# Diameter Formula

The line dividing a circle into two equal parts, each known as a semicircle, is known as the diameter. The circle’s centre serves as its diameter’s midpoint. This indicates that it splits the diameter in half, noting the radius of each half. The length of a diameter is equal to twice the length of the radius. To find the diameter of a circle, the Diameter Formula is used. The Diameter Formula is given by 2 × R, R being the radius. Learn more about diameter formula and how to calculate diameter in this article.

## What is Diameter?

The diameter of a circle is a straight line segment that passes through its center and ends on the circle’s boundary. It is the circle’s longest chord, twice as long as the radius.

### Characteristics of Diameter

1. Straight Line: The diameter is a straight line segment.
2. Center of Circle: It passes through the center of the circle.
3. Endpoints on the Circle: The endpoints of the diameter lie on the circumference of the circle.
4. Twice the Radius: The diameter is always twice as long as the radius of the circle.

## Diameter Formula

The diameter of a circle is a fundamental geometric property that is directly related to the radius of the circle. The formula for the diameter (d) can be derived from the radius (r) and is given by:

D = 2r

### Diameter Formula Using Radius of a Circle

If the radius of a circle is known, the diameter can be found using the formula:

D = 2r

### Diameter Formula using Circumference

The diameter of a circle can be derived from its circumference using the following formula:

d=C/π

Where, C is circumference

### Diameter Formula with Area of Circle

The diameter of a circle can be derived from its area using the following formula:

$d = 2 \sqrt{\frac{A}{\pi}}$

where:

• $$d$$ is the diameter of the circle.
• $$A$$ is the area of the circle.
• $$\pi$$ (pi) is a mathematical constant approximately equal to 3.14159.

### Derivation

The area of a circle is given by the formula:

$A = \pi r^2$

To find the diameter from the area, we first need to express the radius ($$r$$) in terms of the area. Rearrange the area formula to solve for $$r$$:

$r^2 = \frac{A}{\pi}$

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

Since the diameter ($$d$$) is twice the radius:

$d = 2r = 2 \sqrt{\frac{A}{\pi}}$

## Example Using Diameter Formula

Example 1. If the area of a circle is 50 square centimeters, find the diameter

Solution:

Diameter can be calculated as follows:

$d = 2 \sqrt{\frac{50}{\pi}} \approx 2 \sqrt{\frac{50}{3.14159}} \approx 2 \sqrt{15.92} \approx 2 \times 3.99 \approx 7.98 \text{ cm}$

Example 2: If the circumference of a circle is 31.4 cm, Find the diameter

Solution:

the diameter can be calculated as follows:

$d = \frac{31.4}{\pi} \approx \frac{31.4}{3.14159} \approx 10 \text{ cm}$

Example 3: If the radius of a circle is 5 cm, Find the diameter is:

Solution:

The diameter is

$d = 2 \times 5 = 10 \text{ cm}$

### 1. What is the formula for the diameter of a circle given the radius?

The formula for the diameter ($$d$$) of a circle given the radius ($$r$$) is $d = 2r$

### 2. What is a diameter of a circle?

A diameter of a circle is a line inside a circle that can divide it into two equal parts and it is twice the length of the radius. Each part of the circle divided by the diameter is known as a semicircle.

### 3. How to calculate a radius?

If the diameter of a circle is known then the formula for radius is diameter divided by 2.

### 4. How can you find the diameter of a circle from its circumference?

The diameter ($$d$$) can be calculated from the circumference ($$C$$) using the formula: $d = \frac{C}{\pi}$

### 5. How is the diameter related to the circumference?

The circumference ($$C$$) is related to the diameter ($$d$$) by the formula:$C = \pi d$. Thus, the diameter can be derived from the circumference: $d = \frac{C}{\pi}$