How this calculator works
- Step 1Find the radiusrWhatever you enter is turned into the radius first.
- Step 2Diameterd = 2rTwice the radius.
- Step 3CircumferenceC = 2πrThe distance around.
- Step 4AreaA = πr²The space inside, in square units.
Every circle is fixed by its radius. The calculator turns your measure into a radius, then works out the other three. From an area, the radius is the square root of area ÷ π.
Worked example: a sandbox of radius 2.5 ft
- Circumference
C = 2πr- Area
A = πr²
- Circumference2 × π × 2.515.707963 ft
- Areaπ × 2.5²19.634954 sq ft
This is OpenStax’s Example 9.41, which uses π ≈ 3.14 and gets 15.7 ft and 19.625 sq ft. The calculator uses π to full precision, so its answers are a little larger.
π to full precision or 3.14
- Full-precision π12.566371 ftWhat this calculator shows.
- π ≈ 3.1412.56 ftThe textbook’s rounded answer.
Read the result
The headline shows the measure you most likely need; the table lists all four.
Working back from an area of 100 gives a radius of 5.641896. Area is always in square units of whatever length unit you use.
Assumptions and limits
- One unitUse one length unit throughout.
- Full πNot 3.14 or 22/7.
- Six decimalsResults are rounded for display only.
Related shape tools
A circle is fixed by one measurement. Other shapes and solids need a few more.
For rectangles, triangles and other flat shapes, use the area calculator. Cylinders, spheres and cones are covered by the volume calculator, and round columns of concrete by the concrete calculator.
Common mistakes
Mistake: Using the diameter in A = πr².
Instead: Halve the diameter first, or choose Diameter as what you know.
Mistake: Giving area in plain units.
Instead: Area is in square units: sq ft, m², cm².
Mistake: Expecting exactly the textbook answer.
Instead: Textbooks often use 3.14; full π gives slightly different decimals.
Checking the method
Every golden case is rechecked with π computed to 40 digits, and both OpenStax examples are reproduced with π = 3.14.
An independent script computes π by Machin’s formula in Python’s decimal module and recomputes every measure.
Read how we test our calculators, or browse more maths calculators.