Area of a Circle Calculator
Calculate the area, circumference and diameter of a circle from its radius or diameter.
Formula and sources updated · Data sources · 1View algorithm, constants and default inputs (JSON)
About this calculator
Choose radius or diameter. Switching preserves the same circle or sphere.
Worked example
calculated with the default values below
Measurement Radius · Radius 10 cm · Diameter 0 cm Area 314.1593 cm² · Circumference 62.8319 cm · Diameter 20 cm · Radius 10 cm
Method and assumptions
Formula basis and scope
Area = πr²; circumference = 2πr.
Ideal Euclidean shapes; use consistent length units. A diameter is twice the radius.
Data sources
Disclaimer
These calculators give general mathematical results. They suit study, planning and estimation — verify anything that feeds a graded submission, a published figure or a financial commitment.
Implementation source
This record describes the implementation used by this page. It is not independent validation. External references, when available, support only the stated formula or definition; estimates and custom rules retain their own assumptions.
Formula and variables
A = π r²; C = 2 π r
- r
- Radius
- A
- Area
- C
- Circumference
If a positive diameter d is entered, r = d ÷ 2; otherwise the radius input is used.
Frequently asked questions
Why does doubling the radius quadruple a circle's area?
Area is π times the radius squared, so the radius is squared before multiplying. Doubling the radius from 10 to 20 cm turns the area from 314 to 1,257 cm², four times as much, while the circumference only doubles. That non-linear growth is why a 16-inch pizza has more than twice the area of an 11-inch one, not just a wider slice.