Area of a Circle Calculator: Calculate Circle

An Area of a Circle Calculator is a simple online tool that allows you to quickly calculate the area of a circle. This could be for school work, home improvement projects, measuring round garden areas or any geometry related problem.

The area of a circle is how much space there is inside the circle. This can be measured in square units.

All you need to calculate the area of a circle is the radius or diameter. Radius is the distance from the centre of the circle to the outside edge. The diameter is the distance across the middle of the circle.

Our Area of a Circle Calculator uses the standard formula to give accurate results in seconds. All you need to do is input the desired measurement and choose the unit you would like to use.

This calculator can be used by students, teachers, homeowners, builders, designers, engineers and anyone else that needs to measure a circle.
How to Use the Area of a Circle Calculator
This online calculator is very easy to use and doesn’t require any advanced maths knowledge.

Steps:

Choose your input. Choose if you want to calculate the area based off the radius or diameter.

Input your measurement. Enter either the radius or diameter that you know.

Choose your unit. If you have the option to choose your unit of measurement choose the one you want to use (Inches, Feet, Centimetres & Metres).

Calculate your area. Press the calculate button.

View your results. The area of the circle will show up in squared units.

Reset. If required you can reset the calculator and add new measurements.

Example: If the radius of the circular table is 5 inches type this into the calculator.

You can calculate any area you want by repeating the steps above.

Area of a Circle Formula

The formula for calculating the area of a circle is:
A = πr 2

Where:

A = Area of the circle

π (Pi) = Mathematical constant, approximately 3.14159

r = Radius of the circle

r 2 = Radius x Radius

This formula calculates the area inside the circle.

Using the diameter

If you know the diameter of the circle you can use the below formula:

A = πd 2 /4

Where:

A = Area of the circle
π = Approximately 3.14159
d = Diameter of the circle

Alternatively, if you know the diameter you can calculate the radius (half of the diameter) and use the standard formula.

Note: Ensure your unit of measurement is the same for both your radius or diameters. The area will be in squared units.

Example

Let’s look at an example of how to calculate the area of a circle.

Example 1 – Calculating the area from the radius.

Imagine you have a circular garden with a radius of 7 feet. You want to know how much space it takes up.

We know:

Radius (r) = 7ft
Pi (π) = 3.14159

1. Firstly write down the formula.

A = πr 2

2. Substitute in your radius.

A = 3.14159 x 7 2

3. Square your radius.

A = 3.14159 x 49

4. Multiply out.

A = 153.93891 ft 2

Answer:

The area of your garden is approximately 153.94ft 2.

Example 2 – Calculating the area from the diameter.

Imagine you have a circular swimming pool with a diameter of 12ft.

We know:

Diameter (d) = 12ft

Pi (π) = 3.14159

Using the diameter formula:

A = πd 2 /4

Substitute into the formula:

A = (3.14159 x 12 2 ) /4

A = (3.14159 x 144)/4

A = 113.09724 ft 2

Your swimming pool takes up approximately 113.10ft 2.

This shows how you can calculate the area of the same circle using the radius or diameter.

Understanding your result

When using an Area of a Circle Calculator your result will tell you how much 2D space is inside the circle.

It is important to know what each term means.

Area – Tells you how much space is inside the circle.

Circumference – Tells you how long the distance around the circle is.

Radius – Tells you how far it is from the centre to the edge.

Diameter – Tells you how far it is across the circle.

So if the area of a circle was 78.54in 2 this means that the surface area inside the circle is approximately 78.54in 2.

Depending on how accurate the Pi value is and the measurement you have inputted the calculator may give you a decimal answer.

Always remember that your answer will be in squared units. So if your radius was in feet your answer will be in squared feet.

What affects your result?

There are several things that will affect your result. Knowing these will help you input your measurements correctly.

Radius

The radius is the most important part of the formula. As the radius is squared any increase will have a large impact on your result.
For example, if you double the radius from 3ft to 6ft your area will be 4 times bigger.

Diameter

If you are using the diameter the calculator will take into consideration the relationship between the diameter and radius. If you have an inaccurate diameter measurement your area will be inaccurate.

Accuracy of Pi

Pi is an irrational number with infinite decimal places. Most calculators will use an accurate numerical value to calculate your result. For example 3.14159.

Units

Depending on how you measure your circle the calculator will give you your answer in different units. If you have measured the radius in inches but expect your answer to be in squared feet this could cause confusion. Ensure you convert your units.

Accuracy of measurements

Measurements may not be completely accurate. As the radius is squared any inaccuracies in your measurement will have a bigger effect on your final answer.

Benefits & Uses of an Area of a Circle Calculator

There are many benefits to using an Area of a Circle Calculator.

Saves time

As the calculator does the maths for you you can calculate the area in seconds.

Helps students learn

Students can use the calculator to understand the formula for calculating the area of a circle and practice maths problems.

Home improvement

Homeowners can use the calculator to calculate the surface area of circular tables, round rugs, ornamental items, patios etc.

Construction & Landscaping

Builders and landscapers can use the calculator to get an estimate of the area of circular foundations, gardens, flowerbeds etc.

Material estimation

Knowing the area of a circular surface can help you estimate how much paint, flooring, grass seed, mulch etc you will need. You may need to allow extra for wastage.

Engineering & Design

Engineers, architects and designers often work with circular parts. Calculating the area can help plan materials, measurements and calculations.

Consistency

As we are using the same formula it reduces the chance of human error and makes it easier to compare different circle measurements.

Accuracy, Assumptions & Limitations

If your measurements are accurate and the shape is a perfect circle the Area of a Circle Calculator will give you accurate results.

However there are a few limitations and assumptions.

Assumes perfect circle – The calculator assumes that the object is a perfect circle. If you have an irregular or oval shape you will need to measure differently.

• Accurate measurements – The calculator will only give you accurate results if you input accurate measurements.
• Rounded value of Pi – The calculators will generally use a rounded numerical value for Pi. This can give you a very small difference in your results.
• Consistent units – Ensure that your measurements are using consistent units. If not convert them before calculating.
• Flat surface area – The calculator will give you the flat surface area. It will not give the volume or curved surface area of a 3D object.
• No allowance for materials – The calculator will not automatically allow for extra materials. You may need to allow extra for cutting, fitting, overlapping etc.

FAQs

1. How do you calculate the area of a circle?

To calculate the area of a circle you multiply Pi (π) by the radius squared. The formula is A = πr². For example if the radius was 5 inches the area would be approximately 78.54in 2.

2. Can I calculate the area of a circle using the diameter?

Yes. You can calculate the area using the diameter. The formula is A = πd²/4. Simply input your diameter.

3. What is the difference between radius and diameter?

Radius is the distance from the centre of the circle to the edge. The diameter is the distance from one side of the circle to the other through the centre. The diameter will always be twice the radius.

4. What unit is the area of a circle measured in?

The area of a circle is measured in squared units. Common examples are In 2, F 2, Cm 2 & M 2. The unit will depend on what unit you measure your radius/diameter in.

5. Are online calculators accurate?

Yes. If you input accurate measurements you can get very accurate results. The calculator uses the standard formula and rounded value for Pi. However, the accuracy of your real life results will depend on how accurately you measured your circle.