Diameter Formula: Definition, Facts, Examples, Practice Problems

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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

Radius and diameter of a circle

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.

DescriptionFormula
Diameter Formula in terms of radiusDiameter $= 2 \times $Radius
Diameter Formula in terms of circumferenceDiameter $= \frac{Circumference}{\pi}$
Diameter Formula in terms of areaDiameter $= 2\sqrt{\frac{Area}{\pi}}$
Diameter formulas

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

Diameter formula in terms of radius

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

Facts about Diameter Formula

  • 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 formula using radius:

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

Diameter Formula: Definition, Facts, Examples, Practice Problems

Attend this quiz & Test your knowledge.

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
radius
chord
CorrectIncorrect
Correct answer is: chord
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
Correct answer is: 2 units
Radius of a unit circle = 1 unit
Diameter of a unit circle = 2 units
5

Radius is

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.

Frequently Asked Questions about Diameter Formula

No, the diameter of the circle can neither be negative nor zero. It always is a positive value since it represents the length of a line segment.

Yes, the circumference of a circle is directly proportional to the diameter. If the diameter increases, the circumference increases. If the diameter increases, the circumference decreases.

Each circle possesses an uncountable number of the radius that possesses the same length in a circle.

Radius = Diameter $\div$ 2