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Circle Calculator

Calculate area, circumference, radius, and diameter of a circle from any known value.

Measurement

Updates as you type
What do you know?
Input dimension ?
Enter radius
cm
0255075100

Formula

A = π r 2   C = 2π r   d = 2 r
A
Area of the circle
C
Circumference (perimeter)
d
Diameter (straight line through the center)
r
Radius (center to edge)
π
Pi — approximately 3.14159265…
Worked example — your numbers
  1. Pick a radius to see each step.
  2. —
  3. —
  4. Result: —

Every measurement on a circle is tied to the radius. Once you know any one of radius, diameter, circumference, or area, the other three follow directly from π.

Examples

How It Works

A circle is the set of all points in a plane that are exactly the same distance from a fixed center point. That distance is the radius (r). Every other circle measurement flows from the radius: the diameter (d) is twice the radius, the circumference (C) is the distance around the circle, and the area (A) is the space enclosed within it.

The key to all circle math is the constant π (pi), the ratio of any circle's circumference to its diameter. Pi is an irrational number — its decimal expansion never ends or repeats. The first 20 digits are 3.14159265358979323846. Using π, the formulas are: C = 2πr and A = πr². Because every property depends on the radius, knowing any single measurement lets you compute all the others.

This calculator works in reverse too: enter the circumference and it derives the radius (r = C / 2π), or enter the area and it finds the radius (r = √(A / π)). This makes it useful for real-world problems like sizing materials, planning circular structures, or converting between measurements.

Tips & Best Practices

Diameter is always exactly twice the radius — if you know one, you know the other.
Circumference ≈ 3.14 × diameter — a handy approximation for quick mental math.
Area grows with the square of the radius — doubling the radius quadruples the area.
For partial circles (sectors), multiply the full circle value by the angle fraction (e.g., a 90° sector is 1/4 of the full circle).

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Frequently Asked Questions

What is pi (π)?

Pi is the ratio of a circle's circumference to its diameter, approximately 3.14159. It is an irrational number, meaning its decimal representation never ends or repeats. Pi is fundamental to all circle calculations.

First, find the radius from circumference: r = C / (2π). Then calculate area: A = πr². Alternatively, you can use the direct formula A = C² / (4π) to go straight from circumference to area.

The diameter is always exactly twice the radius (d = 2r), and the radius is half the diameter (r = d/2). Knowing either value lets you calculate all other properties of the circle.

A sector is a "slice" of a circle. Its area equals (θ/360) × πr² where θ is the central angle in degrees. For radians, the formula is (1/2) × r² × θ.

Pi (π) is the ratio of every circle's circumference to its diameter — approximately 3.14159265358979. It is a mathematical constant that appears not only in geometry but throughout mathematics and physics, including wave equations, probability, and number theory. Pi is irrational (it cannot be expressed as a simple fraction) and transcendental (it is not the root of any polynomial with rational coefficients).

A semicircle is exactly half of a circle, so its area is (πr²) / 2. For example, a semicircle with radius 10 has an area of (π × 100) / 2 ≈ 157.08 square units. Its perimeter (the distance around the outside) is πr + 2r, because you add the curved arc (half the circumference) plus the straight diameter.

Circumference is the specific term for the perimeter of a circle — the total distance around its curved edge. Perimeter is the general term for the distance around any closed shape. For circles, circumference and perimeter mean the same thing. For other shapes like semicircles or segments, the perimeter includes both curved and straight edges.

Rearrange the area formula A = πr² to solve for r: divide the area by π, then take the square root. The formula is r = √(A / π). For example, if the area is 50 square cm, the radius is √(50 / π) ≈ √15.915 ≈ 3.989 cm.

A unit circle is a circle with radius 1, centered at the origin (0, 0) on a coordinate plane. It is fundamental in trigonometry because any point on it has coordinates (cos θ, sin θ), where θ is the angle from the positive x-axis. The unit circle makes it easy to visualize and derive trigonometric values for common angles like 30°, 45°, 60°, and 90°.

Doubling the radius doubles the circumference (since C = 2πr is linear in r), but it quadruples the area (since A = πr² depends on the square of r). This is why scaling circles can be unintuitive — a pizza with twice the diameter has four times the area, meaning four times as much pizza.