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.
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.
- Circle calc: find c, d, a, r;
- Circle measurements calculator;
- Circle formula calculator;
- Circle perimeter calculator;
- Circle length calculator;
- Circumference to diameter;
- Diameter of a circle calculator;
- Circumference and area of a circle calculator;
- Square footage of a circle calculator; and
- Square inches of a circle calculator.
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.