Calculate the area, circumference, and diameter of any circle from its radius — instantly, with π = 3.14159 or 22/7.
The Area of Circle Calculator instantly computes the area, circumference, and diameter of a circle when you enter the radius. The circle is one of the most fundamental shapes in geometry, and calculating its area and circumference are among the most commonly searched math topics globally — from elementary school students learning geometry to engineers designing circular components.
This calculator supports two values of π: the more precise decimal approximation (3.14159...) and the fraction 22/7, which is commonly used in Indian school textbooks from Class 7 through Class 10 (CBSE and ICSE). The 22/7 approximation gives slightly different answers, so students can match their textbook calculations exactly.
Understanding the Formulas
- Area: The area of a circle is π × r². This is the space enclosed within the circle. If a circle has a radius of 7 cm, its area is π × 7² = π × 49 ≈ 154 cm² (using π = 22/7).
- Circumference: The circumference (perimeter) of a circle is 2 × π × r. This is the total length around the circle. It is also equal to π × diameter.
- Diameter: The diameter is simply twice the radius (d = 2r). It is the longest chord — a straight line passing through the center.
Real-World Applications
Circle area calculations appear everywhere: finding the area of a circular garden or swimming pool, calculating how much material is needed for a circular tabletop, determining the coverage area of a circular antenna or WiFi router, computing the cross-sectional area of a pipe for flow calculations, finding the size of a pizza or circular cake, and much more. In Indian competitive exams (SSC, CAT, banking exams), circle area problems are a standard category in the mensuration chapter.
1. Enter the Radius: Type the radius of the circle (half the diameter).
2. Select Pi Approximation: Choose 3.14159 (more precise) or 22/7 (used in Indian textbooks).
3. View Results: The calculator instantly shows the Area (π×r²), Circumference (2π×r), and Diameter (2×r).
Area = π × r²
Circumference = 2 × π × r
Diameter = 2 × r
Where r is the radius and π ≈ 3.14159 or 22/7.
If you know the diameter instead of radius: r = d/2, then Area = π × (d/2)² = π × d²/4.
If you know the circumference: r = C/(2π), then Area = C²/(4π).
Example 1 (π=22/7): Radius = 7 cm → Area = 22/7 × 49 = 154 cm². Circumference = 2 × 22/7 × 7 = 44 cm. Diameter = 14 cm.
Example 2 (π=3.14159): Radius = 5 cm → Area = 3.14159 × 25 = 78.54 cm². Circumference = 2 × 3.14159 × 5 = 31.42 cm.
Example 3 — From diameter: A circular pool has diameter 10m. Radius = 5m. Area = π × 25 ≈ 78.54 m².