Find the area of a circle.
The radius is squared and multiplied by π (about 3.14159).
Area: π × radius²
The circle area calculator finds how much flat space a circle covers. You enter the radius, the distance from the centre to the edge, and it returns π × r², using the full-precision value of π rather than 22/7 or 3.14.
Circle areas come up whenever something round has to be covered, filled or cut: a round dining table top, a circular rangoli, a pizza, the cross-section of a pipe or a well, or a sprinkler's watering zone. Students use the formula from Class 7 and build on it for cylinders, cones and spheres in later classes. If you know the diameter instead of the radius, halve it first, because the calculator's input is the radius.
1. Measure the radius r. If you have the diameter, divide it by 2. If you have the circumference C, use r = C ÷ (2π).
2. Square the radius: r × r.
3. Multiply by π. Use 3.14159 for accuracy, or 22/7 when the radius is a multiple of 7 in textbook problems.
4. Area = π × r².
5. Write the answer in square units matching the radius, such as cm² or m².
6. Round only at the end, to the precision your problem needs.
Cut a circle into many thin slices like a pizza, and lay them side by side, alternating point up and point down. As the slices get thinner, the shape looks more and more like a rectangle. Its height is the radius r, and its length is half the circumference, πr, because half the curved edges lie on top and half on the bottom. The rectangle's area is r × πr = πr². Archimedes made this argument rigorous using polygons inside and outside the circle.
Area scales with the square of any length. Double the radius and the area becomes four times as large; triple it and the area becomes nine times as large. This explains why a 12-inch pizza has more than twice the area of an 8-inch one, since (6/4)² = 2.25. It also matters in engineering: doubling a pipe's radius quadruples its cross-sectional area, and so roughly quadruples how much fluid can flow at the same speed.
π is irrational: its decimals never end or repeat. 22/7 ≈ 3.142857 is slightly too big, and 3.14 is slightly too small. For a radius of 10 m, the area is about 314.16 m² with the true π, 314.29 m² with 22/7 and 314 m² with 3.14. The differences are small but can matter in costing large areas. The calculator uses JavaScript's built-in Math.PI, accurate to about 15 decimal places, so its answer may differ slightly from a textbook that uses 22/7.
Divya is buying artificial grass for a round lawn patch with a radius of 4.5 metres in her apartment complex's garden.
Answer: Area 63.6173
Entering the diameter as the radius, which makes the area four times too large.
Using 2πr, the circumference formula, instead of πr².
Squaring π × r instead of r alone. The formula is π × r², not (πr)².
Expecting an exact match with a textbook answer that used 22/7 or 3.14.
Writing the answer in metres instead of square metres.
Estimating materials for round tables, rugs, lawns and rangoli designs.
Finding the cross-sectional area of pipes, wires and ducts.
Working out the watering zone of a sprinkler or the coverage of a light.
Comparing pizza or cake sizes by area rather than diameter.
Providing the base area for cylinder and cone volume calculations.
What if I only know the diameter?
First divide the diameter by 2, to get the radius. The area formula needs the radius, not the diameter.