Circle Calculator
Find area, circumference, and diameter from the radius.
Results update as you type.
How it works
A circle is defined entirely by a single measurement, its radius, the distance from the centre to any point on the edge. From that one value every other property follows. This circle calculator takes the radius and returns the three most useful quantities: the area enclosed by the circle, the circumference around its edge, and the diameter across its widest point. The area is found with pi times the radius squared, which gives the amount of flat space inside the circle. The circumference, the perimeter of the circle, is two times pi times the radius, and it represents how far you would travel walking all the way around. The diameter is the simplest of all, just twice the radius, measuring straight across the circle through its centre. The constant pi, approximately 3.14159, is the unchanging ratio that ties these formulas together and appears in every circular calculation. For a circle with a radius of 2, the area is pi times 4, about 12.57 square units, the circumference is 4 pi, also about 12.57 units, and the diameter is exactly 4. Circles are everywhere in design, engineering, and everyday life, from wheels and pipes to plates and clock faces, so being able to convert a radius into area, circumference, and diameter quickly is genuinely useful. Because a radius is a length, this calculator requires it to be zero or positive.
area = πr²; circumference = 2πr; diameter = 2r
Every measurement of a circle flows from its radius, the distance from the centre to the edge. The area is pi times the radius squared, because pi is precisely the constant that links a circle's radius to the space it encloses. The circumference, the distance around the circle, is pi times the diameter, or equivalently two pi times the radius, which is the very definition of pi as the ratio of circumference to diameter. The diameter is simply twice the radius, spanning the full width through the centre.
Source:Euclidean geometry
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter radius (r).
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Area updates instantly as you type — no button to press.
Frequently asked questions
What is the formula for the area of a circle?
The area of a circle is pi times the radius squared, written as A equals pi r squared. You square the radius first, then multiply by pi, which is approximately 3.14159. The result is the amount of flat space enclosed inside the circle, measured in square units. Because the radius is squared, doubling the radius quadruples the area, which is why larger circles enclose disproportionately more space than their radius suggests.
How is circumference different from area?
Circumference measures the distance around the outside of a circle, a length in ordinary units, while area measures the flat space enclosed inside, in square units. They answer different questions: circumference tells you how much edge or fencing you need, area tells you how much surface you cover. Circumference uses two pi r, and area uses pi r squared, so the two grow at different rates as the radius increases.
What is the value of pi?
Pi is a mathematical constant equal to the ratio of any circle's circumference to its diameter, approximately 3.14159. It is an irrational number, meaning its decimal expansion never ends or repeats, so it can only be approximated. Pi appears in every circle formula and in countless other areas of mathematics and physics. For most practical work, using 3.14159 or the pi button on a calculator gives more than enough precision.
How do I find the radius from the diameter?
The radius is exactly half the diameter, so divide the diameter by two. Conversely, the diameter is twice the radius. If you are given a circle's diameter rather than its radius, simply halve it before using the area or circumference formulas, or enter the resulting radius directly into this calculator. This relationship is the simplest of all the circle measurements and never involves pi.
Can I find the radius from the area?
Yes. Since area equals pi times the radius squared, you can reverse it: divide the area by pi, then take the square root of the result to recover the radius. For example, an area of about 12.57 divided by pi gives 4, and the square root of 4 is 2, the original radius. This inverse calculation is useful when you know how much space a circle covers but not its radius.