Area of a Circle Calculator — π × r²
Enter the radius of a circle and instantly get its area, circumference and diameter. The calculator uses the exact formula A = π r² and also shows quarter- and sixth-circle sector areas for common reference.
Area = π × r²
- 1
Square the radius
5 × 5 = 25 - 2
Multiply by π
π × 25 = 78.5398π ≈ 3.14159265 — the constant ratio of circumference to diameter.
How does this calculator work?
Area of a circle = π × r², where r is the radius (π ≈ 3.14159). Circumference = 2 × π × r. If you know the diameter d, use r = d/2. The area is in square units and grows with the square of the radius — doubling r quadruples the area.
Formula
How this is calculated
The area of a circle is the total space enclosed within its boundary (the circumference). The formula A = π × r² comes directly from integration — think of a circle as a set of infinitely thin concentric rings; each ring of radius t and width dt has area 2πt dt, and integrating from 0 to r gives π r². Here π ≈ 3.14159265 is the ratio of a circle's circumference to its diameter, a mathematical constant.
The circumference — the perimeter of a circle — is C = 2 × π × r = π × d, where d = 2r is the diameter. If you know the diameter instead of the radius, simply divide by 2 first. Knowing the area you can recover the radius as r = √(A/π).
These formulas assume a perfect flat circle (a 2-D disk). For a sphere (a 3-D ball), use A = 4πr² for surface area and V = (4/3)πr³ for volume — different formulas. The sector area for a portion of angle θ (in degrees) is Area_sector = (θ/360°) × π × r².
Frequently asked questions
Area = π × r², where r is the radius and π ≈ 3.14159. If you know the diameter d instead, use Area = π × (d/2)² = π × d²/4.
First find the radius: r = C / (2π). Then apply Area = π × r² = C² / (4π). For example, C = 20 cm → r = 20/(2π) ≈ 3.183 cm → Area ≈ 31.83 cm².
Area (A = πr²) measures the flat space inside the circle, in square units (cm², m², etc.). Circumference (C = 2πr) is the length of the circular boundary, in linear units (cm, m, etc.).
Also known as
TG we-Calculate Editorial Team. (2026). Area of a Circle Calculator — π × r² [Online calculator]. TG we-Calculate. https://we-calculate.com/calculator/area-of-a-circle-calculator
TG we-Calculate Editorial Team. "Area of a Circle Calculator — π × r²." TG we-Calculate. 2026. https://we-calculate.com/calculator/area-of-a-circle-calculator.
TG we-Calculate Editorial Team, "Area of a Circle Calculator — π × r²," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/calculator/area-of-a-circle-calculator
@misc{wecalculate_area_of_a_circle_calculator, title = {Area of a Circle Calculator — π × r²}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/calculator/area-of-a-circle-calculator}}, year = {2026}, note = {TG we-Calculate} }
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