Circle Area Calculator FAQ
What is the formula for the area of a circle?
The standard formula is A = π × r², where r is the radius. If you know the diameter: A = π × d² / 4. If you know the circumference: A = C² / (4π). Example: radius 10 cm → A = π × 100 = 314.16 cm².
How do you calculate the area of a circle from the diameter?
Use A = π × d² / 4, or divide diameter by 2 to get radius and apply A = πr². Example: diameter 12 cm → A = π × 144 / 4 = 113.1 cm². Example: diameter 50 m → A = π × 2500 / 4 = 1,963.5 m².
How do you find the radius from the area of a circle?
Rearrange A = πr² to get r = √(A / π). Example: area 200 cm² → r = √(200 / π) = √63.66 = 7.98 cm. Diameter = 2r = 15.96 cm. This is the reverse formula the calculator uses when you enter area as the known input.
How do you calculate the area of a circle from the circumference?
Use A = C² / (4π). Example: circumference 31.4 cm → A = 31.4² / (4 × π) = 985.96 / 12.566 = 78.4 cm². Alternatively find r = C / (2π) first, then apply A = πr². Both routes give the same answer.
What is the area of a semicircle or quarter circle?
Semicircle: A = π × r² / 2. Example: radius 6 cm → full circle ≈ 113.1 cm² → semicircle = 56.55 cm². Quarter circle (quadrant): A = π × r² / 4. Example: radius 6 cm → 28.27 cm².
How do you convert circle area between different units?
Calculate in cm² first, then convert: 1 m² = 10,000 cm², 1 ft² ≈ 929 cm², 1 in² ≈ 6.45 cm². Example: circle radius 1 m → A = π × 1² = 3.14159 m² = 31,416 cm². The calculator converts units automatically.
What are real-world uses of the circle area formula?
Common uses: pizza sizing (12" pizza = 113 in² vs 78.5 in² for 10" — 44% more area), irrigation (radius 25 m → 1,963 m² irrigated), pipe flow (diameter 10 cm → 78.5 cm² cross-section), round rugs (diameter 4 m → 12.6 m² material), land plots and circular pools.
Why does a circle have more area than a square with the same perimeter?
A circle encloses the maximum area for any given perimeter — the isoperimetric inequality. Square with perimeter 40 m: side = 10 m → area = 100 m². Circle with circumference 40 m: r = 40/(2π) = 6.37 m → area = π × 6.37² = 127.3 m² (27% more). This is why round shapes are common in tanks and containers.
