Circle Calculator: Area of a Circle Formula and Circumference Formula
Circle from radius
A = π × r²
Radius r
Divide the circle into sixteen equal sectors whose straight edges have radius r = 3.
A = π × r²
Sixteen finite sectors illustrate an approximation, not an exact rectangle. In the limit of thinner sectors the height approaches r and the base approaches πr. The sectors translate and rotate without changing size. Display size is normalized from the radius; diagram not to scale.
Worked example you can change
Area = π × radius²
- Area ≈ 28.2743338823081 square units
- Diameter = 2 × 3 = 6 units
- Circumference = 2 × π × 3 ≈ 18.8495559215388 units
Calculator
Enter complete decimal numbers using one common unit for dimensions; changing the unit label does not convert numbers. Decimal answers are shown to 15 significant digits.
- Area
- 28.2743338823081 cm²
- Diameter
- 6 cm
- Circumference
- 18.8495559215388 cm
Formula variants
| Shape or method | Formula | Meaning |
|---|---|---|
| Area of a circle | A = πr² | Square the radius and multiply by π. Area is measured in squared units. |
| Circumference formula | C = 2πr = πd | The distance around a circle is π times its diameter. |
| Diameter formula | d = 2r | A diameter crosses the center and consists of two radii. |
Questions
What is the area of a circle formula?
Area is πr², where r is the radius. A radius of 3 cm gives approximately 28.2743338823081 cm².
What is the difference between radius and diameter?
Radius runs from the center to the edge. Diameter runs across the center from edge to edge and is twice the radius.
Why does the animation not make an exact rectangle?
Finite sectors retain curved edges. Thinner sectors approach a rectangle with base πr and height r; the limit explains πr².
What happens if I double the radius?
Diameter and circumference double; area becomes four times as large because the radius is squared.
Does changing the unit convert my numbers?
No. It changes the common unit label only. Enter converted measurements yourself.
Sources and method
Calculate circle area, diameter and circumference from a radius. See why circle area is πr² and circumference is 2πr.
We calculate with 40 significant digits and round only the displayed result. Diagrams are labelled explanations and are not measurement drawings.
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