Circle Area and Perimeter Calculator
Written by Thierno Sadou Diallo, formula verified per our methodology • Last checked on 9/3/2026
A circle's area is π × radius², and its perimeter (circumference) is 2 × π × radius. For a circle with a 5 cm radius, the area is about 78.54 cm² and the perimeter is about 31.42 cm.
Explanation
A circle is fully defined by its radius, the constant distance between its center and any point on its edge. Two main measurements follow from it: the area, the surface covered by the circle, given by the formula π × r², and the perimeter (also called the circumference), the length of the outline, given by 2 × π × r. The constant π (pi), about 3.14159, expresses the constant ratio between a circle's circumference and its diameter, whatever the circle's size. If you know the diameter instead, divide it by two to get the radius before using it here. For a triangle, see our triangle area calculator; for a three-dimensional solid derived from the circle, see the sphere volume calculator.
Example: a circle with a 5 cm radius
Inputs
Radius: 5 cm.
Calculation
Area: π × 5² = π × 25 ≈ 78.54 cm². Perimeter: 2 × π × 5 = 10π ≈ 31.42 cm.
Result
A circle with a 5 cm radius has an area of about 78.54 cm² and a perimeter of about 31.42 cm.
Frequently asked questions
What's the difference between perimeter and circumference?
None, for a circle: "circumference" is simply the name given to a circle's perimeter. "Perimeter" is used for any closed shape, "circumference" is specific to circles.
How do I calculate the area from the diameter instead of the radius?
The radius is half the diameter: divide the diameter by 2 to get the radius, then apply the formula π × radius². For example, a 10 cm diameter gives a 5 cm radius.
Why do we use the constant π?
π represents the ratio, identical for every circle, between its circumference and its diameter. It's an irrational number (its decimals never repeat); this calculator uses its full-precision value, not a rounded approximation like 3.14.
Does the result change depending on the unit used?
The unit selector next to the radius field automatically converts your input (mm, cm, m, or inches): the formula stays the same regardless of the unit chosen, with the area expressed in that unit squared and the perimeter in the same unit.