How to Find the Area of a Circle? [4 Methods]

Do you have to understand how to determine the area of the circle? This is a fairly standard problem in geometry, and the solution is not going to be too challenging to find. The majority of the time, you should get by with the popular equation S = πR². It is not a problem if you are unsure of the radius. Regardless of the information that you have provided, we will assist you in solving the area by utilizing some of our other algorithms.

So how to find the area of a circle? Follow this article to grasp how to calculate the area of a circle by using its radius, diameter, circumference, or even a sector of it.

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how to find the area of a circle

Method 1: Determining the Area by Using Radius

Step 1: Identify the radius of a circle.

The distance that must be traveled to reach the circumference of a circle is known as its radius. You may measure any direction, and the result will still be the same for the radius. In the case of a circle, the radius corresponds to one-half of the diameter. The diameter of a circle is the segment of a line that runs through its center and links the two sides that are on opposite ends of the circle.

In most cases, the distance range will be specified for you. If the precise center of a circle is not indicated on a paper circle that you are using for measurement, it might be challenging to get an accurate measurement of that circle’s center.

Step 2: Square the radius.

To calculate the area of a circle, use the formula S = πR², where the R variable stands for the circumference of the circle. This variable is expressed as a square. Avoid becoming confused and make sure that you square the whole equation. In the example circle with a radius of 6, the square of that number is 36.

Step 3: Multiply by π.

Pi is a mathematical constant that is used to indicate the ratio between a circle’s circumference and its diameter. It is represented symbolically with the Greek letter, which is π. is nearly equivalent to 3.14 when expressed in decimal form. The correct value of the decimal place goes on and on forever. You will often record your response using the symbol for a circle itself, which is denoted by the letter “,” to provide an accurate expression of the area of a circle.

The formula for calculating the area of the circle with a radius of 6 cm and a particular example is as follows:

S = πR²

S = π6²

S = 36π or S = 36(3.14) =113.04

Step 4: Report your outcome

Keep in mind that the results of an area calculation are going to be presented using “square” units. The area will be expressed as many square centimeters if the radius was measured in centimeters. If feet were used to measure the radius, then feet squared would be used to calculate the area. In addition to this, you should be aware of whether the symbol or the numerical approximation should be used when reporting your findings. If you are unsure, you should report both of them.

The area of the sample circle that has a radius of 6 cm will be either 36π cm² or 113.04 cm², depending on whether one is larger.

Method 2: Calculating Area from the Diameter

Step 1: Determine the diameter

Several issues or circumstances will prevent you from obtaining the radius. On the other hand, you can be provided with the circle’s diameter. You will determine the diameter with a ruler if you have drawn it into your design. On the other hand, the value of the diameter can be all that is shared with you.

For the sake of this illustration, we will assume that the circumference of your circle is 20 inches.

Step 2: Divide the diameter in half.

Keep in mind that the diameter is equal to the radius multiplied by two. As a result, whatever figure is provided to you for the diameter, halve it, and that will give you the value for the radius. Because of this, the example circle that has a diameter of 20 inches will have a radius that is equal to 20 divided by two, which is 10 inches.

Step 3: Determine the area using the original formula.

After you have determined the circle’s radius and have converted the diameter to that value, you are prepared to compute the area of the circle by using the formula S = πR^2. To finish the computations, enter the value for the radius, then do the rest as follows:

S = πR²

S = π10²

S = 100π

You may also offer a numerical approximation by multiplying the result by 3.14 rather than using the symbol. The final answer is going to be (100)x(3.14), which is 314 square inches.

how to find the area of a circle

Method 3: Utilizing Circumference to Calculate Area

Step 1: Get familiar with the revised formula.

You may utilize an updated version of the formula for calculating the area of a circle when you already know the circumference of the circle. The area may now be calculated without using the radius thanks to this updated formula, which utilizes the circumference instead. The revised formula is as follows: A= C^{^2}/4π

Step 2: Determine the circumference by measuring

It might be challenging to approximately locate the circle’s center if the diameter is not provided for you to draw or if the circle’s center is not recognized. When it comes to some physical circles, such as a pizza pan or a frying pan, you may use a tape measure to determine the circumference of the circle with more precision than you could determine the diameter of the circle.

Consider for the sake of this illustration that you have either independently determined or been informed that the circumference of a circle (or other round objects) is 42 centimeters.

Step 3: Revise the formula by making use of the connection that exists between the circumference and the radius.

The formula for calculating the circumference of a circle is pi times the diameter. This may be expressed mathematically as d=2R. Then, keep in mind that the diameter is equivalent to twice the radius, which is denoted by the equation C=2R. You may establish the following kind of connection by combining these two kinds of equality: C=π2R

Step 4: Insert into the equation for finding the area of a circle.

By making use of the connection that exists between the circumference and the radius, it is possible to derive an altered form of the formula that is used to calculate the area of a circle. Put this most recent equality into the method for calculating area, and get the following results: S=C^2/4π

Step 5: Solve the problem using the updated formula.

You may use the provided information and the updated formula—which now uses the circumference rather than the radius—to get the area directly. Enter the circumference’s value and carry out the following calculations:

You were given a sample C=42 inches.

S=C²/4π

S=42²/4π

S=441/π

The area of this hypothetical circle, having a diameter of 42 cm, is given by S=441/π sq. cm.

Method 4: Finding an Area from a Sector of the Circle

Step 1: Determine the information

In certain puzzles, you could be given details about a particular circle sector before being asked to determine the size of the whole circle. Look for information that states something like, “A sector of Circle O has an area of 15 cm2,” as you carefully read the issue. Locate Circle O’s area.

Step 2: Specify the preferred sector.

Sometimes referred to as a “wedge,” a sector is a section of a circle. Drawing two radii from the circle’s center to its edge defines a sector. The sector is the area located between these two radii.

Step 3: Calculate the sector’s center angle.

Measure the center angle formed by the two radii using a protractor. The protractor’s central point should be in line with the center of the circle, and its base should be placed along one of the radii. Then, read the angle measurement that relates to where the second radius of the sector is located.

The smaller angle between the two radii or the larger angle outside of them should be identified before measurement. This should be defined for you by the issue you are trying to solve. 360 degrees will be obtained by adding the little angle and the large angle.

In certain cases, the issue may only provide you with the measurement rather than asking you to determine the center angle. For instance, you could be instructed to measure it or informed that the sector’s center angle is 45 degrees.

Step 4: Calculate the area using a modified formula.

The modified formula shown below may be used to determine the area of a circle when you are aware of a sector’s area and the measurement of its central angle:

S(cir)= S(sec) 360/C

S(cir) denotes the whole circle’s surface area.
S (sec) is the area of the sector.
C is the central angle measure

Step 5: Enter the values

In this illustration, you have been informed that the sector’s size is 15 and that the sector’s center angle is 45°. Add these to the equation, then solve as follows: