Free Online Circle Calculator
Calculate radius, diameter, circumference, and area.
The distance from the center to the edge.
Enter a positive measurement. The calculator derives the other three values using the standard circle formulas and π ≈ 3.141592653589793.
Step-by-step working
- Enter a measurement to see the formulas.
About the Circle Calculator
A circle is fully described by one number: its radius. From that single value you can derive the diameter, the circumference, and the area. This calculator works in both directions, so you can start with whichever measurement you actually have. Choose radius, diameter, circumference, or area, enter a value, and the other three are calculated immediately with the formulas shown.
The four circle measurements
- Radius (r): the distance from the center to any point on the circle.
- Diameter (d): the distance across the circle through the center, equal to 2r.
- Circumference (C): the distance around the circle, equal to πd or 2πr.
- Area (A): the space inside the circle, equal to πr².
The diameter is always twice the radius, which makes conversion between those two values exact. Circumference and area involve π, an irrational number, so their decimal results are rounded. The calculator uses a high-precision value of π internally and rounds only for display.
Working backwards from circumference or area
If you know the circumference, divide it by 2π to recover the radius: r = C / (2π). If you know the area, divide by π and take the square root: r = √(A / π). If you know the diameter, halve it. Once the radius is known, every other value follows directly. This is useful when a physical object is easier to measure around its edge than across its center, such as a pipe, a tree trunk, or a round table.
Units and square units
Lengths are reported in the unit you select, while area is reported in that unit squared. For example, a radius in centimeters produces a circumference in centimeters and an area in square centimeters. The tool does not convert between units; it labels the numeric result, so choose the unit that matches your measurement. If you need to switch between metric and imperial units, convert the input first or use a dedicated unit converter.
Where these calculations are used
Circle measurements appear in construction, machining, landscaping, cooking, and design. You might need the circumference to order edging for a round garden bed, the area to estimate paint or seed, or the radius to set a cutting tool. Because all four values are linked, changing one input updates the rest instantly and keeps the numbers consistent.
Frequently asked questions
Why is the area in square units?
Area measures two-dimensional space, so it is always expressed in square units. A radius of 5 cm gives an area of about 78.54 cm², not 78.54 cm.
Can I enter zero or a negative number?
No. A real circle must have a positive radius, diameter, circumference, and area. Zero would describe a single point rather than a circle, and negative lengths have no physical meaning.
How accurate is the result?
The calculator uses double-precision arithmetic and displays up to six decimal places. Very large or very small values may be rounded for readability, but the underlying calculation uses the full precision available in your browser.