Circle (Diameter v. Radius)

We usually measure the size of circles by either their diameter or their radius.  If you buy a circular rug, for example, and check its measurements, they will almost certainly report either the diameter or radius of the rug.  Everyone once in a while you'll see a circular object defined by its circumference, which is the distance around the outside of the circle.

The radius of a circle is the distance from the center to the circumference of a circle.  Any line from the center of a circle to a point on the circumference (the outside) is a radius.  Every radius in a circle is the same length.

The diameter of a circle is the distance, through the center, from one point on the circumference to another point on the circumference of a circle.  Because it goes through the circle, every diameter contains two radii.  Any line from the one point on the circumference of a circle to point on the circumference that goes through the center of the circle, is a diameter. Every diameter of a circle is the same length.  A diameter of a circle is always twice the length of a radius of the same circle.  Diameter = 2(radius)  or $d=2r$.

A chord is any line that goes from one point on the circumference of a circle to another.  Chords that go through the center are called diameters.  If a chord does not go through the center it is just called a chord.

Diameter	Radius	Chord

Look at the circle above with the blue diameter through the middle.  That line goes from one point on the edge or circumference, to the another, through the center.  Either half of the diameter (from the center to either side) is a radius.  Each radius is half as long as the diameter.  So, if the diameter is 10 cm long, each radius is 5 cm long. If one diameter is 10 com long then every diameter in the circle is 10 cm long and every radius in that circle is 5 cm long. 

Look at the circle with the radius.  Note that the radius does not go straight across the circle like the ones that make up half of the diameter.  A radius is any line from the center of a circle to the circumference. 

Finally, look at the chord.  Note that that chord is shorter than the diameter.  But, you could draw another chord that is even shorter.  Because there are not rules about chords having to go through the center of a circle, they come in all different sizes. And, because they are not standard, most circle calculations and measurements use either radius or diameter.  For instance, if you want to figure out the circumference or area of a circle, you need to know either the diameter or radius length.  To learn more read the Circumference or Area of Circles lessons.