as well that lets you examine and calculate all particular parameters of a polygon accurately and flawlessly.

How Online Area Calculator Works?

Follow the guideline arranged below to use this land area calculator.

Input:

From the top drop-down list, select the geometrical figure the area of which you are interested in calculating
After you are done with your selection, write down the required parameters’ values in their designated fields
Also, select the units for each entity entered
Now hit the "CALCULATE" button

Output:

The free area of a composite figure calculator does the following computations:

Calculate area of common figures used in area calculations

FAQ’s:

How do you find the area of irregular figures?

Well, it’s pretty simple. What you need to do is to divide the irregular figure into common shapes as described in the content above. After you are done with this, you can calculate the areas of these geometrical shapes easily by this irregular shape area calculator rectangle. And once it is completed, simply add all tiny areas and you will get the overall area of the shape.

What quadrilateral has the largest area?

Among quadrilaterals, square is the one having the largest area calculations. You can also verify it by this free area of a rectangle calculator as rectangle is quite similar to square.

What is a 4 sided shape with no equal sides called?

A geometrical figure with no equal side is known as scalene quadrilateral. And you can find the area of this particular shape by employing our best find the area of the shaded region calculator.

How do I calculate the area under a curve?

Well, it’s very simple! What you need to do includes a couple of factors. One is the manual calculations of the area by indefinite integral simplification. The other one is the use of the area under the curve calculator that is the best way considered so far.

What is a 100 sided shape called?

It’s hectogon having 100 sides of almost equal lengths.

What shape has the largest area given perimeter?

Among all geometrical figures, the circle is the one having the largest area measurement with perimeter being provided.

What is the area of a cube?

Below we have the formula that helps you calculate the area of the cube:

Area of a cube = Length of side * 6

Conclusion:

No doubt it is hard sometimes to calculate the area of any irregular shape. This is because not everyone is capable of estimating the right dimensions of complicated figures or land areas. But to cope with the situation, we have developed this find the area calculator online so that you people may not feel any hurdle while calculating the area of the irregular figures.

References:

From the source of Wikipedia: Geometry, Axioms, Objects, Congruence and similarity, Contemporary geometry, Applications,

From the source of Khan Academy: Unit squares, Measuring area with partial unit squares, Creating rectangles

From the source of Lumen Learning: Area of Irregular Figures, Surface Area of Rectangular Solids, A Bit of Geometry, Similar Triangles

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