Circle Area Calculator
Calculate the area, circumference, diameter, and radius of any circle from a single known measurement. Supports millimetres, centimetres, metres, inches, and feet — with a full formula breakdown every time.
Circle Measurements
Enter any one known value — radius, diameter, or circumference
The distance from the centre of the circle to its edge
The full width of the circle through its centre (= 2 × radius)
The perimeter — total distance around the circle
The total surface enclosed within the circle boundary
Controls rounding in all output values
Circle Results
Area, circumference, diameter & radius
Enter a radius, diameter, circumference, or area value and click Calculate Circle to see all measurements and the step-by-step formula breakdown.
Circle Quick Reference Table
Pre-calculated area and circumference values for standard circle sizes (using radius as the base measurement).
| Radius (r) | Diameter (d = 2r) | Area (A = πr²) | Circumference (C = 2πr) |
|---|---|---|---|
| 1 cm | 2 cm | 3.1416 cm² | 6.2832 cm |
| 2 cm | 4 cm | 12.5664 cm² | 12.5664 cm |
| 5 cm | 10 cm | 78.5398 cm² | 31.4159 cm |
| 10 cm | 20 cm | 314.1593 cm² | 62.8318 cm |
| 15 cm | 30 cm | 706.8583 cm² | 94.2478 cm |
| 25 cm | 50 cm | 1,963.4954 cm² | 157.0796 cm |
| 50 cm | 100 cm | 7,853.9816 cm² | 314.1593 cm |
| 1 m | 2 m | 3.1416 m² | 6.2832 m |
| 5 m | 10 m | 78.5398 m² | 31.4159 m |
| 1 inch | 2 inches | 3.1416 in² | 6.2832 in |
| 6 inches | 12 inches | 113.0973 in² | 37.6991 in |
| 1 foot | 2 feet | 3.1416 ft² | 6.2832 ft |
Circle Area FAQ
Key concepts behind circle geometry, the area formula, and how to calculate any circle measurement from a single known value.
The area of a circle is A = π × r², where r is the radius (the distance from the centre of the circle to its edge) and π (pi) is the mathematical constant approximately equal to 3.14159265. If you know the diameter (d) instead of the radius, use A = π × (d ÷ 2)². For example, a circle with a radius of 5 cm has an area of π × 25 = 78.5398 cm².
The circumference is the perimeter of a circle — the total distance around its outer edge — calculated as C = 2πr or C = πd. It is measured in linear units (cm, m, inches). The area, on the other hand, measures the surface enclosed within the circle and is calculated as A = πr². Area is expressed in square units (cm², m², in²). A circle with a radius of 5 cm has a circumference of 31.4159 cm and an area of 78.5398 cm².
To find the radius from a known area, rearrange the area formula: r = √(A ÷ π). For example, if the area is 200 cm², then r = √(200 ÷ 3.14159) = √63.6620 = 7.9788 cm. Once you have the radius, you can derive the diameter (d = 2r) and circumference (C = 2πr) instantly.
The area of a semicircle is exactly half of a full circle’s area: A = (π × r²) ÷ 2. For example, a semicircle with a radius of 5 cm has an area of (π × 25) ÷ 2 = 39.2699 cm². The perimeter of a semicircle is the half-circumference plus the diameter: P = πr + 2r = r(π + 2).
Pi (π) is the ratio of any circle’s circumference to its diameter, and it is the same for every circle regardless of size. Pi is an irrational number — it never ends and never repeats — with a value of approximately 3.14159265358979. It appears in all circle and sphere calculations because it is the fundamental constant connecting a circle’s linear dimensions to its curved properties. In everyday engineering and construction, π is rounded to 3.14159 or 3.1416.
Circle area calculations appear across many practical fields. In construction and landscaping, they are used to calculate paving areas, sprinkler coverage zones, or circular room layouts. In engineering, they determine pipe cross-sections, wheel dimensions, and gear sizes. In cooking, they help scale recipes based on circular tin sizes. In science, circle and sphere formulas underpin astronomy, fluid dynamics, and optics. Knowing how to quickly convert between radius, diameter, area, and circumference is a core applied geometry skill.