Circle Calculator
| Property | Value |
|---|---|
| Radius | 5 |
| Diameter | 10 |
| Circumference | 31.415927 |
| Area | 78.539816 |
d = 2r · C = 2πr · A = πr²
Circle Formulas Explained
A circle is the set of all points in a plane at a fixed distance r (the radius) from a center point. The diameter d passes through the center and equals twice the radius: d = 2r. The circumference C is the distance around the circle, given by C = 2πr = πd. The area A enclosed by the circle is A = πr².
Because these four quantities are tightly related, knowing any one determines the other three. If you know the area, recover the radius with r = √(A/π). If you know the circumference, r = C/(2π). This calculator accepts whichever value you have and computes the rest using π ≈ 3.14159265359.
When you enter an optional central angle θ in degrees, the calculator also finds arc length, sector area, and chord length. Arc length is the portion of the circumference subtended by the angle: L = (θ/360) × 2πr. Sector area is the "pie slice" region: A_sector = (θ/360) × πr². Chord length is the straight-line distance between the arc endpoints: chord = 2r·sin(θ/2).
The live SVG diagram shows the circle with radius and diameter marked, and when an angle is provided, highlights the corresponding sector. These formulas apply to any circular geometry problem — wheels, pizza slices, gear teeth, and orbital paths all rely on the same relationships.
Enter your known measurement, optionally add an angle, and copy the full set of results for homework, engineering sketches, or quick sanity checks in the field.
Examples
| Example | Result |
|---|---|
| Radius 5 | C ≈ 31.416, A ≈ 78.54 |
| Diameter 10 | r = 5 |
| Area π | r = 1 |
| r=4, θ=90° | Arc ≈ 6.283 |
Frequently asked questions
Yes. Select circumference as the known value and enter C; radius and area are derived automatically.
Degrees. A full circle is 360°.
chord = 2r·sin(θ/2), where θ is the central angle in degrees.