# Diameter Formula: Definition, Facts, Examples, Practice Problems

## What Is the Formula for Diameter?

To determine the length of the diameter of a circle, we use the diameter formula. The diameter of a circle is twice the length of its radius.

Diameter $= 2 \times$ Radius

What is the diameter of a circle?

A diameter is a line segment that passes through the center of a circle connecting distinct points on the boundary of the circle. A circle has infinite diameters since there are an infinite number of points on the circumference of a circle.

## Diameter of a Circle: Formulas

We can write the formula for diameter in different ways since we can express it in terms of radius, circumference, and area.

## How to Calculate Diameter

We must have information about the radius or the other above-mentioned measurements to calculate the diameter of the circle. We can calculate the diameter using the circle’s distinct diameter formula. They are as follows.

Finding diameter using circumference

Circumference of a circle $= 2\pi r$

Since $2r =$ diameter $= d$, we write the above formula as:

Circumference of a circle $= \pi d$

Thus, by rearranging the formula, we get the circle diameter formula using circumference,

Diameter $= \frac{Circumference}{\pi}$

Example: If the circumference of a circle is 72 units, find the diameter.

$C = 72$ units

Diameter $= d = \frac{72}{\pi}$

$d = \frac{72}{3.14}$

$d = 22.92$ units

Finding diameter using radius of a circle

Let’s understand how to find diameter with radius.

The radius is the distance from the center of a circle to the boundary.

Therefore, the diameter formula using radius is given as

Diameter $= 2 \times$ Radius of the circle

Example: A circle has a radius of 14 units. Find its diameter.

Diameter $= 2\times$ Radius $= 2 \times 14 = 28$ units

Finding diameter using area of circle

Area of a circle is the total 2D region covered by the circle.

Area of a circle $= \pi r^{2}$

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

Radius $= \sqrt{\frac{Area}{\pi}}$

Diameter $= 2 \times$ Radius

Diameter $= 2 \times \sqrt{\frac{Area}{\pi}}$

• Diameter is the longest chord of a circle.
• Not every chord is a diameter of the circle, but every diameter of the circle is a chord.
• A chord is the line segment that joins the two points on the circle’s circumference.
• Any tangent line identified to a circle at its point of contact must be perpendicular to its diameter. Thus, the tangent line and the circle’s diameter form a 90 degree angle between them.

## Conclusion

In this article, we learned different formulas to find the diameter of a circle. We can express the diameter of a circle in terms of radius, area, and also the circumference. Let’s solve a few examples and practice MCQs based on the diameter formulas.

## Solved Examples of Diameter Formula

1. The radius of a circle is given as 25 units. Find the diameter of the circle.

Solution:

Radius $= 25$ units

Diameter  $= 2\times$ Radius

Diameter $= 2 \times 25$

Diameter $= 50$ units

Therefore, the diameter of the circle with the radius of 25 units is 50 units.

2. If the circumference of a circle is 5 units. Find the diameter of the circle.

Solution:

Circumference of the circle $= 5\pi$ units

Using the diameter formula with circumference, we get

Diameter $= \frac{Circumference}{\pi}$

Diameter $= \frac{5}{\pi}$

Diameter $= 5$ units

3. Find the radius of the circle using the diameter formula when the diameter given is 14 inches.

Solution:

Diameter $= 14$ inches

Diameter $= 2 \times$ Radius

By altering the formula, we get

Radius $= \frac{Diameter}{2}$

Radius $= \frac{14}{2}$

Radius $= 7$ inches

4. Find the diameter of the circle with area 72 unit2.

Solution:

Area $= 72\; unit^{2}$

$\pi r^{2} = 72$

$r^{2} = \frac{72}{3.14}$

$r ≈ 4.78$ units

Thus, diameter $= 2r ≈ 9.57$ units

## Practice Problems on Diameter Formula

1

### The diameter formula using the area of the circle is

Radius $= 2\sqrt{\frac{Area}{\pi2}}$
Radius $= 2\sqrt{\frac{2 \times Area}{\pi}}$
Radius $= 2\sqrt{\frac{Area}{\pi}}$
Radius $= 2\sqrt{\frac{Area}{\pi^{2}}}$
CorrectIncorrect
Correct answer is: Radius $= 2\sqrt{\frac{Area}{\pi}}$
The formula to find the diameter of the circle using area is expressed as
Radius $=2\sqrt{\frac{Area}{\pi}}$
2

### The formula for the circumference of the circle is

Circumference$= \pi \times Diameter$
Circumference$= \frac{Diameter \times \pi}{2}$
Circumference$= \pi \times Radius$
Circumference $= \pi \times Radius^{2}$
CorrectIncorrect
Correct answer is: Circumference$= \pi \times Diameter$
The circumference of the circle can be calculated using the formula Circumference $= \pi \times Diameter$.
3

### Diameter is the longest ________ of a circle.

tangent
secant
chord
CorrectIncorrect
Diameter is the longest chord of a circle.
4

### Diameter of a unit circle is

1 unit
0.5 unit
2 units
4 units
CorrectIncorrect
Radius of a unit circle = 1 unit
Diameter of a unit circle = 2 units
5

half of the diameter’s length.
square of the diameter’s length.
the square root of the diameter’s length.
None of the above
CorrectIncorrect
Correct answer is: half of the diameter’s length.
Radius is defined as half of the length of the circle’s diameter.

Radius = Diameter $\div$ 2