Area Calculator

  • Triangle
  • Square
  • Rectangle
  • Parallelogram
  • Rhombus
  • Circle
Base & Height
  • Base & Height
  • 3 Sides
  • 2 Sides & Incl. Angle

Base =

Height =

area illustration

Hello there!

Please provide your input and click the calculate button
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About the Area Calculator

This area calculator lets you calculate the area for several different planar shapes. The shapes currently supported are triangles, squares, rectangles, parallelograms, rhombuses, and circles.

For most shapes, you have the option to choose what combination of inputs you want to provide. And to top it all, the calculator will give you not just the answer, but also the step by step solution.

Usage Guide

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i. Valid Inputs

Each of the inputs provided must be a non-negative real number. In other words, the input must be 0 or greater. Here are a few examples.

  • Whole numbers or decimals → 2\hspace{0.2em} 2 \hspace{0.2em}, 4.25\hspace{0.2em} 4.25 \hspace{0.2em}, 0\hspace{0.2em} 0 \hspace{0.2em}, 0.33\hspace{0.2em} 0.33 \hspace{0.2em}
  • Fractions → 2/3\hspace{0.2em} 2/3 \hspace{0.2em}, 1/5\hspace{0.2em} 1/5 \hspace{0.2em}
  • Mixed numbers → 51/4\hspace{0.2em} 5 \hspace{0.4em} 1/4 \hspace{0.2em}

ii. Example

If you would like to see an example of the calculator's working, just click the "example" button.

iii. Solutions

As mentioned earlier, the calculator won't just tell you the answer but also the steps you can follow to do the calculation yourself. The "show/hide solution" button would be available to you after the calculator has processed your input.

iv. Share

We would love to see you share our calculators with your family, friends, or anyone else who might find it useful.

By checking the "include calculation" checkbox, you can share your calculation as well.

Here's a quick overview of the concept of volume and its formula for a few important shapes.

Area — Concept and Formulas

The area of any two-dimensional or plane figure is a measure of the region it cobers.

For example, the area of the circle above refers to the shaded region.

Alright, here are formulas for the areas of some of the most popular shapes.

Area of a Circle

A labeled diagram of a circle

For a circle with a radius r\hspace{0.2em} r \hspace{0.2em}, the area is given by —

A=πr22A = \frac{\pi \cdot r^2}{2}

Area of a Parallelogram

A labeled diagram of a circle

The formula for the area of a parallelogram with a base b\hspace{0.2em} b \hspace{0.2em} and height h\hspace{0.2em} h \hspace{0.2em} is —

A=bhA = b \cdot h

Rectangles, rhombuses, and squares are just parallelograms with certain additional properties. So the formulas for the area of a parallelogram also work for those other shapes.

However, because of their additional properties, the relevant formulas can look a bit different, often simpler.

Area of a Rectangle

A labeled diagram of a rectangle

For a rectangle with a length l\hspace{0.2em} l \hspace{0.2em} and width w\hspace{0.2em} w \hspace{0.2em}, the area would be —

A=lwA \hspace{0.25em} = \hspace{0.25em} l \cdot w

Area of a Rhombus

A labeled diagram of a rhombus

The most popular formula for the area of a rhombus is —

A=d1d22A \hspace{0.25em} = \hspace{0.25em} \frac{d_1 \cdot d_2}{2}

Here, d1\hspace{0.2em} d_1 \hspace{0.2em} and d2\hspace{0.2em} d_2 \hspace{0.2em} are the diagonal-lengths of the rhombus.

Alternatively, if you know the length of the rhombus' sides a\hspace{0.2em} a \hspace{0.2em} and one internal angle θ\hspace{0.2em} \theta \hspace{0.2em}, you can use the formula —

A=a2sinθA = a^2 \cdot \sin \theta

Area of a Square

A labeled diagram of a square

The area of a square with sides of length a\hspace{0.2em} a \hspace{0.2em} is given by the formula —

A=a2A = a^2

Area of a Triangle

A labeled diagram of a triangle

Here are the two most commly used formulas for the area of a triangle.

1. The area of a triangle with a base b\hspace{0.2em} b \hspace{0.2em} and height h\hspace{0.2em} h \hspace{0.2em} would be —

A=bh2A = \frac{b \cdot h}{2}

2. (Heron's formula) For a triangle with sides a\hspace{0.2em} a \hspace{0.2em}, b\hspace{0.2em} b \hspace{0.2em}, and c\hspace{0.2em} c \hspace{0.2em}, the area is given by —

A=s(sa)(sb)(sc)A = \sqrt{s (s - a) (s - b) (s - c)}

Here, s\hspace{0.2em} s \hspace{0.2em} is the semi-perimeter of the triangle.

s=a+b+c2s = \frac{a + b + c}{2}

Area Calculations — Examples


Calculate the area of a circle with a radius of 4\hspace{0.2em} 4 \hspace{0.2em} inches.


