Find the area of a circle from its radius, diameter, or circumference using A = πr². Enter any one of the four values below and leave the rest blank — the calculator fills in the radius, diameter, circumference, and area for you.
The area of a circle calculator works out how much space a circle covers using the classic formula A = πr². You do not need to start from the radius, though — enter the radius, the diameter, the circumference, or even the area itself, and the calculator instantly finds all the others. Because the four measurements of a circle are all linked through π, knowing any one of them is enough to determine the rest. Whether you are sizing a round table, a pizza, a garden bed, or solving geometry homework, this tool gives you an exact answer in a single step, along with the formula it used.
The area of a circle is one of the most useful results in all of geometry, and it turns up everywhere from construction and design to science and everyday life. This calculator makes it effortless and shows its working so you can learn as you go.
The area of a circle is the amount of two-dimensional space enclosed within its boundary — the region inside the curve. Like all areas, it is measured in square units: square inches, square centimeters, square meters, and so on. The larger the circle, the more area it contains, and because area depends on the radius squared, it grows very quickly: doubling the radius of a circle multiplies its area by four, not two. That squared relationship is the single most important thing to understand about circle area, and it explains why a pizza twice the diameter of another gives you four times as much to eat.
The fundamental formula for the area of a circle is:
A = π × r²
where A is the area, r is the radius (the distance from the center to the edge), and π (pi) is the mathematical constant approximately equal to 3.14159. If you know a different measurement, the formula adapts easily:
From radius: A = π × r²
From diameter: A = π × (d / 2)² = π × d² / 4
From circumference: A = C² / (4π)
These are all the same formula in disguise, because the diameter is twice the radius (d = 2r) and the circumference is C = 2πr. The calculator uses the full precision of π built into your device — not just 3.14 — so your results are as accurate as possible.
Suppose a circle has a radius of 5 units. Squaring the radius gives 25, and multiplying by π gives the area:
A = π × 5² = π × 25 ≈ 78.54 square units
The same circle has a diameter of 10 units (twice the radius) and a circumference of about 31.42 units (2πr). These are the default values in the calculator, so you can press Calculate to see them, then enter your own number in any of the four fields. Enter a diameter of 10 and you will get the same area; enter an area of 78.54 and the calculator will work backward to a radius of 5.
Because the tool works in every direction, you can use it as a plain area calculator, as a reverse calculator to find the radius from a known area, or as a quick converter between a circle's radius, diameter, and circumference.
Often you can measure a circle's diameter more easily than its radius — measuring straight across a round object is simpler than finding its exact center. To find the area from the diameter, first halve the diameter to get the radius, then apply A = πr². Combined into one step, that is A = π × d² / 4. For a circle with a diameter of 10, the area is π × 100 / 4 = 25π ≈ 78.54 square units — exactly the same as starting from a radius of 5, as it must be. The calculator does this halving automatically, so you can enter whichever measurement you have on hand.
Sometimes the only thing you can measure is the distance around a circle — its circumference — perhaps by wrapping a tape measure around a pipe or a tree trunk. From the circumference you can still find the area. Since C = 2πr, the radius is r = C / (2π), and substituting into A = πr² gives the compact formula A = C² / (4π). For example, a circle with a circumference of 31.42 units has an area of 31.42² / (4π) ≈ 78.54 square units. This is a genuinely handy trick for real-world objects where the center is hard to reach, and the calculator handles it for you when you enter a circumference.
The squared term in A = πr² has big practical consequences that surprise many people. Because area scales with the square of the radius, small increases in size lead to large increases in area. A circle with twice the radius has four times the area; three times the radius gives nine times the area. This is why a 16-inch pizza is not just a bit bigger than a 12-inch one — it has nearly 78% more area — and why the price difference between sizes is often well worth it. The same principle governs the coverage of a sprinkler, the strength of a cable (which depends on its cross-sectional area), and the light-gathering power of a telescope. Understanding that area grows with the square of the radius turns the formula from an abstract rule into a genuinely useful mental model.
The formula A = πr² can feel like something to memorize, but there is a lovely intuition behind it. Imagine slicing a circle into many thin wedges, like the slices of a pie, and then arranging those wedges alternately point-up and point-down. As the slices get thinner and more numerous, the shape they form gets closer and closer to a rectangle. The long side of that rectangle is half the circumference (πr), and the short side is the radius (r). The area of the rectangle — and therefore the circle — is length times width, πr × r = πr². This "unrolling" argument is a favorite in classrooms because it turns an abstract formula into something you can almost see, and it explains why both π and the radius-squared appear.
At the heart of every circle calculation is π (pi), the ratio of a circle's circumference to its diameter. Remarkably, this ratio is exactly the same for every circle, no matter its size — a small coin and a giant Ferris wheel share the identical value of π. It is an irrational number, meaning its decimal expansion goes on forever without repeating: 3.14159265358979… For everyday work, 3.14 or 3.1416 is plenty, but this calculator uses the full precision available in your device so that your answers carry no unnecessary rounding error. Pi appears not only in the area formula but in the circumference (C = 2πr), the volume of spheres and cylinders, and countless formulas across mathematics and physics, which is part of why it is one of the most famous numbers in the world.
Here are the areas of a few round sizes, which you can confirm in the calculator by entering the radius or diameter:
The pizza comparison is a memorable illustration of the squared relationship: bumping the diameter from 12 to 16 inches — only a third larger across — gives you almost twice the food.
The area of a circle is the starting point for the surface area and volume of many 3D shapes. The volume of a cylinder is simply the circle's area multiplied by the height: V = πr²h — picture stacking many identical circular disks. The volume of a cone is one-third of that, V = πr²h / 3. A sphere has a surface area of 4πr² — exactly four times the area of a circle with the same radius — and a volume of (4/3)πr³. In every one of these, the πr² of the flat circle is doing the heavy lifting. Master the area of a circle and you have the foundation for the geometry of round three-dimensional objects, which is why this formula is introduced early and used everywhere afterward.
The area of a circle is A = πr², where r is the radius and π is about 3.14159. From the diameter, A = πd²/4; from the circumference, A = C²/(4π).
Divide the diameter by 2 to get the radius, then use A = πr². Equivalently, use A = π × d² / 4 directly. For a diameter of 10, the area is 25π ≈ 78.54 square units.
Yes. Rearranging A = πr² gives r = √(A / π). Enter the area in this calculator and leave the other fields blank to get the radius, diameter, and circumference.
It uses the full-precision value of π built into your browser (about 15 digits), which is far more accurate than the rounded 3.14 often used by hand.
The area is in the square of whatever length unit you use for the radius, diameter, or circumference. Enter lengths in centimeters and the area is in square centimeters.
Because the area depends on the radius squared. If the radius doubles, r² becomes (2r)² = 4r², so the area is multiplied by four.
This Area of a Circle Calculator is provided for educational and general informational purposes. It applies the exact formula A = πr² using high-precision π. Results are rounded for display; verify independently for critical engineering or construction work.