Find a circle’s area, circumference and diameter from the radius.
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How is a circle's area and circumference calculated from the radius?
Area = π r², circumference = 2 π r, and diameter = 2 r. Enter the radius and the tool finds all three, using the value of π and rounding for display. For example, a radius of 5 gives an area of about 78.54 and a circumference of about 31.42.
Understanding your result
Results use the value of π and are rounded for display.
Formula and method
Area = π r², circumference = 2 π r, diameter = 2 r.
Assumptions and limitations
It works from the radius of a flat, two-dimensional circle to give area, circumference and diameter. It does not calculate the surface area or volume of a sphere, and results use the stored value of π rounded for display, so long decimals are shown to a fixed precision.
Worked example
A radius of 5 gives an area of about 78.54 and a circumference of about 31.42.
How to use this tool
- Enter the radius.
- Read the area, circumference and diameter.
Common mistakes to avoid
- Entering the diameter where the radius is expected.
About the Circle Calculator
Enter a circle’s radius to find its area, circumference and diameter.
Who should use this tool
Geometry students checking circle answers, gardeners and landscapers pricing circular beds or patios, and makers who know a radius and need the area, circumference and diameter of a round object without reaching for π and a calculator.
Benefits
- Gives area, circumference and diameter from a single radius
- Uses an accurate stored value of π throughout
- Removes the need to remember three separate formulas
- Handles very small or very large radii cleanly
Practical use cases
- Pricing turf or paving for a circular garden feature
- Finding the circumference of a wheel or pipe
- Checking a geometry homework answer for circle area
- Working out fabric needed for a round tablecloth
Frequently asked questions
How do I use the diameter instead?
Halve the diameter to get the radius, then enter it.
How do I work from the diameter instead of the radius?
The radius is exactly half the diameter, so halve your diameter first and enter that. A 10 unit diameter means a radius of 5, giving an area of about 78.54 and a circumference of about 31.42. All three circle measures follow from that radius.
What is the difference between circumference and area?
Circumference is the distance around the edge of the circle, found with 2 times π times the radius. Area is the space inside it, found with π times the radius squared. One is a length; the other is measured in square units.