Circle area Calculator

Circle Area Calculator will help you to calculate your circle area and circumference. You have to provide the radius of the circle and hit the calculate button. You will get the results of a circle area and Circle Circumference

Area & Circumference Circle Calculator

Fill the form with your data click on calculate button to calculate


radius
Units
Area & Circumference Circle Calculato
Radius of Circle r 0
Area π r 20
Circumference 2πr 0

What is Circle?

A circle is a geometrical figure in a plane whose points are equidistant from a fixed point. The fixed point is the center of the circle. The closed path traced by a point that keeps its distance from the fixed center is a circle. The distance from the center is the radius of the circle.

In our day-to-day life, we observe and use some objects which are circular in shape. For example, wheel of a car, bangle, clock, button, plate, coin, etc. We notice that the second's hand of the watch goes rapidly in a round path. The path traced by the tip of the second's hand is a circle. We use circular bodies in a variety of ways.

Put a coin on a piece of paper and press it with the left thumb in the middle. Now, move a pencil around the coin. Remove the coin and notice the closed curved line. The traced line is a circle.

Draw Circle with Pencil Compass

A pencil compass is used to draw a circle precisely. Put its pointed leg on a point on a sheet of paper. Open the other leg to some distance. Keeping the pointed leg fixed, rotate the other leg through one revolution. The closed figure traced by the pencil on paper as shown in the picture is a circle. So, we can draw a circle at a fixed distance from a fixed point. The fixed point is called the center of the circle and the fixed distance is called the radius of the circle.

Chord and Arc of a circle with Example

An arc is the piece of the circle between any two points of the circle. Look at the pieces of the circle between two points A and B in the figure. We find that there are two pieces, one comparatively larger and the other smaller. The larger one is called the major arc and the smaller one is called the minor arc. 

Chord and Arc of Circle

In the above figure, a circle is drawn with the center at O. Taking any two pointsP, Qon the circle, draw their joining line segment PQ. The line segment PQ is called a chord of the circle. The chord divides a circle into two parts.

Taking two points Y, Z on two sides of the chord, and then we get two parts is PYQand PZQ. Each part of the circle divided by the chord is called an arc of a circle or in brief an arc. In the picture, two arcs, arc PYQ,and arc PZQ are produced by the chord PQ.

The joining line segment at any two points of a circle is the chord of the circle. Each chord divides a circle into two arcs.

How do you find the length of an arc of a circle?

Assuming you want the length of an arc in terms of the radius and central angle, you would use the following formula:

Length of Arc = r * θ

Where r is the radius of the circle and θ is the central angle in radians.

Diameter and Circumference

In the figure, such chord AB of a circle is drawn which passes through the center at O. In that case we call the chord diameter of the circle. The length of a diameter is also called the diameter.

Diameter and Circumference of Circle

The arcs made by the diameter AB are equal; they are known as a semi-circle. Any chord that A passes through the center is a diameter. The diameter is the largest chord of the circle. Half of the diameter is the radius of the circle.

Obviously, the diameter is twice the radius.

The complete length of the circle is called its circumference. That means, starting from a point P, the distance covered along the circle until you reach point P, is the circumference.

The circle is not a straight line, so its circumference cannot be measured with a ruler. We can apply an easy trick to measure the circumference, draw a Circle on art paper and cut along the circle. Mark a point on the circumference. Now, draw a line segment on paper and put the circle in an upright position so that the marked point can coincide with the endpoint of the line segment.

Now roll the circle along the line segment until the marked point touches the line segment again. Locate the touching point and measure the length from the other end of the line segment. This is the length of the circumference.

Observe that the diameter of a small circle is small; so is the circumference. On the other hand, the diameter of a larger circle is large, the circumference is also larger.

Circumference of a circle 

The length of a circle is called its circumference. Let, r be the radius of a circle, its c= 2πr, where 3.14159265••• which is an irrational number. Value of 3.1416 is used as the approximate, Therefore, if the radius of a circle is known, we can find the approximate value of the circumference of the circle by using the value of Example 18. The diameter of a circle is 26 cm. Find its circumference. 

