Diameter of a Circle
The diameter of a circle is a line that passes through the center and meets the circumference at opposite ends. It is twice as long as the radius of the circle. In other words, the diameter of a circle is the line that passes through the center and divides the circle into two equal parts. Let us learn more about the diameter definition, the diameter formula, and learn how to find the diameter of a circle in this article.
| 1. | What is Diameter of a Circle? |
| 2. | Diameter of Circle Formula |
| 3. | How to Find the Diameter of a Circle? |
| 4. | Diameter vs Radius |
| 5. | FAQs on Diameter |
What is Diameter of a Circle?
The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints lie on the circumference of the circle. The diameter is also known as the longest chord of the circle.
Diameter of a Circle Definition
The diameter is defined as twice the length of the radius of a circle. The radius is measured from the center of a circle to one endpoint on the boundary of the circle, whereas, the distance of diameter is measured from one end of the circle to a point on the other end of the circle, passing through the center. It is denoted by the letter D. There are infinite points on the circumference of a circle, this means that a circle has an infinite number of diameters, and each diameter of the circle is of equal length.
Diameter Symbol
Ø is the symbol that is used in engineering to represent diameter. This symbol is commonly used in technical specifications and drawings. A Ø25 mm means the diameter of the circle is 25 mm.
Diameter of Circle Formula
We all know that diameter is a part of a circle. Let us understand a few terms before we learn the formula for the diameter of a circle.
- The radius (r) is the length of the line segment from the center of the circle to an endpoint on the circle.
- Circumference (C) refers to the enclosed boundary of the circle. It is also known as the perimeter of the circle.
- The area of a circle is the total space present inside the boundary of a circle. It is calculated using the formula πr2, where 'r' is the radius.
We can derive the diameter formula from the circumference, area, and radius of the circle.
Diameter of a Circle Using Circumference
We can easily derive the diameter formula from the circumference. The formula for the circumference of a circle is C = πd; here, C = Circumference, d = Diameter of a circle, π = 22/7 or 3.142 approx. The diameter formula using circumference is,
Diameter = Circumference ÷ π
Diameter of a Circle Using Radius
Radius is the length of the line segment from the center of the circle to an endpoint on the circle and diameter is twice the length of the radius of the circle. Using this definition, the formula for the diameter is D = Radius × 2.
Diameter Formula Using Area of Circle
We can derive the diameter of a circle formula using the area of the circle formula that is, area (A) = π(Radius)2. By substituting the value of radius as D/2, we get, A/π = (D/2)2
⇒ D/2 = √(A/π)
⇒ D = 2 × √(A/π)
Hence, the diameter of the circle formula using area, D = 2√Area/π
How to Find the Diameter of a Circle?
The diameter of a circle can be calculated if the radius, circumference, or area is given. Follow the steps given below to find the diameter of a circle:
- Step 1: The first step is to identify the parameters that are given in the question: radius, area, or circumference.
- Step 2: Apply the appropriate formula from the three formulas discussed in the section given above.
- Step 3: Simplify and get the answer.
Let us try using the formulas mentioned above in an example to find the diameter. Observe the example given below.
Example: Find the diameter of the circle whose radius is 3 units.
Solution:
Given: Radius of the circle = 3 units
The diameter of the circle is = 2 × Radius
= 2 × 3 = 6 units
Therefore, the diameter of the circle is 6 units.
Diameter vs Radius
As we have already discussed, the length of the diameter is twice of radius. There are some similarities and differences between diameter and radius. Before moving on to the difference between diameter and radius, let us first talk about their similarities. Both diameter and radius are parts of a circle that define various properties like the size of the circle, circumference, and area of a circle. They share a relationship in the form of an equation, Diameter = 2 × Radius.
