Radius Of A Circle

The radius of a circle is a line segment with one end at the center of the circle, and the other end on the circle itself. The radius is identified with a lower-case, italic r.

Radius Of A Circle Definition In Math

Radius Of A Circle Formula

The formula you use depends on what is known about the circle. Below are three different formulas you can use to find the radius, r, of a circle.

Radius Formulas

If given... Then...
Circumference (C) r = C2π
Area (A) r = Aπ
Diameter (d) r = d2

The relationship between radius and diameter is an important one to know when learning to how to calculate the radius.

Since the radius is a line segment from the center to the circle, and the diameter, d, is a line segment from on side of a circle through the center of a circle and out to the other side of the circle, it follows that a radius is 12 a diameter.

How To Find The Radius Of A Circle

To find the radius of a circle, plug the given information into the correct formula. You can find the radius of any circle if you are given the circumference, area, or diameter.

Radius Of A Circle Formulas

How To Find Radius From Circumference

No matter the size of the circle, the relationship of the radius to the circumference, C, is a constant, giving us the formula to find radius from circumference:

r = Circumference (C)2π

How To Find Radius From Circumference

You can also calculate the circumference of a circle with a given radius by using algebra to isolate the C in our formula.

The radius to circumference formula is: C = 2πr

Radius Of Circle From Area

You can use the area to find the radius and the radius to find the area of a circle. The area of a circle is the space it occupies, measured in square units.

Given the area, A, of a circle, its radius is the square root of the area divided by pi:

r = Aπ

The formula for radius to area is: A = πr2

How To Find Radius From Area

How To Find Radius From Diameter

If you know the diameter of a circle, you can find its radius by dividing the diameter by 2:

r = d2

This is the simplest formula you can use to get the radius.

How To Find Radius From Diameter

If you need to go from radius to diameter, multiply radius times 2: d = 2r

Radius Of A Circle Example

  1. A circle has a diameter of 6 inches. What is its radius?
  2. A circle has a radius of 98 feet. What is its diameter?
  3. A circle with a circumference of 365 meters will have a radius of how many meters?
  4. A circle with a radius of 11 inches will have a circumference of how many inches?
  5. With a radius of 41 mm, a circle will have an area equal to, what?
  6. What is the radius of the following circle?
  7. Radius Of A Circle Example Problem

We don't like to talk in circles, but make sure you work these out before checking the answers below!

  1. The radius of a 6 inch circle is 3 inches.
  2. A circle has a radius of 98 feet, so its diameter must be 196 feet.
  3. A circle with a circumference of 365 meters will have a radius of 58.4 meters.
  4. A circle with a radius of 11 inches will have a circumference of 69.12 inches.
  5. With a radius of 41 millimeters, a circle will have an area of roughly 5,281.02 square millimeters or mm2.
  6. The radius of the circle in the image above is 75 m.

Next Lesson:

Area Of A Circle

What you learned:

After working your way through this lesson and video, you have learned:

  • The definition of radius in geometry
  • The radius of a circle formula
  • How to find the radius of a circle based on the given information
  • Hot to use the radius to calculate the diameter, circumference, and area of a circle
Instructor: Malcolm M.
Malcolm has a Master's Degree in education and holds four teaching certificates. He has been a public school teacher for 27 years, including 15 years as a mathematics teacher.
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Ashburn, VA

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