Radius, circumference, and disk area
Radius, diameter, and circumference are lengths in your chosen unit. Area uses that unit squared. The primary area result describes the full disk enclosed by the circumference, not just its boundary.
For rectangular sections that accompany the circular area, use the Square Footage Calculator with matching units before combining the areas.
The formula
Here r is radius, d is diameter, C is circumference, and A is area. The calculator first finds r: divide diameter by 2, divide circumference by 2π, or take the square root of area/π. The remaining measurements follow from that radius.
A circle with radius 5
Choose Radius and enter 5. Diameter is 10, circumference is approximately 31.415927, and area is approximately 78.539816 square units. If the radius is in metres, the circumference is in metres and the area is in square metres.
How to use this calculator
- Choose the measurement you know and a length unit. An area input uses that length unit squared.
- Enter the positive measurement and read the live circle dimensions.
- Switch the known measurement to continue from the same valid circle, or change units to convert its physical dimensions.
Radius and diameter describe different spans
A radius runs from the centre to the edge. A diameter passes through the centre from one edge to the opposite edge and is twice as long. Confusing these two inputs changes the calculated area by a factor of four.
When measuring a round object, identify whether you measured the full width or half of it. A string wrapped around the edge measures circumference, which is longer than the diameter by a factor of π.
Why area grows faster than circumference
Doubling the radius doubles the circumference because C is proportional to r. The same change quadruples the area because A depends on r squared. This matters when comparing circular lawns, tables, or printed disks.
A circular opening or ring needs a separate subtraction. For a ring, calculate the outer area and subtract the inner area. This page calculates one complete circle at a time and does not include material waste.
Switching measurements and units
When a valid radius of 5 m is entered, choosing Diameter carries 10 m into the field; choosing Area carries 25π m². You can then edit that measurement directly. An invalid value cannot supply a new measurement, so correct it before relying on a switch. Reset restores the radius-five example in meters.
Changing meters to centimeters multiplies a radius, diameter or circumference by 100, and an area input by 10,000. The field label and unit suffix distinguish length from area. Unit conversion keeps the physical circle rather than assigning the old number to a different unit. The tool uses international feet and inches, with numerical approximations for π.
Assumptions & limitations
What this calculation assumes
- The shape is a complete circle in a flat plane.
- The known measurement uses a consistent length or squared-length unit.
What to keep in mind
- Ellipse dimensions, arc lengths, sectors, and spheres are not modeled.
- π and the displayed results use numerical approximations.
Common questions
Is circumference the same as perimeter?
For a circle, yes. Circumference is the total distance around its boundary.
Can I enter area to find the radius?
Choose Area. The tool divides that value by π and takes its positive square root.
Does changing metres to centimetres multiply area by 100?
The unit selector converts the physical circle. A length is multiplied by 100; an area input is multiplied by 10,000. The field shows cm or cm² to distinguish them.
Sources & further reading
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