Every circle is fixed by a single number. Once you know the radius, the diameter, circumference and area all follow from π — so this calculator lets you start from whichever measurement you actually have.
How to use the circle calculator
- Choose the measurement you know: radius, diameter, circumference or area.
- Enter its value and pick the unit.
- The tape lists all four measurements; the steps show how each was derived.
Circle formulas
| Measurement | From radius | From diameter |
|---|---|---|
| Diameter | d = 2r | — |
| Circumference | C = 2πr | C = πd |
| Area | A = πr² | A = πd² ÷ 4 |
And working backwards to the radius:
Worked example: a round tabletop
A tabletop measures 48 inches across, so d = 48 in and r = 24 in.
- Circumference: π × 48 ≈ 150.80 in — the length of edge banding you would need.
- Area: π × 24² ≈ 1,809.56 in², or about 12.57 ft² (divide by 144), which tells you how much finish to buy.
Why π shows up everywhere
π is the ratio of any circle’s circumference to its diameter, about 3.14159. Because that ratio is the same for every circle, doubling the radius doubles the circumference — but quadruples the area, since area depends on r². A 16-inch pizza has four times the area of an 8-inch pizza, not twice.
Parts of a circle
- Center: the point every edge point is the same distance from.
- Radius (r): the distance from the center to the edge.
- Diameter (d): a straight line through the center from edge to edge — always twice the radius.
- Circumference (C): the distance around the circle, its perimeter.
- Chord: any straight line joining two points on the circle; the diameter is the longest chord.
- Arc and sector: a piece of the circumference, and the pie-slice region it encloses with two radii. A sector with central angle θ (in degrees) has area θ/360 × πr².
Quick reference
| Radius | Diameter | Circumference | Area |
|---|---|---|---|
| 1 | 2 | 6.2832 | 3.1416 |
| 2 | 4 | 12.566 | 12.566 |
| 5 | 10 | 31.416 | 78.540 |
| 10 | 20 | 62.832 | 314.16 |
| 12 | 24 | 75.398 | 452.39 |
Related shapes
For a ring between two circles use the annulus calculator. For three-dimensional versions, see the sphere and cylinder calculators.
Frequently asked questions
What is the formula for the area of a circle?
A = πr², where r is the radius. A circle with a 5 cm radius has an area of π × 25 ≈ 78.54 cm².
How do I find the radius from the circumference?
Divide the circumference by 2π. A circumference of 31.4 m gives a radius of 31.4 ÷ 6.2832 ≈ 5 m.
What value of pi does the calculator use?
JavaScript's built-in value of π, accurate to about 15–16 significant digits (3.141592653589793). Results are rounded for display.
Why is the area in square units?
Area measures a two-dimensional surface, so it is counted in squares — square centimeters, square feet and so on — even though the radius is a plain length.