Area Calculator – Calculate Area of 15 Shapes

Calculate area by selecting a shape and entering your measurements in any metric or US customary unit. See the formulas to find the area for each shape below.

Select a Shape:

Rectangle

Square

Border

Trapezoid

Parallelogram

Rhombus

Triangle

Circle

Ellipse

Sector

Segment

Pentagon

Hexagon

Octagon

Regular Polygon

Rectangle Area Result:

 

Formula:

A = l × w

l = length
w = width
Learn how we calculated this below


On this page:


How to Calculate Area

In geometry, area is the space inside the perimeter or boundary of a space, and its symbol is (A). Area is the measurement of the size of a two-dimensional surface, unlike length, which is a unidimensional measurement.

Because it’s two-dimensional, area is measured in square units, for example, square feet or square meters, to indicate that it’s a measurement of one dimension by another dimension.

Square feet can also be expressed as ft2 or sq. ft. Use our formulas to find the area of many geometric shapes.

It’s essential to measure all lengths in the same unit of measure or convert all lengths to the same unit before calculating area. Try our length conversion calculator or area conversion calculator for converting between imperial and metric measurements.

Area Formulas

Every geometric shape has a unique formula to calculate its area. Use the formulas below to find the area of many popular shapes.


Square Area Formula

A = a2
A = a × a

a = edge length

Diagram of a square showing a = edge length

Rectangle Area Formula

A = l × w

l = length
w = width

Diagram of a rectangle showing l = length and w = width

Border Area Formula

A = (l1 × w1) – (l2 × w2)

l1 = outer length
w1 = outer width
l2 = inner length
w2 = inner width

Diagram of a border showing l1 = outer length, w1 = outer width, l2 = inner length, and w2 = inner width

Trapezoid Area Formula

A = 1/2(a + b)h

a = base a
b = base b
h = height

Diagram of a trapezoid showing a = base a, b = base b, and h = height

Parallelogram Area Formula

A = b × h

b = base
h = height

Diagram of a parallelogram showing b = base and h = height

Rhombus Area Formula

A = a × h

a = edge length
h = height

Diagram of a rhombus showing a = edge length and h = height

Triangle Area Formula

s = 1/2(a + b + c)
A = s(s – a)(s – b)(s – c))

a = edge a
b = edge b
c = edge c

This formula is known as Heron’s formula. You can also use a simplified formula if the height of the triangle is known.

A = 1/2bh

b = edge b
h = height

Diagram of a triangle showing a = edge a, b = edge b, and c = edge c

Circle Area Formula

A = πr2

r = radius

If you know the circle’s diameter, you can find the radius by dividing the diameter in half.

Did you know we also have a calculator to find the area of a circle?

Diagram of a circle showing r = radius

Ellipse Area Formula

A = πab

a = axis a
b = axis b

Try our ellipse calculator to find the area, circumference, and other attributes of an ellipse.

Diagram of an ellipse showing a = axis a and b = axis b

Sector Area Formula

A = (θ ÷ 360)πr2

r = radius
θ = angle in degrees

Learn more about sectors and see more detailed examples on our sector area calculator.

Diagram of a sector showing r = radius and θ = angle

Segment Area Formula

A = (θ × π / 360sin(θ) / 2) × r²

r = radius
θ = angle in degrees

Learn more about segments and see more detailed examples on our segment area calculator.

diagram of a circular segment showing the radius, central angle, chord length, height, and arc length

Pentagon Area Formula

A = (a2 × 5) ÷ (4 × tan(π ÷ 5))

a = edge length

Diagram of a pentagon showing a = edge length

Hexagon Area Formula

A = (a2 × 6) ÷ (4 × tan(π ÷ 6))

a = edge length

Diagram of a hexagon showing a = edge length

Octagon Area Formula

A = (a2 × 8) ÷ (4 × tan(π ÷ 8))

a = edge length

Diagram of an octagon showing a = edge length

Regular Polygon Area Formula

A = (a2 × n) ÷ (4 × tan(π ÷ n))

a = edge length
n = number of sides

Diagram of a regular polygon showing a = edge length

Irregular Polygons and Complex Shapes

The trick to finding the area of an irregular polygon or complex shape is to break the shape up into regular polygons such as triangles and squares first, then find the area of those simpler shapes first, and then add them together to find the total.

Diagram of an irregular polygon/complex shape showing that it can be broken up into a triangle, rectangle, and square

How to Measure Area

Now that you know the formulas, let’s cover the steps to measure area from start to finish.

  • Start by measuring the appropriate dimensions of the shape using a ruler or tape measure. For instance, for a rectangle, measure the length and width.
  • Use one of the formulas above for the desired shape, then substitute the measurements in the formula. For instance, for a rectangle, add the length and width measurements to the formula, then multiply length × width.

How to Calculate the Area of a Large Space

You can find the area of a larger space, such as a plot of land or a city just like you would for a small shape and using the same formulas above. The difference is how you might measure the dimensions and the units used.

Large spaces are usually measured in acres, hectares, square miles, or square kilometers.

If you already know the dimensions of the space, simply plug them into one of the formulas above and solve. If you don’t have the dimensions yet, use a tool like our acreage calculator to measure using a map.

After you have the area, you might need to convert it to acres or square miles. For instance, if you have a measurement in square feet, you can convert it to acres by dividing the square feet by 43,560 to get the result.

What’s the Difference Between Area and Surface Area?

You might be wondering how area is different from surface area. While area is the size of a two-dimensional plane, surface area is the size of the surface of a three-dimensional solid shape.

What’s the Difference Between Area and Perimeter?

So what is the difference between perimeter and area? Perimeter is the distance around a two-dimensional shape, while area is the size of the shape itself.

The perimeter is a length measurement of the boundary around the shape. Imagine you have a rectangle shape; if you took a string and wrapped it around the rectangle, the perimeter would be the length of the string.

Of course, we have a perimeter calculator to help solve this length measurement.

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