MATHS & STATISTICS / GEOMETRY

Circle calculator: area, circumference and diameter

Enter a circle's radius, diameter, circumference or area to get all four measurements, calculated with the full precision of pi.

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Your numbers

Area is in square units of the same length unit as the other measurements.
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YOUR RESULT

Enter your numbers to see a result.

WORKED EXAMPLE

Circle calculator: area, circumference and diameter: a worked example

With i know the Radius, value 5, the area is 78.53981634.

Inputs
I know theRadius
Value5
Results
Area78.53981634
Radius5
Diameter10
Circumference31.41592654
Area78.53981634
THE METHOD

How it works

Choose the measurement you already know and enter it. The calculator turns it into the radius, then works out the diameter, circumference and area. Pi is used to full double precision (3.141592653589793), not rounded to 3.14, which matters for large circles.

FormulaDiameter = 2r. Circumference = 2πr. Area = πr². From an area A, r = √(A ÷ π).
ASSUMPTIONS

Assumptions and limits

  • The shape is a perfect circle on a flat surface.
  • All lengths share one unit and the area is in that unit squared.
  • Pi is used at double precision; displayed values are rounded to ten significant figures.
  • Results are estimates based on the inputs and assumptions on this page, not professional advice.
  • Try this: use “Save scenario A”, change one input and compare the two results side by side.
QUESTIONS

Frequently asked questions

How is the result of the “Circle calculator: area, circumference and diameter” calculated?

Diameter = 2r. Circumference = 2πr. Area = πr². From an area A, r = √(A ÷ π). Choose the measurement you already know and enter it. The calculator turns it into the radius, then works out the diameter, circumference and area. Pi is used to full double precision (3.141592653589793), not rounded to 3.14, which matters for large circles.

What does the worked example show?

With i know the Radius, value 5, the area is 78.53981634. Radius: 5; Diameter: 10; Circumference: 31.41592654; Area: 78.53981634.

What assumptions and limits apply?

This is an estimate based on the inputs and assumptions shown on this page, not professional advice. Check anything with financial, health or safety consequences independently.

Is my data private?

Yes. Calculations run in your browser and your numbers are not sent to a server. A share link contains the inputs you choose to share, so check it before sending it to anyone.

How do I find the area from the diameter?

Halve the diameter to get the radius, then multiply π by the radius squared. A 10 cm diameter gives r = 5 cm and an area of about 78.54 cm².

How do I get the diameter from the circumference?

Divide the circumference by π. A circumference of 100 cm gives a diameter of about 31.83 cm.

Does doubling the radius double the area?

No. Area grows with the square of the radius, so doubling the radius makes the area four times larger, while the circumference only doubles.

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