This circumference-to-radius calculator helps you quickly find the relationship between a circle’s circumference and its radius. Enter either value, and the calculator will instantly determine the other.
You can use this circumference-to-radius converter in practical situations where measuring the circumference is easier than measuring the radius directly, such as finding the radius of a tank, pipe, circular table, or wheel by wrapping a measuring tape around it.
Keep scrolling on this article if you want more details on how to use this calculator or how to find the radius from the circumference manually using the circumference-radius formula.
How to use this circumference-to-radius calculator
To use this circumference-to-radius calculator, you only need to input one quantity, and we’ll calculate the rest for you.
- You can use it not only to convert from circumference to radius, but also to convert the other way. Therefore, if you need to calculate the circumference, just enter the radius (or use our circumference of a circle calculator).
- This circumference-to-radius calculator also lets you bring the diameter and area to the picture. Enable these variables in the “Show additional calculations” section, and we’ll calculate them for you. Alternatively, you can use our circumference-to-diameter or our circumference and area of a circle calculators for the same purpose.
- You can also express quantities in terms of pi (). For example, if the circumference equals , you have two options:
- Enter
28pi; or - Tick the option “Always express the circumference in terms of pi (𝝅)” and input
28.
- Enter
Convert from circumference to radius — The formula
To find the radius from the circumference, use the formula:
where:
- — Radius
- — Circumference; and
- .
FAQs
How do I find the radius from the circumference?
As an example of how to find the radius from the circumference, let’s do it for a 24-inch circumference. Follow these steps:
- Write the circumference (
C) to radius (r) formula:r = C / (2π). - Substitute the circumference:
r = C / (2π) = 24 / (2π). - Calculate the denominator:
2π ≈ 6.2832. - Then,
r ≈ 24 / 6.2832 ≈ 3.82.
You can use the circumference-to-radius converter to double-check this calculation.
Is the radius half of the circumference?
No, the radius is not half of the circumference.
If you’re asking whether the radius is half the circumference, you may be confusing the circumference with the diameter.
- The radius is half of the diameter, not half of the circumference.
- The circumference is the perimeter of the circle.
What is the difference between radius and circumference?
The radius and circumference are two different parts of a circle.
- 👉 The radius is the distance from the center of the circle to any part of its edge.
- 👉 The circumference is the total distance around the circle (the circle’s perimeter).
What’s the circumference of a circle with a radius of 5?
The circumference of a circle with a radius of 5 is 31.42 or 10π.
This calculation applies to any unit. Therefore, if the radius is 5 cm, the circumference is 31.42 cm or 10π cm. If the radius is 5 inches, the circumference is 31.42 inches (10π inches).
What’s the radius of a circle with a circumference of 28 pi?
The radius is 14.
To obtain such an answer, we can use the circumference-to-radius formula:
Radius = Circumference / (2π) = 28π / (2π) = 14
This answer applies to any unit. So, if the circumference is 28π inches, the radius is 14 inches — the same for cm or any other unit.