Radius of a Circle Calculator

Q: What is the radius of a unit circle?

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

Q: 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: Write the circumference as c = 6 ft . Recall the formula for the radius of a circle from circumference: r = c / (2 × π) . Inject the circumference into the equation: r = (6 ft) / (2 × π) = 3/π ft . If needed, substitute π ≈ 3.14 : r = 3/π ft ≈ 0.96 ft .

Creators

Maciej Kowalski, PhD candidate

Maciej KowalskiPhD candidate

Research Gate

Maciej holds a PhD in Theoretical Mathematics from the Polish Academy of Sciences. He loves patterns and structure, be it in datasets, equations, or everyday life. He is curious and meticulous, and balances his analytical side with a passion for fantasy, CrossFit, good cinema, and a diverse array of games. See full profile

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Reviewers

Hanna Pamuła, PhD

Hanna PamułaPhD

Website

Research Gate

Hanna (Hania) Pamuła holds a Ph.D. in Bioacoustics / Mechanical Engineering, obtained at AGH University of Science and Technology. She has participated in research work in labs in France and the UK and presented papers at several international conferences. Hania has a penchant for photography and graphic design. When not in the office, she’s probably traveling, hiking, or out in the field, watching birds and recording their calls. See full profile

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Welcome to the radius of a circle calculator, where we'll focus on how to find the radius of a circle from the circumference, area, or diameter. The concept is not too difficult, and, in essence, it's enough to follow a few simple steps 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 known as 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.
The 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 relatively simple. After all, since the MVP is in all the equations, we can get the circle radius from the area or the radius of a circle from the circumference.

How do you find the radius of a circle?

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

The radius of a circle from the area: if you know the area A, the radius is r = √(A / π).
The radius of a circle from circumference: if you know the circumference c, the radius is r = c / (2 × π).
The 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 into the tool, and it will automatically process the radius of a circle equation tailored for your needs.

Other tools like this circle radius calculator

Remember that the radius of a circle calculator is not our only tool dealing with those pesky round objects. Below, we list the others, all ready to deal with your day-to-day circular problems.

FAQs

What is the radius of a unit circle?

By definition, a unit circle is a circle with a radius of 1. It is a general object used in mathematics (e.g., when explaining trigonometric functions), so the 1 usually 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:

Write the circumference as c = 6 ft.
Recall the formula for the radius of a circle from circumference: r = c / (2 × π).
Inject the circumference into the equation: r = (6 ft) / (2 × π) = 3/π ft.
If needed, substitute π ≈ 3.14: r = 3/π ft ≈ 0.96 ft.