Circle With Radius 9
See the diameter, circumference, and area below, or try a different value.
Radius
9
Diameter
18
Circumference
56.5487
Area
254.469
Summary
A circle with a radius of 9 has a diameter of 18, a circumference of 56.5487, and an area of 254.469 square units.
Diagram (not to scale)
What is a Circle?
A circle is a simple closed shape representing the set of all points in a plane that are equidistant from a fixed center point. That constant distance is the radius, and every other measurement of a circle — diameter, circumference, and area — can be derived from it.
The constant π (pi), approximately 3.14159, is the ratio of a circle's circumference to its diameter and appears in every circle formula. Pi is both irrational and transcendental, which is why the ancient geometric problem of "squaring the circle" using only a compass and straightedge was proven mathematically impossible in 1880.
The Circle Formulas
All four circle measurements relate back to the radius. Once you know any single one, the other three follow directly from these relationships.
Why Area Grows Faster Than Radius
Because area depends on the radius squared, doubling a circle's radius doesn't just double its area — it quadruples it. A circle with twice the radius of another has four times the area, which is why even modest increases in radius can dramatically increase the amount of material needed to fill a circular shape.
Circumference vs. Perimeter
"Circumference" is simply the name given to the perimeter of a circle specifically — the distance you'd travel walking once around its edge. Because a circle has no straight sides, circumference can't be measured by adding up side lengths the way a polygon's perimeter can, which is exactly why it needs its own formula involving π.
Every Point on a Circle Is the Same Distance From Center
This defining property — every point exactly one radius from the center — is what makes circles perfectly round and is also the basis for the circle's equation in coordinate geometry: a point (x, y) lies on a circle centered at the origin when x² + y² = r².
Example — Your Current Inputs
A circle with a radius of 9 has a diameter of 18, a circumference of 56.5487, and an area of 254.469 square units.
Additional Example — A Pizza
A 16-inch pizza has a diameter of 16 inches, so its radius is 8 inches — giving it an area of π × 8² ≈ 201 square inches. A "personal" 8-inch pizza, by contrast, has only a quarter of that area (about 50 square inches), even though its diameter is only half as large.
Frequently Asked Questions
What value of π does this calculator use?
This calculator uses the standard double-precision value of π (about 3.14159265358979), which is far more precise than the commonly rounded 3.14159 used in manual calculations.
Can I enter a negative or zero value?
No — radius, diameter, circumference, and area must all be positive numbers, since a circle with zero or negative size isn't geometrically meaningful.
Is the area in square units of the same unit as the radius?
Yes — if you enter the radius in inches, the area comes out in square inches; in centimeters, the area is in square centimeters, and so on. The calculator doesn't convert between different units of measurement.