To find the area of a circle, square its radius and multiply by π: A = πr². For a radius of 5 meters, the area is 25π ≈ 78.54 m². If you know the diameter, halve it first.
The circle area formula, without guesswork
The symbol A stands for area and r for radius. π (pi) is the same constant used for every circle, approximately 3.14159265. You can leave your answer as an exact multiple of π or use a decimal approximation.
- Measure the radius in one length unit.
- Square the radius: multiply r × r.
- Multiply by π. The answer is in square units, such as cm² or ft².
Worked example: a circular garden
A circular garden measures 10 meters across. The 10-meter measurement is its diameter, not its radius. Divide by two to obtain r = 5 m.
r = 10 ÷ 2 = 5 m
A = π × 5² = 25π m²
A ≈ 78.54 m²
For landscaping, that is the idealized area of a perfectly circular garden. Stones, paths and uneven boundaries may change how much material you actually need. If you are ordering material, use the measured outline rather than treating the garden as exactly round.
What if you have the diameter or circumference?
You do not need to measure the radius directly. Convert your known value to radius first, or use the equivalent expression in the table.
| Known measurement | Area expression | Example |
|---|---|---|
| Radius r | A = πr² | r = 5 → 25π |
| Diameter d | A = πd² ÷ 4 | d = 10 → 25π |
| Circumference C | A = C² ÷ (4π) | C = 10π → 25π |
The Area Calculator's circle mode accepts radius, so convert diameter or circumference to radius before typing your measurement.
A useful check: doubling the radius quadruples the area
Compare two concentric circles. If the smaller radius is 3 cm, A = 9π cm². If the larger radius is 6 cm, A = 36π cm²—four times as much area, not twice. This is a quick way to catch errors when comparing differently sized circular objects.
Three common errors
Using diameter for r: squaring the diameter instead of the radius makes the result four times too large. Rounding π early: use your calculator's π key and round at the end. Writing linear units: 78.54 m and 78.54 m² describe very different things; only the latter represents area.
Questions students often ask
Is circle area the same as circumference?
No. Circumference describes the distance around the circle and equals 2πr. Area describes the space inside and equals πr².
Can I calculate the area from a diameter alone?
Yes. Use A = π(d/2)²; no other measurement is needed for a circle.
Formula reference: OpenStax, Contemporary Mathematics, section 10.6.