CircleLab

Circle Area Calculator

Enter a radius — get area, circumference, and diameter with the exact formulas used.

Radius

Area

78.54

Circumference: 31.416
Diameter: 10

A = π × r²

What you entered

Radius: 5

1
Diameter
2 × 5= 10
2
Circumference
2π × 5= 31.4159
3
Area
π × 5²= 78.5398

Result

Area: 78.54

A circle with radius 5 has an area of 78.54 square units and a circumference of 31.416 units.

Circle area and circumference by radius

Area is pi times the radius squared; circumference is 2 pi r. Values are rounded to two decimals.

Radius	Diameter	Circumference	Area
1	2.00	6.28	3.14
2	4.00	12.57	12.57
3	6.00	18.85	28.27
5	10.00	31.42	78.54
7	14.00	43.98	153.94
10	20.00	62.83	314.16
12	24.00	75.40	452.39
15	30.00	94.25	706.86
20	40.00	125.66	1256.64

Every value is in the same unit family as the radius: a radius in cm gives a circumference in cm and an area in square cm. Notice the r=2 row, where circumference and area both read 12.57 - a coincidence at that radius only, because 2*pi*r equals pi*r^2 exactly when r=2. Area grows with the square of the radius while circumference grows linearly, so doubling the radius doubles the circumference but quadruples the area. That is why the 20 row has twice the circumference of the 10 row and four times the area.

Why r² and not just r

A circle's area scales with the square of the radius — double the radius and you quadruple the area, not just double it. That's because area is fundamentally two-dimensional; π·r² comes from summing up infinitely thin rings from the center out to the edge.

Why people need this

Circle area shows up constantly: sizing a pizza to compare value per dollar, figuring out how much material covers a round table, estimating paint or fertilizer for a circular garden bed, or sanity-checking a pipe's cross-sectional flow capacity.

Frequently asked questions

How do I calculate the area of a circle?

Area = π × r² (pi times the radius squared). If you know the diameter instead, divide it by 2 to get the radius first. Example: radius = 5 cm → Area = π × 25 = 78.54 cm². If using the diameter (10 cm): Area = π × (10/2)² = 78.54 cm².

What is the area of a 10-inch pizza vs a 12-inch pizza?

A 10-inch pizza has area π × 5² = 78.5 in². A 12-inch pizza has area π × 6² = 113.1 in². That's 44% more pizza — not 20% more. This is why area scales with the square of the radius: a small increase in diameter yields a much bigger increase in area.

How do I find the radius if I know the area?

Rearrange the formula: r = √(A / π). Example: if the area is 200 cm², then r = √(200 / 3.14159) = √(63.66) = 7.98 cm. The diameter would be about 15.96 cm.