Diameter Formula

The Diameter of a Circle Formula

The formula to calculate the diameter of a circle or a perfectly round shaped figure describes the relationship between its diameter and the radius. The diameter is essentially composed up of two segments that are each a radius. Thus, the diameter formula is Diameter = 2 × the measurement of the radius. You can write this formula in shorthand as d=2r.

That said, calculating a circle's diameter is easy if we are familiar with the other dimensions of the circle i.e.: the radius, the circumference, or the area. However, calculating the diameter is still possible if you don't know any of the above dimensions but you do have a sketch of the circle. 


Complete Representation of a Circle

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Circle with Diameter

The line segment AB within a circle is a diameter. Point C is the midpoint or center of the circle of segment AB. Segments AC and CB are of equal length and are both half the length of the diameter, meaning that each is the radius of the circle. A radius of a circle or sphere is a line segment with one endpoint on the circle and the other endpoint at the center of the circle. It is derived from a Latin term that means ray.

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The Diameter of a Circle Equation

There is just one diameter drawn on circle C. Even though every circle has an innumerable number of possible diameters. Imagine you have to cut a round pizza into two equal pieces. Nevertheless, how you turn the pizza, as long as you make one straight cut right through the center point of the pizza, you will divide it along a diameter.

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How to Calculate Diameter

We can find out the diameter of a circle in the following ways:-


A. Calculate the Diameter of a Circle Using the Radius

If you already know the measure of the radius of the circle, just double it to get the diameter. The radius is the distance from the center point of the circle to its perimeter. As an example, if the radius of the circle is 7 cm, then the diameter of the circle is 7 x 2, or 14 cm.

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B. Calculate the Diameter of a Circle Using Circumference

If you have the measurement of the circumference of a circle, divide it by π and you will get the diameter. The value of π is approximately equal to 3.14 but you must use the calculator to obtain the most accurate results. As an example, if the circumference of the circle is 25 cm, then the diameter is 25 cm/π, or 7.96 cm.

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C. Calculate the Diameter of a Circle Using Area of the Circle

If you have the area of the circle, divide the outcome by π and find its square root in order to get the radius; then multiply by 2 to obtain the diameter. This slides back to maneuvering the formula to find the area of a circle i.e.: A = πr2, to get the diameter. You can modify this into area of a circle diameter formula as below:-

r = √ (A/π) cm.

As an example, if the area of the circle is 12cm2, divide it by π and find the square root.

Using the diameter to area formula, we have 12 / 3.14 = √3.82

So the diameter of the circle is 1.95 x 2 = 3.90 cm.

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Quiz Time 

Q1. Spot the Diameter in the Given Figure 

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  1. F

  2. E

  3. D

  4. B

Ans: 3 (D)


Q2. Find the Value of the Radius of the Circle in the Figure Shown:-

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  1. 40cm

  2. 10cm

  3. 5cm

  4. 20cm

Ans: 2 (10cm)


Solved Examples


Example1:

Find the diameter of a circle with a circumference of 32 cm


Solution1:

To solve this problem, you will require the formula to find the circumference of a circle using the diameter i.e.

C=πd

Now, fill in the given details

32 = (3.14)d

Next, divide both sides by 3.14. Thus, 3.14 will neutralize on the right side of the equation, leaving d. Then divide 32 by 3.14 = 10.19

The answer is, the diameter is 10.19cm.

This also means that the radius is 5.09 cm (10.19/2)


Example2:

The circumference of Susanne’s car tire is given 24 inches. Find out the diameter, closest distance traveled, in feet, after 3 full rotations of the tire?


Solution2:

Given that the circumference = 24

Use the formula: C = πd

24 = πd

D= 24/3.14 = 7.64 inches

The diameter is 7.64 inches

And the closest distance traveled after 3 full rotations = 24 x 3= 72inches

Since, we need to provide the answer in feet, convert the value to feet

12 inches = 1ft

Thus,

72/12 = 6feet

FAQ (Frequently Asked Questions)

1. What is Meant By Diameter?

Are you confused with exactly what is the diameter of a circle? Simply, the diameter of a circle is a segment whose endpoints are situated on the circle and whose midpoint lies in the center of the circle. When we say ' on the circle,' that means on the perimeter (outline) that traces the circle, not the space inside or surrounding that outline. A midpoint of the circle is a point absolutely in the middle of the space within the outline. The center of a circle is also equidistant from every point on the outline of the circle. The distance from the midpoint to a point on the circle is called a radius. You can also easily find the area of a circle using diameter i.e. A=1/4πd2.

2. How the Diameter of a Circle Formula is Derived?

The derivation of finding the diameter using the circumference of a circle has its own significance in terms of pi (π). Here, the Greek notation π denotes a constant, approximately equal to 3.14159, which is equivalent to the ratio of the circumference of any circle or sphere to its diameter. One way of deriving this formula, which emancipated with Archimedes, involves seeing the circle as the limit of a series of regular polygons.