mathematics calculator
Circumference Area Circle Calculator
Convert between circle area and circumference while deriving radius and diameter.
Circumference Area Circle Calculator
Converted circumference
Choose the known measure and enter a positive value.
This converter uses full-precision π and rounds only the displayed values.
Formula version 1.0.0
How to use this calculator
- Choose area or circumference as the known measure.
- Enter a positive value.
- Select Calculate.
- Read the converted measure plus derived radius and diameter.
Symbols and units
| Symbol | Meaning | Unit or domain |
|---|---|---|
A | Circle area | square length |
C | Circumference | length |
r | Radius | length |
d | Diameter | length |
Checked examples
Area to circumference
Inputs: Area π
Calculation: r=√(π÷π)=1; C=2πr
Result: Circumference 2π
A unit-radius circle has area π and circumference 2π.
Check: circle-area-circumference-core.test.ts
Circumference to area
Inputs: Circumference 2π
Calculation: r=2π÷(2π)=1; A=πr²
Result: Area π
The reverse conversion returns the same unit circle.
Check: circle-area-circumference-core.test.ts
Assumptions, rounding, and limits
- The shape is a perfect Euclidean circle.
- The known measure is positive.
- Area units correspond to the square of the circumference unit.
- Displayed rounding does not change working precision.
Frequently asked questions
Can area and circumference use the same unit?
No. Area uses square units, while circumference uses length units.
Why derive radius first?
Both formulas are naturally linked through radius.
Will converting there and back preserve the value?
Yes within floating-point precision when consistent units are used.
Sources and review
- OpenStax: Polygons, Perimeter, and Circumference — Circle circumference
- OpenStax: Area — Circle area
- Formula version
- circle.area-circumference@1.0.0
- Formula review
- Equatara formula review
- Editorial review
- Equatara editorial review
- Last verified
- 2026-10-25
- Applicability
- Two-way conversion for an ideal Euclidean circle.
- Next review
- On material formula/source change, or by 2028-10-25.
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Found a problem?
Report a formula, result, example, source, or accessibility issue through the calculator correction process. Do not include sensitive input values.