The area of a circle is given by the formula —

A=πr2A \hspace{0.25em} = \hspace{0.25em} \pi r^2

Substituting the value of r\hspace{0.2em} r \hspace{0.2em}, we get

A=π42=50.26\begin{align*} A \hspace{0.25em} &= \hspace{0.25em} \pi \cdot 4^2 \\[1em] &= \hspace{0.25em} 50.26 \end{align*}

So the area of the circle is 50.26 cm2\hspace{0.2em} 50.26 \text{ cm}^2 \hspace{0.2em}.


The sides of a triangle measure 4\hspace{0.2em} 4 \hspace{0.2em} cm, 5\hspace{0.2em} 5 \hspace{0.2em} cm, and 7\hspace{0.2em} 7 \hspace{0.2em} cm. Calculate its area.


When we have the length of each side of a triangle, we can find it's area using the Heron's formula.

A=s(sa)(sb)(sc)A = \sqrt{s (s - a) (s - b) (s - c)}

So, let's start by finding the semi-perimeter (s)\hspace{0.2em} (s) \hspace{0.2em}.

s=a+b+c2=4+5+72=8\begin{align*} s \hspace{0.25em} &= \hspace{0.25em} \frac{a + b + c}{2} \\[1em] &= \hspace{0.25em} \frac{4 + 5 + 7}{2} \\[1em] &= \hspace{0.25em} 8 \end{align*}

Now, substituting the values of a\hspace{0.2em} a \hspace{0.2em}, b\hspace{0.2em} b \hspace{0.2em}, c\hspace{0.2em} c \hspace{0.2em}, and s\hspace{0.2em} s \hspace{0.2em} into the Heron's formula, we get —

A=s(sa)(sb)(sc)=8(84)(85)(87)=72=8.48\begin{align*} A \hspace{0.25em} &= \hspace{0.25em} \sqrt{s (s - a) (s - b) (s - c)} \\[1em] &= \hspace{0.25em} \sqrt{8 \cdot (8 - 4) \cdot (8 - 5) \cdot (8 - 7)} \\[1em] &= \hspace{0.25em} \sqrt{72} \\[1em] &= \hspace{0.25em} \sqrt{8.48} \end{align*}

The area of the triangle is 8.48 cm2\hspace{0.2em} 8.48 \text{ cm}^2 \hspace{0.2em}.


Calculate the area of a rectangular farm that is 75 m\hspace{0.2em} 75 \text{ m} \hspace{0.2em} long and 60 m\hspace{0.2em} 60 \text{ m} \hspace{0.2em} wide.


Using the formula for the area of a rectangle —

A=lw=7560=4500\begin{align*} A \hspace{0.25em} &= \hspace{0.25em} l \cdot w \\[1em] &= \hspace{0.25em} 75 \cdot 60 \\[1em] &= \hspace{0.25em} 4500 \end{align*}

So, the area of the farm is 4500 m2\hspace{0.2em} 4500 \text{ m}^2 \hspace{0.2em}.


If the area of a rhombus is 60 in2\hspace{0.2em} 60 \text{ in}^2 \hspace{0.2em} and one diagonal measures 6 in\hspace{0.2em} 6 \text{ in} \hspace{0.2em}, what is the length of the other diagonal.


We know that for a rhombus with diagonals d1\hspace{0.2em} d_1 \hspace{0.2em} and d2\hspace{0.2em} d_2 \hspace{0.2em}, the area is

A=d1d22A \hspace{0.25em} = \hspace{0.25em} \frac{d_1 \cdot d_2}{2}

Substituting the values of A\hspace{0.2em} A \hspace{0.2em} and d1\hspace{0.2em} d_1 \hspace{0.2em} and solving for d2\hspace{0.2em} d_2 \hspace{0.2em}, we have

A=d1d2260=6d22d2=20\begin{align*} A \hspace{0.25em} &= \hspace{0.25em} \frac{d_1 \cdot d_2}{2} \\[1.75em] 60 \hspace{0.25em} &= \hspace{0.25em} \frac{6 \cdot d_2}{2} \\[1.75em] d_2 \hspace{0.25em} &= \hspace{0.25em} 20 \end{align*}

So the other diagonal is 20 in\hspace{0.2em} 20 \text{ in} \hspace{0.2em} long.

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