How to use the circle calculator
- Choose what you know: the radius, the diameter, the circumference or the area.
- Enter the value and pick a unit, or "no unit" if you just want the numbers.
- Read the area at the top (or the radius, if you entered the area), with all four measurements underneath.
- Optionally enter a central angle in degrees to get the arc length, sector area and chord for that slice of the circle.
Circle formulas
r is the radius, the distance from the center to the edge, and d is the diameter, straight across through the center. π (pi) is about 3.14159265, the ratio of every circle's circumference to its diameter. The calculator first turns whatever you entered into the radius, then uses it for everything else. An arc and a sector are the same fraction of the circumference and area as the angle θ is of 360°.
Worked example
The calculator starts with a radius of 5 cm.
- Diameter: 2 × 5 = 10 cm.
- Circumference: 2 × π × 5 = 10π ≈ 31.4159 cm.
- Area: π × 5² = 25π ≈ 78.5398 cm².
Now add a central angle of 60°, one sixth of the circle. The arc length is 31.4159 × 60 ÷ 360 ≈ 5.236 cm, the sector area is 78.5398 ÷ 6 ≈ 13.09 cm², and the chord across the ends of the arc is 2 × 5 × sin 30° = 5 cm, the same as the radius.
Going the other way, a circumference of 100 gives r = 100 ÷ 2π ≈ 15.9155 and an area of about 795.7747. An area of 50 gives r = √(50 ÷ π) ≈ 3.9894.
Quick reference
| Radius | Diameter | Circumference | Area |
|---|---|---|---|
| 1 | 2 | 6.2832 | 3.1416 |
| 2 | 4 | 12.5664 | 12.5664 |
| 5 | 10 | 31.4159 | 78.5398 |
| 10 | 20 | 62.8319 | 314.1593 |
| 12 | 24 | 75.3982 | 452.3893 |
Doubling the radius doubles the circumference but multiplies the area by four, because the area depends on the radius squared. That is why a 16-inch pizza has about 1.8 times the area of a 12-inch one, not 1.33 times.
Common mistakes
- Using the diameter as the radius. A 12-inch pizza has a radius of 6 inches, so its area is π × 36 ≈ 113.1 in², not π × 144.
- Mixing up circumference and area. Circumference is a length (inches, cm); area is in square units (in², cm²).
- Squaring after multiplying by π. πr² means π × (r × r), not (π × r)².
- Rounding π too early. Using 3.14 instead of the full value makes a 10 m radius area 314 m² instead of 314.16 m², which adds up on big jobs.
Frequently asked questions
How do I find the radius from the circumference?
Divide the circumference by 2π, about 6.2832. A tree trunk that measures 94.2 cm around has a radius of about 15 cm and a diameter of about 30 cm. Choose "Circumference" in the calculator to do this automatically.
What is the difference between a sector and a segment?
A sector is a pizza slice: the area between two radii and the arc. A segment is the part between the arc and the straight chord joining its ends, so it is the sector minus the triangle formed by the two radii. The calculator shows both when you enter an angle.
What unit is the area in?
The square of the unit you chose. A radius in feet gives an area in square feet (ft²). If you need another unit, convert the radius first: 1 ft = 12 in, so a 2 ft radius is 24 in and the area is about 1,809.6 in².
Why is π about 3.14159?
It is the same for every circle: the circumference is always a little more than three times the diameter. π can't be written exactly as a fraction or a finished decimal, so the calculator uses JavaScript's built-in value, accurate to about 15 digits.
Related calculators
- Area Calculator — Area of a square, rectangle, triangle, circle, ellipse, trapezoid, parallelogram, sector or regular polygon.
- Triangle Calculator — Solve any triangle from three sides or angles: missing sides and angles, area, perimeter, heights and radii.
- Volume Calculator — Volume of a cube, box, cylinder, cone, sphere, pyramid, capsule or tube, in cubic units, liters and gallons.
- Surface Area Calculator — Lateral and total surface area of a cube, box, cylinder, cone, sphere, pyramid, capsule or tube.
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