Area of a Circle Calculator
This calculator works out the area, circumference and diameter of a circle from just one measurement, using the standard formula A = πr². Knowing a circle's area is useful for everyday and trade tasks, from working out how much turf, paint or fabric covers a circular space, to schoolwork on geometry, to trade jobs like sizing a pipe or a circular garden bed. To use it, choose whether you are entering the radius (the distance from the centre to the edge) or the diameter (the distance straight across the circle), type in your measurement, and pick the unit you are working in, from millimetres and centimetres through to metres, feet, inches and miles. The calculator instantly returns the area (highlighted in square units), the circumference, and the diameter and radius, so you can check your figures converted the right way. You can also choose how many decimal places to show, handy if you need extra precision for technical work or just a rounded figure for a quick job. Below the results, a step-by-step working panel shows exactly how pi was multiplied through to reach the final area and circumference, so you can follow the maths or check your own working by hand. Because the calculation uses a fixed geometric formula rather than an estimate, the figures are exact to the precision you choose.
1. Circle Measurement
2. Unit
Step-by-Step Working
How to Calculate the Area of a Circle
The area of a circle is the amount of space enclosed within the boundary of the circle. It is calculated using the formula:
A = π × r²
Where:
- A is the area (in square units)
- π (pi) is the mathematical constant approximately equal to 3.14159265
- r is the radius of the circle (the distance from the centre to any point on the circumference)
If you know the diameter (d) rather than the radius, the relationship is r = d / 2. You can substitute this into the formula to get A = π × (d/2)² = πd² / 4.
Worked Example
A circle has a radius of 5 cm. What is its area and circumference?
- Radius r = 5 cm
- Area A = π × r² = π × 5² = π × 25 = 78.5398 cm²
- Circumference C = 2 × π × r = 2 × π × 5 = 31.4159 cm
- Diameter d = 2 × r = 2 × 5 = 10 cm
These match the calculator's default output when the radius is set to 5 cm.
Common Circle Calculations
| Radius (cm) | Diameter (cm) | Area (cm²) | Circumference (cm) |
|---|---|---|---|
| 1 | 2 | 3.1416 | 6.2832 |
| 3 | 6 | 28.2743 | 18.8496 |
| 5 | 10 | 78.5398 | 31.4159 |
| 7 | 14 | 153.9380 | 43.9823 |
| 10 | 20 | 314.1593 | 62.8319 |
| 15 | 30 | 706.8583 | 94.2478 |
| 25 | 50 | 1963.4954 | 157.0796 |
Circumference of a Circle
The circumference is the perimeter of a circle, the total distance around its edge. The formula is:
C = 2 × π × r (equivalently, C = π × d)
Notice that the circumference uses the same linear unit as the radius (for example, centimetres), while the area uses square units (square centimetres).
Frequently Asked Questions
What is the area of a circle with diameter 10 cm?
A circle with diameter 10 cm has a radius of 5 cm. Area = π × 5² = π × 25 = 78.5398 cm².
How is pi used in circle calculations?
Pi (π) is the ratio of a circle's circumference to its diameter. It is an irrational number with no repeating decimal pattern, beginning 3.14159265... For most practical calculations, using 3.14159 or the built-in Math.PI in a calculator is sufficient. This calculator uses the full precision value provided by JavaScript's Math.PI (approximately 15 significant digits).
What is the difference between radius and diameter?
The radius is the distance from the centre of the circle to any point on its edge. The diameter is the distance across the circle through its centre, passing through two points on the circumference. The diameter is always exactly twice the radius: d = 2r.
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Method: Area calculated using A = πr² where π is Math.PI (IEEE 754 double precision). Circumference calculated as C = 2πr. All results are mathematically exact to the precision of 64-bit floating-point arithmetic.