Circle Calculator
Calculate the area, circumference, and diameter of a circle from any known value.
Enter any value — radius, diameter, circumference or area — and all others are calculated instantly.
cm
r
cm
d = 2r
cm
C = 2πr
cm²
A = πr²
Definitions
A circle is the set of all points in a plane at a given distance (called the radius) from a fixed point (called the center).
Diameter: a straight line segment that passes through the center of a circle, with both endpoints on the circle. It equals twice the radius: d = 2r.
Arc: a continuous portion of the circumference between two points on the circle.
Chord: a straight line segment connecting any two points on the circle. The diameter is the longest possible chord.
Equation of a circle
The equation of a circle with center (, ) and radius is:
Frequently asked questions
The circumference of a circle is the total length of its outer boundary — the distance you would travel walking all the way around. It is calculated with C = 2πr, where r is the radius and π ≈ 3.14159. Because the diameter d = 2r, you can also write C = πd. For a circle of radius 5 cm, circumference = 2 × π × 5 ≈ 31.416 cm. This formula is fundamental in engineering, architecture and everyday life — from calculating the tread length of a wheel to the perimeter of a round table.
The area of a circle is the two-dimensional surface enclosed by the circumference. It is calculated with A = πr². Doubling the radius quadruples the area because area grows with the square of the radius. For a circle of radius 5 cm, A = π × 25 ≈ 78.54 cm². In practice, this formula is used to calculate the cross-section of a pipe, the coverage of a circular sprinkler, or the size of a pizza.
Pi (π) is approximately 3.14159265358979. It is defined as the ratio of any circle's circumference to its diameter: π = C/d. This ratio is the same for every circle. Pi is an irrational number — its decimal expansion never ends and never repeats. It has been calculated to trillions of decimal places. For most practical applications 3.14159 is more than sufficient.
The diameter (d) is always exactly twice the radius (r): d = 2r. The circumference (C) is π times the diameter, or 2π times the radius: C = πd = 2πr. If you know any one of the three you can find the other two. For example, if you measure the circumference of a round object with a tape measure, the radius is r = C / (2π). Very useful in carpentry or metalwork.
Circle formulas appear constantly in everyday and professional contexts. In construction, architects calculate circular windows, round columns and curved walls. In manufacturing, engineers size round pipes, gears and wheels. In cooking, baking-pan size adjustments use the area formula — a 10-inch pan has about 56% more area than an 8-inch pan. In sports, the radius of a circular track determines the total distance per lap.