# Diameter Formula

Before we begin with the diameter formula, let us recall what is a diameter. Diameter is one of the important parts of a circle. The straight line connecting a point from one end of the circle to a point on the other end of the circle and passing through the center is called a diameter. Since there are infinite points on its circumference, this means that a circle has an infinite number of diameters and each diameter of the circle has an equal length..

## What Is the Diameter Formula?

To understand the diameter formula. Let us consider the different cases of the Diameter Formula. We can find the diameter of a circle when the radius, area, or circumference is known.

### Diameter Formula Using Radius of a Circle

Formula 1: The diameter is twice the length of the radius.

Diameter Formula = 2 × Radius

### Diameter Formula Using Circumference of a Circle

Formula 2: The diameter is the ratio of circumference to π.

Diameter Formula = Circumference ÷ π

### Diameter Formula Using Area of Circle

Formula 3: We can derive the diameter formula using the area formula which is

Area = π(Radius)^{2}

Diameter Formula = 2√Area/π.

## Examples on Diameter Formula

Let us solve some interesting problems using the diameter formula.

Example1: Using the diameter formula find the diameter of a circle whose radius is 24 inches long.

**Solution:**

We will use the first formula to find the diameter of the circle.

Diameter Formula =2×Radius

D=2×24 inches=48 inches

**Answer: **Diameter of the given circle = 48 inches.

**Example 2:** Find the diameter of a circle whose circumference is 8π units. Use diameter formula.

**Solution:**

We will use the diameter formula of the circle when the circumference is given.

Diameter formula = Circumference/π = 8 units

Answer: The diameter of the given circle is 8 units.

**Example 3:** Using the diameter formula, can you determine the value of the radius if the diameter of a circle is 12 units?

**Solution:**

Given : Diameter = 12 Units

We know that diameter is twice the value of the radius. This means the radius is half of the value of the diameter.

Diameter = 2 × Radius

R = D ÷ 2

Radius = 12 ÷ 2 = 6 units

Therefore, radius of circle is 6 units.

## FAQs on Diameter Formula

### What Is the Diameter Formula When Area of a Circle Is Known?

If the area of a circle is given in square units then it is easy to derive the diameter formula as given below:

Area = π(Radius)^{2}

The formula for diameter = 2√Area/π.

### What Is the Diameter Formula When Radius of a Circle Is Known?

If the radius of a circle is given in 'r' units then it is easy to determine the diameter formula as given below:

Diameter formula = 2r.

The radius of the circle is half the diameter of the circle.

### What Is the Diameter Formula When Circumference of a Circle Is Known?

If the circumference of a circle is given in 'C' units then it is easy to derive the diameter formula as given below:

Circumference, C = 2πr.

Diameter = 2r.

The formula for diameter = C/π units

### How To Find Circumference With Diameter Formula?

If a diameter of a circle is given then by substituting the given values in the following diameter formula we can easily find the circumference of a circle.

The formula for diameter = Circumference/π.

C = πd units.

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