How do you find the circumference of a circle?

There are a few different ways that you can find the circumference of a circle. 

If you know the diameter of the circle, you can simply multiply it by pi (3.14). So, if the diameter is 8 inches, the circumference would be 8 x 3.14, or 25.12 inches. 

If you know the radius of the circle, you can multiply that by 2 and then multiply it by pi. So, if the radius is 5 inches, the circumference would be 5 x 2 x 3.14, or 31.4 inches. 

You can also use the formula C = pi x d, where C is circumference and d is diameter.

How do you find the diameter of a circle?

To find the diameter of a circle, one could use a ruler or measuring tape to measure the distance from one side of the circle to the other. The diameter would be the length of this line.

The ratio of Circumference and Diameter of a Circle (  π PI )

Let us see if there is any relationship between the diameter and the circumference of circles. The ratio of the circumference and the diameter of a circle is constant. This ratio is denoted by the Greek letter π (PI).

Thus, if the circumference and the diameter are denoted by c and d respectively, we can say that the ratio is

c ⁄ d = π

c = πd

We know that diameter (d) of a circle is twice the radius (r) i.e., d = 2r; Therefore, 2r. Since ancient times mathematicians put effort into the evaluation of approximately. Indian mathematician Arya Bhatta (476-550 AD) estimated (PI) as 62832/20000 which is approximately 3.1416. Mathematician Sreenibash Ramanujan (1887-1920) estimated PI correct to million places after the decimal. Exactly speaking, PI is an irrational number. In our day-to-day life, we approximate use PI by 22/7

 

Example 1. The diameter of a circle is 10 cm. What is the circumference of the circle?

Solution: 

Diameter of the circle, d = 10 cm

Circumference of the circle =  πd

= 3.14 x 10 cm

=314 cm

 

Example 2. What is the circumference of the circle with a radius of 14 cm?

Solution:

The radius of the circle, r = 14 cm

Circumference of the circle =  2πr

Therefore, the circumference of the circle is 88 (2 x 3.14 x 14 ) cm.

 

Relationship between the radius and the circumference of a circle

The relationship between the radius and the circumference of a circle is that the circumference is equal to 2 times the radius times pi.

Area of a Circle Formula

The area of the region in a plane bounded by a circle is known as the circular region. 

Area of the circle = (Half of the circumference) x radius

Area of the circle = 1 ⁄ 2  x 2 π r x r

Area of the circle =  π r² 

 

Example. What is the area of a circular garden of diameter 9.8 m?

Solution:

The diameter of the circular garden, d = 9.8 m

The radius of the circular garden,  r = 9.8 ⁄ 2 = 4.9 m

Area of  the circular garden =  π r 2   = 3.14 x 4.9 x 4.9 = 75.39 square metre

Relationship between the radius and the area of a circle

The area of a circle is directly proportional to the square of the radius. This means that, as the radius increases, the area of the circle will also increase.

 

How do you calculate area of a circle?

The basic formula to calculate the area of a circle is: 

Area of the circle =  π r², where r is the radius of the circle. 

What is the area of a 1.5 inch circle?

Solution: The diameter of the circle, d= 1.5 inch

The radius of the circle, r= d/2 = 1.5 / 2 = 0.75 inch

The area of the circle = π r² = 1.76715 square inches (π = 3,1416)

What is the area of a 20cm circle?

Solution: The diameter of the circle, d= 20cm

The radius of the circle, r= d/2 = 20 / 2 = 10cm 

The area of the circle = π r² = 314.16 square centimeters

What is radius of circle ?

In geometrical term, the radius is the line segments from the centre to the perimeter of the circle.

How do you find the radius of a circle given the area?

If you know the area of the circle, you can use the formula:

A = πr^2

to solve for the radius. In this equation, A is the area of the circle and r is the radius. π is a mathematical constant with a value of 3.14159.

To use the formula, simply plug in the known value for the area and solve for the radius. For example, if the area of the circle is 9, then:

9 = πr^2

r^2 = 9/π

r = √(9/π)

r ≈ 1.5