Radius of a Circle Calculator

Created by Maciej Kowalski, PhD candidate
Reviewed by Hanna Pamuła, PhD candidate
Last updated: Mar 15, 2022

Welcome to the radius of a circle calculator, where we'll focus on how to find the radius of a circle based on other data: the circumference, area, or diameter. The concept is not too difficult, and, in essence, it's enough to follow a few simple steps that we describe in detail below, all of which take you straight to a radius of a circle formula.

What is the radius of a circle?

By definition, a circle is a 2-dimensional shape consisting of all the points lying at the same, fixed distance from a given point. That distance is called the radius of the circle.

All the special lines of a circle, including the radius (green).

Now that we know what the radius of a circle is (marked with green) let's get familiar with the rest of the lines.

  • Circumference (blue) is the perimeter length of the circle.
  • Diameter (red) is a line with both endpoints on the circle going through the center.
  • Chord (purple) is any line with both endpoints on the circle.

In some sense, the radius is the MVP here: it plays a crucial role in all the formulas, so it's essential to learn how to find the radius of a circle. Fortunately, the task is fairly simple. After all, since the MVP is there in all the equations, we can get the radius of a circle from the area, or we can get the radius of a circle from the circumference.

How do you find the radius of a circle?

There are three radius of a circle formulas, depending on what number you know:

  1. Radius of a circle from area: if you know the area A, the radius is r = √(A / π).
  2. Radius of a circle from circumference: if you know the circumference c, the radius is r = c / (2 * π).
  3. Radius of a circle from diameter: if you know the diameter d, the radius is r = d / 2.

Fortunately, our radius of a circle calculator handles all of the above cases. Even better! You don't have to choose which radius of a circle formula you need: simply input the measurement you have into the tool, and it will automatically process the radius of a circle equation tailored for your needs.

FAQ

What is the radius of a unit circle?

By definition, a unit circle is a circle with radius 1. It is a general object used in mathematics (e.g., when explaining trigonometric functions), so usually, the 1 has no unit assigned.

What is the radius of a 6-foot circle?

To find the radius whose circumference is equal to 6 feet, we follow the steps below:

  1. Write the circumference as c = 6 ft.
  2. Recall the formula for the radius of a circle from circumference: r = c / (2 * π).
  3. Inject the circumference into the equation: r = (6 ft) / (2 * π) = 3/π ft.
  4. If needed, substitute π ≈ 3.14: r = 3/π ft ≈ 0.96 ft.
Maciej Kowalski, PhD candidate
Image of a circle with radius, diameter, circumference and area marked.
Circumference (c)
in
Area (A)
in²
Diameter (d)
in
Radius of the circle
Radius (r)
in
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