What the Circle Area Calculator Does
This Circle Area Calculator finds the area enclosed by a circle from a single measurement: the radius. The radius is the distance from the centre of the circle to its edge. Enter that value and the calculator instantly returns the area, and as a useful bonus it also works out the circumference and the diameter from the same input.
How to Use It
- Radius: Type the radius of your circle in whatever unit you are working in (cm, m, inches, etc.).
- The result is returned in those same units squared — for example, a radius in metres gives an area in square metres.
- If no value is entered, the tool defaults the radius to 3.
The Formula Explained
The area of a circle is calculated with the classic geometry formula:
A = π r²
Here r is the radius and π (pi) is approximately 3.14159. The calculator multiplies pi by the radius squared (radius × radius). Behind the scenes it also derives:
- Circumference: C = 2 π r — the distance around the circle.
- Diameter: D = 2 r — the full width across the centre.
Worked Example
Suppose you enter a radius of 5:
- Area = π × 5 × 5 = π × 25 ≈ 78.54 square units.
- Circumference = 2 × π × 5 ≈ 31.42 units.
- Diameter = 2 × 5 = 10 units.
So a circle with a 5 cm radius has an area of about 78.54 cm², a circumference of roughly 31.42 cm, and a diameter of 10 cm.
Frequently Asked Questions
What if I only know the diameter? Divide the diameter by 2 to get the radius, then enter that. For example, a 10 cm diameter means a 5 cm radius.
Why is the area squared? Area measures a two-dimensional surface, so the unit is always squared — square centimetres, square metres, and so on. The radius is multiplied by itself, which is why the unit gains its second dimension.
How accurate is the result? The calculator uses the full precision value of pi (Math.PI), so the answer is accurate to many decimal places. Any rounding you see is only for display.
