Circle: properties & formulas
Every point on a circle is the same distance from its center. This distance, the radius, connects its boundary, area, and angle measurements.
- 1 center
- 0 vertices
- 360° in a full turn
- ∞ lines of symmetry
Properties of a circle
| Boundary | One continuous curve: the circumference |
|---|---|
| Radius | Center to any point on the circle |
| Diameter | Twice the radius; the longest chord |
| Vertices / straight edges | None |
| Full turn | 360° = 2π radians |
| Symmetry | Infinitely many reflection axes through the center |
Circle formulas
| Area | A = πr² |
|---|---|
| Circumference | C = 2πr = πd |
| Diameter | d = 2r |
| Radius from area | r = √(A / π) |
| Arc length | s = (θ / 360°) × 2πr |
| Sector area | A = (θ / 360°) × πr² |
Circle area calculator
Give your shape a size.
Use the same unit for every dimension. Changing the unit relabels the measurements; it does not convert them.
From dimensions to an answer
A worked example
A radius of 5 gives area 25π ≈ 78.540 square units and circumference 10π ≈ 31.416 units.
Circle: common questions
Wondering about the why? Start here.
What is the length of a circle?
The length around a circle is its circumference: C = 2πr, or πd using the diameter. A circle with a 10 cm diameter is about 31.42 cm around. The diameter is the length across, through the center.
Should I enter a circle’s radius or diameter?
Enter the radius: the distance from the center to the circumference. The diameter is twice the radius, so divide a given diameter by two first. A diameter of 10 cm means a radius of 5 cm.
Read the area formulasHow do I calculate a circle’s area and circumference?
Area is πr² and circumference is 2πr. For radius 3, these are 9π square units and 6π length units. The calculator displays rounded decimal results, so keep π in your working when you need an exact answer.
Explore part of a circle