Circle Area Calculator
Calculate the area of a circle from its radius, diameter or circumference. Explore semicircles and circular sectors, find circumference and arc length, and convert your result into different area units instantly.
Circle area calculator with diagram
A circle is the set of points in a plane that are a fixed distance from a central point. That distance is the radius. The diameter passes through the centre and equals twice the radius.
A = πr²
Square the radius and multiply by pi.
A = πd² / 4
The radius is half the diameter.
A = C² / (4π)
Find the area using the circumference.
C = 2πr = πd
The distance around the full circle.
A = ½πr²
Half the area of a complete circle.
A = (θ / 360°)πr²
A fraction of the full circle determined by its central angle.
How to calculate the area of a circle
1. Using the radius
The standard circle area formula is A = πr². Multiply pi by the radius squared. For a circle with a radius of 5 metres, the area is approximately 78.54 square metres.
2. Using the diameter
If you know the full width through the centre, divide the diameter by two to obtain the radius. Alternatively, use the equivalent formula A = πd² / 4.
3. Using the circumference
The circumference is the distance around a circle. Rearranging C = 2πr gives r = C / (2π). Substituting this into the area formula gives A = C² / (4π).
4. Calculating a sector
A sector is a portion of a circle bounded by two radii and the arc between them. Its area is the same fraction of the full circle's area as its central angle is of 360 degrees.
5. Calculating a semicircle
A semicircle is half of a circle. Divide the full circle's area by two. If you also need its perimeter, include the straight diameter as well as the curved half-circumference.
Circle area examples
| Calculation | Measurement | Formula | Result |
|---|---|---|---|
| Area from radius | r = 5 cm | π × 5² | 78.540 cm² |
| Area from diameter | d = 10 cm | π × 10² / 4 | 78.540 cm² |
| Area from circumference | C = 20π cm | C² / (4π) | 100π cm² ≈ 314.159 cm² |
| Semicircle | r = 4 m | π × 4² / 2 | 25.133 m² |
| 90° sector | r = 4 cm | 90 / 360 × π × 4² | 12.566 cm² |
Area and circumference: what is the difference?
Area and circumference describe different properties of a circle. Area measures the space inside the boundary and uses square units. Circumference measures the length of the boundary and uses linear units.
A = πr²
Examples: cm², m² and ft².
C = 2πr
Examples: cm, m and ft.
d = 2r
Twice the radius, measured in linear units.
Circle area unit conversions
Converting an area requires squared conversion factors. For example, one square metre is equal to 10,000 square centimetres, not 100 square centimetres.
| Area unit | Equivalent in square metres | Typical application |
|---|---|---|
| 1 mm² | 0.000001 m² | Small components |
| 1 cm² | 0.0001 m² | Small surfaces |
| 1 m² | 1 m² | Rooms and surfaces |
| 1 km² | 1,000,000 m² | Large areas |
| 1 in² | 0.00064516 m² | Imperial measurements |
| 1 ft² | 0.09290304 m² | Floor plans |
| 1 yd² | 0.83612736 m² | Landscaping |
| 1 acre | 4,046.8564224 m² | Land measurement |
| 1 hectare | 10,000 m² | Agriculture |
Frequently asked questions
What is the formula for the area of a circle?
The formula is A = πr², where A is the area, r is the radius and π is approximately 3.14159265358979.
How do I calculate circle area from its diameter?
Divide the diameter by two to get the radius, then calculate A = πr². Equivalently, use A = πd² / 4.
How can I calculate area from circumference?
Use A = C² / (4π), where C is the circumference. This formula comes from substituting r = C / (2π) into A = πr².
Does doubling the radius double the area?
No. Doubling the radius makes the area four times larger because the radius is squared in A = πr². The circumference, however, doubles.
What is the difference between a circle and a semicircle?
A full circle encloses area πr². A semicircle encloses half that area, πr² / 2. The perimeter of a semicircle includes the curved edge and the diameter.
How do I calculate the area of a circular sector?
Multiply the full circle area by the fraction θ / 360°. Therefore, sector area = (θ / 360°) × πr², where θ is the central angle in degrees.
Why are area measurements expressed in square units?
Area measures two-dimensional space. Multiplying two lengths gives square units, such as metres multiplied by metres resulting in square metres.
Are my measurements sent to a server?
No. The calculator performs its calculations in your browser. It does not submit the entered dimensions to this PHP page or store them in a database.
Can I share my circle calculation?
Yes. Select Copy calculation link to create a URL containing your chosen method, dimensions, unit settings and precision. You can also print the result or copy the calculation text.
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