Circle Area Calculator

Radius (r)

Diameter (d)

Circumference (C)

Area (A)

Add a sector (slice) of the circle

Enter a central angle to get the sector area and arc length.

Enter any one measurement, the radius, diameter, circumference, or area, and the calculator fills in the other three for you.

Your circle

Please input values into the fields

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Show how the area scales with the radius

A bar chart of how the area changes as the radius grows.

This tool to calculate the area of a circle is not just for finding out the area of a circle. If you enter any known value such as radius, diameter, circumference or area, this tool will calculate the remaining values.

By entering one value and selecting a unit, the other measurements are automatically filled in with the area being shown as the main result. You can also use the sector option to find out the area of a circle segment.

What is the area of the circle?

The area of a circle is the size of the flat surface inside the circumference of the circle. Being a two-dimensional space, it is measured in square meters or square feet like other areas. A circle is a geometrical shape that consists of all points equidistant from a center point; this distance being the radius. When the radius is known, then the area can be calculated using a simple formula. In addition, diameter and circumference can also be derived from the radius.

How to use this calculator:

Enter a known value for Radius, Diameter, Circumference or Area into the corresponding field and select a unit such as centimeter or inch. After entering a value, the tool will automatically fill out the other fields and display the area as the main result. It is not necessary to specify which value was entered. To start over with another value, simply delete the previously filled-out field and enter the new value. If you want to calculate the area of a circular segment and arc length, open the "Sector" option and enter the central angle in degrees.

Formula for the area of a circle

The area is determined only by the radius. The formula is pi times the square of the radius.

A = \pi r^2

Here A is the area, r is the radius and π is approximately 3.14159. The same relationship can be used if you know the diameter or circumference of a circle instead of the radius. The diameter is twice the length of the radius, and the circumference is π times the diameter.

A = \pi \left(\frac{d}{2}\right)^2 = \frac{\pi d^2}{4} \qquad A = \frac{C^2}{4\pi}

Let's say a circle has a radius of 5 centimeters. Squaring the radius gives us 25, and multiplying that by pi gives us the area.

A = \pi \times 5^2 = 25\pi \approx 78.54 \ \text{cm}^2

Conversely, one can calculate the radius from the area by dividing the area by π and then taking the square root.

r = \sqrt{\frac{A}{\pi}}

Check all measurements of the circle in one place.

All measurements of a circle are interrelated through the radius. The following table summarizes the relationships used by the calculator so that when one value is entered, the remaining values can be calculated.

Measurement	Symbol	Formula from the radius
Diameter	d	d = 2r
Circumference	C	C = 2 pi r
Area	A	A = pi r squared
Radius from area	r	r = square root of (A / pi)

Example calculation:

The following table shows examples of areas for common radii with decimals rounded. Note that the area increases very quickly as the radius gets larger because it is squared.

Radius	Calculation	Area
3 cm	pi times 3 squared	28.27 sq cm
7 cm	pi times 7 squared	153.94 sq cm
10 cm	pi times 10 squared	314.16 sq cm
20 cm	pi times 20 squared	1256.64 sq cm

If you start with the diameter instead of the radius, then after halving it to get the radius, follow the same procedure. If the diameter is 12 cm, for example, then the radius is 6 cm, and the area is π times 6 squared or about 113.10 square centimeters. You can also simply put the value of the diameter into the "diameter" field of this calculator, which will automatically compute the area for you.

You could also calculate the area of a sector, let's say a 90 degree sector of the circle.

What is the area of a circle used for?

Because circles are everywhere, this calculation shows up in a lot of different careers. Construction workers and landscape architects plan the dimensions of patios, ponds, fountains, and roundabouts. Chefs adjust recipes to fit different sizes of pizza or cake pans. Engineers calculate cross-sections of pipes, cables, and cylinders to determine flow and strength. The same numbers also show up in statistics, because pi is part of the formula for a normal distribution.

For accurate results, please follow these tips:

Either measure the radius from the exact center or determine the diameter at its widest point and enter half of that value into a calculation tool. Make sure your units are consistent. If you're measuring in centimeters, for example, you'll get an area in square centimeters. Note that area varies as the square of the radius, so small errors in the radius can lead to large errors in the area.

Frequently asked questions

What is the formula for the area of a circle?

The area is calculated as A = π * (radius)^2. Since pi is approximately 3.14159, the area with a radius of 5 would be approximately 78.54 units squared.

How do you find the area of a circle using its diameter?

Divide the diameter by 2 to find the radius and then use the formula A = π*(radius)^2. Alternatively, you can also use the formula A = π*(diameter)^2 and divide by four; it will give you the same result. This calculator shows area once diameter is entered.

If the radius is doubled, how does that change the area?

The area changes according to the square of the radius' scale factor; it does not simply double. This is because the area depends on the square of the radius. Increasing the radius by a given factor also increases the area by the square of that factor.

What is the difference between area and perimeter?

The area is the space inside a circle and is expressed in square units. The circumference is the length of the line that goes around the edge of the circle, and it's expressed in regular length units. To calculate the area, use the formula A = πr², while to find the circumference, use C = 2πr.

Is it possible to calculate the radius if only the area is known?

Yes. You divide the area by π and then take the square root. The formula is: r = √(A/π). This calculator will automatically perform the calculations for you simply by entering the value of the area into its corresponding field.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

Wikipedia: Area of a circle
Definition, derivations, and history of the area formula.
Wikipedia: Circle
The parts of a circle and the relationships between them.
Math is Fun: Circle
Plain-language explanations of radius, diameter, circumference, and area.