Parts of a circle
The radius runs from the centre to the edge. The diameter crosses the circle through the centre and equals twice the radius. The circumference is the distance around the edge, and the area is the surface inside. The constant that links them is π (pi), about 3.14159, the circumference divided by the diameter.
Circle formulas
| To find | Formula |
|---|---|
| Diameter | d = 2r |
| Circumference | C = 2πr = πd |
| Area | A = πr² |
| Radius from circumference | r = C ÷ 2π |
| Radius from area | r = √(A ÷ π) |
Worked examples
From the radius
For r = 7, the diameter is 14, the circumference is 2π × 7 = 14π, about 43.98, and the area is π × 49, about 153.94.
From the circumference
A circumference of 31.416 gives r = 31.416 ÷ 2π, which is 5. The diameter is 10 and the area is 25π, about 78.54.
Comparing two pizzas
A 12-inch pizza has radius 6 and area π × 36, about 113.1 square inches. Two 8-inch pizzas have radius 4, so each is about 50.27 square inches, or 100.5 together. The single 12-inch pizza is larger, because area grows with the square of the radius.
Common circle mistakes
The most frequent slip is using the diameter in a formula that needs the radius, which makes the area four times too big. Another is mixing up circumference and area: one is a length and the other is in square units. Rounding π to 3.14 early also adds error, so round only at the end. To find the volume of a cylinder or sphere built from a circle, use the volume calculator, and for other flat shapes the area calculator.
Frequently asked questions
What is the formula for the circumference of a circle?
Circumference equals two times pi times the radius, C = 2πr, which is the same as π times the diameter. A circle with radius 7 has circumference 14π, about 43.98.
What is the difference between radius and diameter?
The radius runs from the centre to the edge, and the diameter runs across the whole circle through the centre. The diameter is always twice the radius. Most formulas need the radius, so halve a diameter before using them.
What is pi?
Pi, written π, is the ratio of a circle’s circumference to its diameter. It is about 3.14159 for every circle, and its decimal digits never end or repeat. Using 3.14 gives a small rounding error; the calculator uses a far more precise value.
How do you find the radius from the area?
Divide the area by pi, then take the square root: r = √(A ÷ π). An area of 50 gives r = √(50 ÷ π), which is about 3.989. The calculator does this when you choose area as your known value.
What is the difference between circumference and area?
Circumference is the distance around the edge, a length measured in units such as centimetres. Area is the surface inside, measured in square units. Doubling the radius doubles the circumference but multiplies the area by four.
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Related topics on this page: radius and diameter, circumference of a circle, area of a circle, pi, circle formulas