Observe the table given below to understand diameter vs radius.
| Diameter | Radius |
|---|---|
| The diameter of a circle is twice its radius. | Radius is half of the length of the diameter. |
| For any circle, length of diameter > length of the radius. | The length of the radius is smaller than the diameter. |
| It starts from the boundary of the circle and ends at the boundary itself. | It starts from the center and touches the circle's circumference at a point. |
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FAQs on Diameter
What is the Diameter of a Circle?
A diameter is a straight line that passes through the center of a circle and divides the circle into two sections/semicircles. It is the longest chord of the circle that meets the circumference at opposite ends.
Which Symbol is Used to Represent Diameter?
The symbol used to represent the diameter in engineering is ⌀. It is often referred to as 'phi'. This phi symbol is used to describe the diameter of a circular section. For example, "⌀20" means the diameter of a circle is 20 units in dimensions.
What are Radius and Diameter?
The radius and diameter of a circle are two important parts of a circle that are interdependent on each other. The radius of a circle is a line segment that starts from the center of a circle and ends at the circumference of the circle. It is half the length of the diameter of a circle, i.e., Radius = Diameter/2. The diameter of a circle is a line segment that passes through the center of a circle and has two endpoints at the circumference. It is twice the length of the radius of a circle, i.e., Diameter = 2 × Radius.
How to Calculate Diameter?
The diameter of a circle can be calculated according to the given parameters. If the parameters like radius, circumference, or area are given then we can directly use the following formulas.
- Diameter = Circumference ÷ π (when the circumference is given)
- Diameter = 2 × Radius (when the radius is given)
- Diameter = 2√[Area/π] (when the area is given)
What is an Example of a Diameter?
If you observe the wheel of a cycle, the spikes running from one end to another end through the center are an example of diameter. We can relate this to the diameter of a circle, as the diameter is the line segment that starts from one end of a circle and ends at the other end of the circle passing through the center.
How to Find Diameter from Circumference?
If the circumference of a circle is known then we can easily find the value of the diameter by substituting the values in the formula: Diameter = C ÷ π; where 'C' is the circumference and the value of π is 22/7 or 3.14 approximately.
How to Find the Area of a Circle With the Diameter?
The area of a circle is calculated with the help of the formula: Area of circle = πr2. If the diameter is given we can find the radius by dividing the value of diameter by 2. After getting the radius, we can substitute its value in the formula: Area of circle = πr2 to get the area of the circle or directly apply the area formula with diameter, A = π(d/2)2 = πd2/4
What is the Use of Diameter to Circumference Calculator?
The diameter to circumference calculator is an online tool used to determine the value of the circumference of a circle. In the diameter to circumference calculator enter the dimension of the diameter and get the value of circumference within a few seconds. You can also try the diameter calculator for direct calculations.
What is the Diameter of a Circle 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 of the circle formula. The relationship between a radius and a diameter is expressed by the formula, diameter = 2 × radius.
What is Half of a Diameter of a Circle Called?
The diameter of a circle is a line segment from one end of the circle to the other end of the circle passing through the center of the circle. Whereas, the radius of a circle is the length of the line segment from the center of a circle to a point on the circumference of the circle. Hence, the radius is half of the diameter of a circle.
How is Diameter Related to the Radius of the Circle?
The radius of a circle is half the diameter. The relation between radius and diameter can be mathematically expressed in the formula: Diameter = 2 × radius.
Is Diameter Half of Radius?
No, the diameter is not half of the radius. It is twice the radius of a circle. It is represented by the formula: Diameter = 2 × Radius.
How to Measure the Diameter of a Circle?
The diameter of a circle can be measured using a scale (ruler). The diameter represents the distance or length of the line segment from one end of the circle to the other end of the circle passing through the center of the circle. In case the radius of the circle is known, then the diameter can be calculated using the formula, Diameter = 2 × Radius.
How to Convert Diameter to Radius?
In order to convert diameter to radius, we use the formula, Radius = Diameter/ 2 because we know that radius is always half the value of the diameter of a particular circle. For example, if the diameter of a circle is 8 units, then the radius = 8/2 = 4 units.