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

Where, r is the radius

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

\[ d = 2 \times 5 = 10 \text{ cm} \]