Diameter (of a circle)
The distance across a circle through its center point.
Try this Drag the orange dot. The blue line will always remain a diameter of the circle.
The diameter of a circle is the length of the line through the center and touching two points on its edge.
In the figure above, drag the orange dots around and see that the diameter never changes.
Sometimes the word 'diameter' is used to refer to the line itself. In that sense you may see "draw a diameter of the circle".
In the more recent sense, it is the length of the line, and so is referred to as "the diameter of the circle is 3.4 centimeters"
The diameter is also a
chord.
A chord is a line that joins any two points on a circle.
A diameter is a chord that runs through the center point of the circle.
It is the longest possible chord of any circle.
The center of a circle is the midpoint of its diameter. That is, it divides it into two equal parts, each of which is a
radius of the circle.
The radius is half the diameter.
If you know the radius
Given the radius of a circle, the diameter can be calculated using the formula
where:
R is the radius of the circle
If you know the circumference
If you know the circumference of a circle, the diameter can be found using the formula
where:
C is the circumference of the circle
π is Pi, approximately 3.142
If you know the area
If you know the area of a circle, the diameter can be found using the formula
where:
A is the area of the circle
π is Pi, approximately 3.142
Calculator
Use the calculator on the right to calculate the properties of a circle.
Enter any single value and the other three will be calculated.
For example: enter the diameter and press 'Calculate'. The area, radius and circumference will be calculated.
Similarly, if you enter the area, the radius needed to get that area will be calculated, along with the diameter and circumference.
Related items
Radius
The radius is the distance from the center to any point on the edge.
As you can see from the figure above, the diameter is two radius lines back to back,
so the diameter is always two times the radius.
See radius of a circle
Circumference
The circumference is the distance around the edge of the circle. See
Circumference of a Circle for more.
Things to try
 In the figure above, click 'reset' and drag any orange dot. Notice that the diameter is the same length at any point around the circle.
 Click on "show radius". Drag the orange dot at the end of the radius line. Note how the radius is always half the diameter.
 Uncheck the "fixed size" box. Repeat the above and note how the radius is always half the diameter no matter what the size of the circle.
Thales' Theorem
Thales' Theorem states that the diameter of a circle
subtends a
right angle
to any point of the circle's circumference. (see figure on right).
No matter where the point is, the triangle
formed is always a right triangle.
See Thales Theorem for an interactive animation of this concept.
Other circle topics
General
Equations of a circle
Angles in a circle
Arcs
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