Circle formula chart
Every common circle measurement and its formula: area, circumference, diameter, arc length, sector area, and chord length. All of them revolve around the radius and the constant pi, roughly 3.14159.
Circle formulas
| Quantity | Formula |
|---|---|
| Area | A = πr² |
| Circumference | C = 2πr = πd |
| Diameter | d = 2r |
| Radius | r = d / 2 |
| Arc length | s = rθ (radians) |
| Arc length (degrees) | s = (θ / 360) × πd |
| Sector area | A = ½r²θ (radians) |
| Chord length | 2r × sin(θ / 2) |
Pi is the ratio of any circle circumference to its diameter, about 3.14159, the same for every circle. The radius is the key input: double it for the diameter, and the area grows with the radius squared, so doubling the radius quadruples the area.
Need full geometry references?
See the Area Formula Chart and the Unit Circle Chart.
Radius, diameter, and circumference
The diameter is twice the radius, straight across through the center. The circumference, the distance around, is pi times the diameter, or equivalently two pi times the radius. Because pi is a little over three, the distance around a circle is always a bit more than three times its width.
Arcs and sectors
An arc is part of the circumference and a sector is a pie slice of the area, each scaled by its angle. In radians the formulas are clean: arc length is the radius times the angle, and sector area is one half the radius squared times the angle. In degrees, you take that fraction of the full 360.
FAQ
What is the circumference formula?
C = 2πr, or equivalently πd, where r is the radius and d the diameter. Pi is about 3.14159.
How does area change if I double the radius?
It quadruples. Area depends on the radius squared, so doubling the radius multiplies the area by four.
What is the difference between an arc and a sector?
An arc is a portion of the circle edge (a length); a sector is a pie-slice region bounded by two radii and an arc (an area).