Every measure of a circle, from any one.
Enter a radius, diameter, circumference, or area and see all the others at once. Pick an angle to get the arc length and the sector area, with a live drawing of the circle.
Your circle
The distance from the center to the edge of the circle.
The slice angle used for arc length and sector area.
What these numbers mean
The four measures at a glance
How the circle grows with its radius
Diameter grows in step with the radius, circumference grows with 2πr, and area grows with the square of the radius.
| Radius | Diameter | Circumference | Area |
|---|
Circles, explained
Circle Formulas
Diameter = 2r. Circumference = 2πr (or πd). Area = πr². These three formulas, all based on the radius, describe the most important properties of a circle. The constant π (pi) ≈ 3.14159 is the ratio of circumference to diameter for every circle.
Radius, Diameter, and Circumference
The radius extends from the center to the edge. The diameter is twice the radius and passes through the center. The circumference is the perimeter, the total distance around the circle. Knowing any one of these lets you calculate the other two.
Area of a Circle Explained
The area formula A = πr² means the area is about 3.14 times the square of the radius. Doubling the radius quadruples the area (because 2² = 4). This quadratic relationship means small changes in radius have a proportionally large effect on area.
Circles in Engineering and Design
Circles appear in wheels, gears, pipes, coins, clocks, and countless other applications. Circumference determines belt length around pulleys. Area determines the cross-section of pipes (affecting flow rate). Arc length and sector area are used in pie charts and angular measurements.
Common questions
How do I find the radius if I know the area?
Use r = √(A/π). For example, if the area is 50 square units, the radius is √(50/π) ≈ √15.92 ≈ 3.99 units.
How do I find the radius if I know the circumference?
Use r = C/(2π). For example, if the circumference is 31.42 units, the radius is 31.42/(2π) ≈ 5 units.
What is the difference between a circle and an ellipse?
A circle is a special case of an ellipse where both axes are equal. An ellipse has two different radii (semi-major and semi-minor axes). Every circle is an ellipse, but not every ellipse is a circle.
What is a sector of a circle?
A sector is a "pie slice" of a circle, bounded by two radii and an arc. Its area is (θ/360) × πr² for degrees, or (θ/2π) × πr² for radians, where θ is the central angle.
Results use π ≈ 3.14159265. Values are rounded for display; the underlying math keeps full precision. Units are whatever you enter (area is in square units, arc and circumference in linear units).