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About this tool
Enter a circle's radius, diameter, circumference or area to get the other three, plus arc length, sector area and chord, with units, π options and steps.
The Circle Calculator works from any one measurement. Pick what you know — radius, diameter, circumference or area — type the value, and it finds the radius first (r = d/2, r = C/2π or r = √(A/π)) and then derives everything else from it. Choose an input unit and a result unit to convert at the same time; areas scale by the square of the unit factor. When π is set to full precision the answers are also written in terms of π, such as 25π. You can switch π to 3.14, 3.1416 or 22/7 to match a textbook. Enter a central angle to get the arc length, sector area, chord, segment area and arc height. All calculations happen in your browser.
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Under I know the…, choose Radius, Diameter, Circumference or Area and type the value, for example a diameter of 10.
Set the Input unit and Result unit (such as cm and m), the Value of π and the Decimal places.
Read all four measures in Results with their formulas and the exact π form, then use Copy all or the copy icon on any value.
Enter a Central angle θ such as 60° to get arc length, sector area, chord and segment area, and follow the Steps list.
Radius, diameter, circumference or area — enter whichever you have and the other three are calculated, with the given value marked.
Enter in one unit and read results in another, from millimetres to miles; areas are shown in the matching square unit.
Use full-precision π with answers also written in terms of π, or set π to 3.14, 3.1416 or 22/7 so results match the method your class uses.
A central angle in degrees or radians gives arc length, sector area, chord, segment area, sector perimeter and arc height, drawn on the diagram.
| Radius r | Diameter d | Circumference 2πr | Area πr² |
|---|---|---|---|
| 1 | 2 | 2π ≈ 6.2832 | π ≈ 3.1416 |
| 2 | 4 | 4π ≈ 12.5664 | 4π ≈ 12.5664 |
| 3 | 6 | 6π ≈ 18.8496 | 9π ≈ 28.2743 |
| 4 | 8 | 8π ≈ 25.1327 | 16π ≈ 50.2655 |
| 5 | 10 | 10π ≈ 31.4159 | 25π ≈ 78.5398 |
| 6 | 12 | 12π ≈ 37.6991 | 36π ≈ 113.0973 |
| 7 | 14 | 14π ≈ 43.9823 | 49π ≈ 153.938 |
| 8 | 16 | 16π ≈ 50.2655 | 64π ≈ 201.0619 |
| 9 | 18 | 18π ≈ 56.5487 | 81π ≈ 254.469 |
| 10 | 20 | 20π ≈ 62.8319 | 100π ≈ 314.1593 |
Lengths are in any unit; areas are in that unit squared.
Multiply π by the radius squared: A = πr². For a radius of 5 cm, A = π × 25 ≈ 78.54 cm². If you have the diameter, halve it first, or use A = πd²/4. The area is in square units, so a radius in centimetres gives an area in square centimetres.
Circumference is the distance around the circle: C = 2πr, or C = πd using the diameter. A circle with a diameter of 10 inches has a circumference of about 31.42 inches. Because the formula is linear, doubling the diameter doubles the circumference.
Divide the circumference by 2π: r = C / (2π). A circumference of 50 cm gives r = 50 / 6.2832 ≈ 7.96 cm. This is the usual way to find the size of a pipe, tree trunk or wheel, since it is easier to wrap a tape around it than to measure across.
Divide the area by π and take the square root: r = √(A / π). An area of 100 m² gives r = √(100 / 3.1416) ≈ 5.64 m. Double the radius to get the diameter, about 11.28 m. Make sure the area is in square units of the length you want back, such as m² for metres.
The radius is the distance from the centre of the circle to its edge. The diameter goes all the way across through the centre, so it is twice the radius: d = 2r. Most formulas use the radius, so halve a measured diameter before using A = πr².
Both are approximations. π is about 3.14159265, so 3.14 is slightly low and 22/7 (about 3.142857) slightly high; each is accurate to roughly 0.05%. Use whatever your teacher or exam specifies. For real measurements, full-precision π avoids adding rounding error.
Arc length is the part of the circumference cut off by a central angle: s = rθ with θ in radians, or s = (θ / 360°) × 2πr with θ in degrees. A 60° arc in a circle of radius 5 is (60 / 360) × 2π × 5 ≈ 5.24 units long.
A sector is a pizza-slice shape between two radii. Its area is (θ / 360°) × πr², or ½r²θ with θ in radians. A 90° sector of a circle with radius 4 has area ¼ × π × 16 ≈ 12.57 square units.
A chord is a straight line joining two points on the circle. For a central angle θ, its length is 2r·sin(θ/2). The diameter is the longest possible chord, at θ = 180°. The region between a chord and its arc is called a segment.
The area becomes four times as large, because area depends on the radius squared. Tripling the radius gives nine times the area. The circumference only doubles or triples, because it depends on the radius directly. This is why a 16-inch pizza has more than 1.7 times the area of a 12-inch one.
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