r Diameter of a circle definition and calculator- Math Open Reference

# 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

 ENTER ANY ONE VALUE Radius clear Diameter clear Area clear Circumference clear

Use the calculator above 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

1. 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.
2. Click on "show radius". Drag the orange dot at the end of the radius line. Note how the radius is always half the diameter.
3. 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.