# How To Find The Radius Of A Circle?

Do you find difficulty in understanding how to find the radius of a circle while solving your maths problem? Relax a bit, you’ve arrived at the right place! The radius of a circle is defined as the distance from the center of the circle to any point on its circumference. It is often identified with a lower-case italic r. In today’s post, I will focus on how to find the radius of a circle. There are many radius formulas that can be used to find the value of r. Without wasting much time, let’s now check out how to find the radius of a circle in more detail.

Contents

## How To Find The Radius Of A Circle?

Using the following ways, you can easily learn how to find the area of a circle.

• By Using The Diameter
• By Using The Circumference
• By Using The Area
• By Using An Circle Equation
• By Using The Distance Formula
• By Using The Area Of A Sector Formula

If you know the diameter, circumference, or area of the circle, you can easily find the value of r. You can even use the distance formula or area of a sector formula to determine the radius of a circle. If you have very less time to find the value of r, you can even use an online radius of a circle calculator.

## Find The Radius Of A Circle By Using The Diameter

In mathematical language, diameter is a straight line passing from side to side through the center of a circle. If you know the diameter of a circle, you can easily use it to calculate its radius.

Follow these steps to know how to find the radius of a circle with the diameter.

1. Using a ruler, measure the diameter of the circle by passing through the circle’s center.
2. Substitute this value in this diameter formula: D= 2 r.
3. Solve this equation to get the value of r.

A radius is always half of its diameter. So, you can even use this formula: r = D/2 to calculate the radius of a circle.

## Find The Radius Of A Circle By Using Circumference

The term circumference is defined as the enclosing boundary of a curved circle. Basically, it’s the linear distance of a circle’s edge. Follow these steps to know how to find the radius of a circle with the circumference.

1. First, let’s recall the circumference formula which is: C = 2πr.
2. Here, C is the circle’s circumference, and π is pi (a special number that equals 3.14).
3. Substitute the value of C and π in this equation.
4. Now, solve this equation to obtain the value of r.

If you have a scientific calculator, you can press the π button and enter the circle’s circumference. The final result will be the radius of a circle.

## Find The Radius Of A Circle By Using The Area

Surprisingly, you can use the circle’s area to find its radius. The area of a circle is defined as the space it occupies and is measured in square units. You can follow these steps to know how to find the radius of a circle with the area.

1. First, recall the area of a circle formula which is: A = πr2.
2. Here, A represents the area of a circle and π is pi (a special number that equals 3.14).
3. Substitute the value of A and π in this equation.
4. Now, solve this equation to get the value of r.

In the end, the equation will become r = square root (A/ π). Make sure you don’t forget to take the square root of the final value.

You can keep on reading to know how to find the radius of a circle on a graph.

## Find The Radius Of A Circle By Using An Circle Equation

With the help of the equation of a circle, you can easily find the radius of the circle. Follow these steps to know how to find the radius of the circle from an equation.

1. Recall the equation of a circle which is: (x−h)2 ​​​+ (y−k)2 ​=r2.
2. Here, (h, k) are the coordinates of the center of the circle.
3. Solve the equation by substituting the values of h and k.
4. First, find the coefficient of x.
5. Substitute the value of x and then find the value of y.
6. Now, solve the circle equation to get the value of r.

While solving the circle equation, you can rule out the negative sign as a radius of a circle can never be negative.

## Find The Radius Of A Circle By Using The Distance Formula

Do you know how to calculate the radius of a circle with two points? Here, I will be using the Distance formula for coordinate points to find the radius of a circle.

1. Recall the distance formula which is: D = √(x2 – x1)2 + (y2 – y1)2.
2. Here, x and y are the two coordinate points.
3. Substitute the value of x and y in this distance formula and solve the equation.
4. The final result you’ll get will be the diameter of the circle.
5. Make sure you divide the final answer by 2 to get the value of r.

This method is a bit lengthy to get the radius of a circle.

## Find The Radius Of A Circle By Using The Area Of A Sector Formula

The area of a sector is defined as the amount of space enclosed within the boundary of the sector. If you have the value of the area of a sector of a circle, then you can easily find the value of its radius.

Follow these steps to get the value of r by using the area of a sector formula.

1. Recall the area of a sector of a circle formula which is: Asector = 𝚹/ 360 (π) (r2).
2. Here, Asector stands for the area of the sector, 𝚹 is the central angle of the sector, and π is pi.
3. Substitute the values of A, 𝚹, and π in this formula.

Make sure you use your calculator to solve this equation quickly.

## Find The Area Of A Circle

After calculating the radius of the circle, let us move forward to the area of a circle. Follow these steps to know how to find the area of a circle with the radius.

1. The formula for the area of a circle is A = πr2.
2. Here, substitute the value of r and π to solve the equation.
3. The final result you’ll get will be the area of a circle.

You can also calculate the area of a circle if you know its diameter, circumference, or area of a sector.

## Find The Circumference Of A Circle

You can follow these steps to know how to find the circumference of a circle with the radius.

1. The formula for the circumference of a circle is C = 2πr.
2. Here, substitute the value of r and π to solve the equation.
3. The final result you’ll get will be the circumference of a circle.

## FAQ

### What Is Radius In A Circle?

Radius of a circle is the distance from the center of the circle to any point on it’s circumference. It is usually denoted by ‘R’ or ‘r’.

### How Do You Find The Radius Given The Diameter?

Divide the circumference by π, or 3.14 for an estimation. The result is the circle’s diameter. Divide the diameter by 2. There you go, you found the circle’s radius.

### How Do You Find The Radius Without The Circumference?

Just remember to divide the diameter by two to get the radius. If you were asked to find the radius instead of the diameter, you would simply divide 7 feet by 2 because the radius is one-half the measure of the diameter.

### How Do You Find The Radius With The Diameter And Height?

The radius of a cylinder(r) = √(V / π × h), where V is the volume of a cylinder, h is the height of the cylinder, and π(Pi) is a mathematical constant with an approximate value of 3.14.

## Conclusion

In the above post, I’ve explained how to find the radius of a circle in detail. The terms radius and diameter are directly related to each other. Radius is the distance from the center of the circle, while the diameter is the distance across the circle through the center. If you know the diameter of a circle, you can calculate its radius by using D= 2 r. The value of r can also be calculated if you the circumference or area of a circle. Thus, you can now easily solve any maths problems related to circles by learning how to find the radius of a circle!

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