A circular opening
A radius of 5 cm gives a diameter of 10 cm, circumference approximately 31.41592654 cm, and area approximately 78.53981634 cm².
Circle Calculator inputs
Changing the unit relabels the numbers. Convert measurements to one common unit before entering them.
Choose one known measurement. An area input uses square units, such as cm². Positive measurements must be from 0.000000001 to 1,000,000,000; derived defining lengths must also remain in this range.
Calculated measurements
Area
78.53981634 units²
| Measurement | Value |
|---|---|
| Area | 78.53981634 units² |
| Circumference | 31.41592654 units |
| Radius | 5 units |
| Diameter | 10 units |
Formula: A = πr²; C = 2πr; d = 2r
A full circle in a flat plane. Area input is in square units; all other inputs are lengths.
Results use full floating-point precision internally and display up to 10 significant digits. Angles are in degrees.
Calculations run locally in your browser. Measurement values are not sent to a calculation service. The downloadable text contains your selected inputs and computed results.
How to use the Circle Calculator
- 01
Select your known measurement: radius, diameter, circumference, or area.
- 02
Enter a positive number in the selected unit; area inputs use that unit squared.
- 03
Review radius, diameter, perimeter, and area in the results.
- 04
Load a worked example or download the results and formula as plain text.
Examples
Recover radius from area
An area of 144π square units corresponds to radius 12. Enter a numeric approximation of the area, about 452.3893421; the input does not parse π expressions.
Measure around an edge
A circumference of 100 units gives radius 100/(2π), approximately 15.91549431 units, and diameter approximately 31.83098862.
Radius and diameter are different inputs
A radius goes from the center to the edge. A diameter crosses the center from edge to edge and equals twice the radius. Using diameter as radius makes the calculated area four times too large. Check the diagram and input label before reading an area result.
The four circle relationships
For radius r, area is πr², circumference is 2πr, and diameter is 2r. To reverse these relationships, divide circumference by 2π or take the square root of area/π. The calculator uses JavaScript’s built-in approximation of π rather than a shortened classroom constant such as 3.14.
Units and circular measurements
Circumference, diameter, and radius share a linear unit. Area uses the square of that unit: a circle measured in meters produces square meters. Relabeling meters as centimeters does not multiply the input by 100. Convert the original measurement first, including the correct squared factor for area.
Where a full-circle model stops
An ellipse, sector, ring, or circular segment needs additional geometry. For an annulus, calculate the two complete circle areas and subtract the smaller from the larger. Edge thickness, cut allowances, and measurement uncertainty are not included. The displayed precision describes the computation, not the accuracy of a physical measurement.
What to know
- Only complete circles in a flat plane are modeled.
- Input values and the derived radius must remain within the stated numeric bounds.
Common questions
Can I type 5π or a fraction?
Enter a decimal or scientific notation such as 1e3. Symbolic π expressions and fractions must be evaluated before entry.
Is circumference the same as perimeter?
For a complete circle, circumference is its perimeter: the length around the edge.
Can the calculator solve a semicircle?
It calculates a full circle. Half the area gives a semicircle’s area, but its perimeter also includes the straight diameter.
Why is an extremely small diameter rejected?
The derived radius must remain within the supported range of 10⁻⁹–10⁹ units. Raw positive inputs use that same numeric range.