Circle Calculator
A circle is defined by a single measurement — its radius. From the radius, every other property follows exactly: the diameter is twice the radius, the circumference is 2πr, and the area is πr². This calculator lets you start from whichever measurement you know — radius, diameter, circumference, or area — and instantly computes the other three with full precision.
Whether you are working in geometry, engineering, architecture, or everyday projects, circle calculations appear constantly. Knowing the relationship between radius, diameter, circumference, and area allows you to switch between measurements without manual formula lookup. Enter any one value and all four properties are resolved in real time.
How it works
r = radius; d = 2r; C = 2πr; A = πr². Inverse derivations: from diameter r = d/2; from circumference r = C/(2π); from area r = √(A/π).
Use cases
- Calculating the amount of fencing needed to enclose a circular garden
- Finding the area of a circular floor for tiling or carpet estimates
- Converting between wheel diameter and circumference for speed calculations
- Determining pipe cross-section area in plumbing or engineering design
- Computing circular track lengths for athletics or motorsport planning
Frequently asked questions
How do I calculate the area of a circle from its diameter?
Divide the diameter by 2 to get the radius, then apply A = πr². For example, a circle with a 10 cm diameter has a 5 cm radius, so its area is π × 5² ≈ 78.54 cm². You can also use the direct shortcut A = πd²/4.
How do I find the radius of a circle if I only know the area?
Rearrange the area formula to r = √(A/π). Divide the area by π and take the square root of the result. Once you have the radius, the diameter is simply 2r and the circumference is 2πr.
Is the circumference the same as the perimeter of a circle?
Yes. Circumference is the specific name for the perimeter of a circle — the total distance around its edge. It is calculated as C = 2πr, or equivalently C = πd using the diameter.
How do I get the diameter of a circle from its circumference?
Divide the circumference by π: d = C/π. This works because C = πd, so a circle with a circumference of 31.4 cm has a diameter of about 10 cm. To get the radius instead, divide the circumference by 2π.
What value of pi should I use in circle calculations?
For quick estimates, 3.14 or 22/7 is usually close enough. For precise work in engineering or construction, use more decimal places, such as 3.14159. This calculator uses full floating-point precision for π, so rounding only happens in the displayed result.