Area of Circle Calculator

The standard area of a circle formula is A = πr², where A is the area, π (pi) is approximately 3.14159, and r is the radius. You can also express the area of a circle using the diameter: A = (πd²) / 4, or from the circumference: A = C² / (4π). All three formulas produce identical results because radius, diameter, and circumference are geometrically related: d = 2r and C = 2πr.

To calculate the area of a circle with the radius, use A = πr². Multiply π (3.14159…) by the square of the radius. For example, if the radius is 5 cm: Step 1 — Square the radius: 5² = 25. Step 2 — Multiply by π: 25 × 3.14159 ≈ 78.54 cm². Our area of a circle calculator with radius performs this computation instantly in centimeters, inches, feet, meters, or any supported unit.

When you know the diameter, either divide it by 2 to get the radius (r = d / 2) and then apply A = πr², or use the direct diameter formula: A = (πd²) / 4. For a diameter of 10 inches: A = π × (10)² / 4 = π × 100 / 4 = π × 25 ≈ 78.54 square inches. Our area of a circle calculator with diameter handles this conversion automatically.

If you know the circumference (C), derive the radius using r = C / (2π), then compute A = πr². The direct formula is A = C² / (4π). For a circumference of 31.42 cm: A = (31.42)² / (4 × 3.14159) = 987.22 / 12.566 ≈ 78.54 cm². Our area of circle calculator with circumference automates this for any unit you choose.

Use the reverse formula: r = √(A / π). Divide the known area by π (3.14159…), then take the square root. For example, if the area is 314.16 cm²: r = √(314.16 / 3.14159) = √(100) = 10 cm. You can also find diameter from area: d = 2 × √(A / π), or circumference: C = 2 × √(πA). Our calculator handles all reverse computations automatically — just type the area value into the Area field.

Select 'in' (inches) as the unit in the radius, diameter, or circumference input field. Enter your measurement, and the calculator returns the area in square inches (in²). You can also switch the area output unit to square feet, square meters, or acres. This makes our area of circle calculator inches-ready for woodworking, crafting, and home improvement projects.

Yes. Our area of circle calculator supports square feet (ft²), square meters (m²), square centimeters (cm²), square inches (in²), square millimeters (mm²), hectares (ha), and acres (ac). Simply select the desired area unit from the dropdown and enter the circle dimension in the corresponding linear unit — feet for square feet, meters for square meters, and so on.

Circumference measures the one-dimensional distance around the circle's edge (perimeter), expressed in linear units like cm or inches. Area measures the two-dimensional surface enclosed inside the circle, expressed in square units like cm² or in². The circumference formula is C = 2πr (linear), while the area formula is A = πr² (quadratic). If you double the radius, the circumference doubles but the area quadruples.

This calculator supports eight linear units — millimeters (mm), centimeters (cm), meters (m), kilometers (km), inches (in), feet (ft), yards (yd), and miles (mi) — plus nine area units: mm², cm², m², km², in², ft², yd², hectares, and acres. You can mix input and output units freely; the calculator converts everything through a common base unit (meters and square meters internally).

Pi (π ≈ 3.14159265…) is the ratio of a circle's circumference to its diameter (C / d = π). This irrational constant appears in every circle formula because it defines the fundamental geometric relationship between a circle's linear dimensions (radius, diameter, circumference) and its curved area. Without π, you cannot convert between straight-line measurements and the curved area enclosed by a circle. Pi is the same for every circle, regardless of size.

Choose the matching unit for your input: cm for centimeters, mm for millimeters, or m for meters. Enter the radius (or diameter/circumference), and the calculator instantly returns the area in cm², mm², or m². For example: a radius of 7 mm gives A = π × 7² ≈ 153.94 mm². A radius of 3 m gives A = π × 9 ≈ 28.27 m².

Our calculator uses JavaScript's full-precision Pi value (π = 3.141592653589793, 15 significant digits). You can choose 2, 3, 4, or 6 decimal places for display output. Internally, all conversions use exact conversion factors (e.g., 1 inch = 0.0254 m exactly), ensuring engineering-grade accuracy for professional, academic, and everyday use. Results match scientific calculator outputs to the selected decimal precision.

Yes. Select 'ac' (acres) from the area unit dropdown. The calculator converts the computed area in square meters to acres using the exact factor (1 acre = 4,046.8564224 m²). This is especially useful for land-area calculations in agriculture, real estate, and landscaping where circular irrigation, ponds, or plots need acreage estimates.

The area of a semicircle is exactly half the area of the full circle: A(half) = (πr²) / 2. First calculate the full circle area using our calculator, then divide the result by 2. For example, a semicircle with radius 8 cm has area = (π × 64) / 2 ≈ 100.53 cm².

The area of a circle is used in engineering (pipe cross-sections, wheel design, wire gauge), construction (circular foundations, columns, domes), agriculture (irrigation coverage, silo capacity), cooking (pan and pizza sizing), science (cell biology, optics, orbital mechanics), and everyday life (calculating paint for circular walls, fabric for round tables, concrete for stepping stones). Our calculator helps students, teachers, DIY enthusiasts, and professionals get instant, verified answers.