Circle Area Calculator
The circle area calculator works from either a radius or a diameter. Choose the measurement you know, enter its value and unit, and the calculation with your numbers appears beside the answer.
The result also includes the radius, diameter, and circumference. The arithmetic uses the full available value of π and rounds only the displayed numbers.
Circle area
78.539816 cm²
Substitution: A = π × r² = π × 5² = 78.539816 cm²
Radius
5 cm
Diameter
10 cm
Circumference
31.415927 cm
How to calculate circle area from a radius
The area of a circle is pi times the radius squared: A = π × r². The radius is the distance from the center to the edge. It is measured in a length unit, while the resulting area uses the square of that unit.
For example, a radius of 5 cm gives A = π × 5² = π × 25 ≈ 78.539816 cm². The same circle has a circumference of 2 × π × 5 ≈ 31.415927 cm.
Circle area from a diameter
A diameter crosses the center and equals two radii, so divide it by two first. The area formula in terms of diameter is A = π × (d ÷ 2)², which can also be written as A = πd² ÷ 4.
With a diameter of 12 m, the radius is 6 m and the area is π × 6² ≈ 113.097336 m². Selecting “Diameter” makes the calculator perform that conversion before finding the area.
Square units and precision
- A radius entered in millimeters produces mm²; centimeters produce cm²; meters produce m².
- Do not label an area with plain meters or inches. Those are length units rather than square units.
- Area conversions square the length factor. One square meter is 10,000 square centimeters, not 100 square centimeters.
- Pi is irrational. The calculator keeps its machine precision through the arithmetic and rounds only the value shown on screen.
Circle area and circumference examples
| Radius | Diameter | Area | Circumference |
|---|---|---|---|
| 1 | 2 | 3.141593 | 6.283185 |
| 2.5 | 5 | 19.634954 | 15.707963 |
| 5 | 10 | 78.539816 | 31.415927 |
| 10 | 20 | 314.159265 | 62.831853 |
Common calculation mistakes
- Using the diameter as r makes the answer four times too large because the measurement is squared.
- Multiplying the radius by two instead of squaring it calculates neither the area nor the circumference.
- Mixing units leads to a mislabeled answer, such as entering centimeters but reading the result as square meters.
- Rounding π or the radius too early can noticeably change a large area. Keep full precision until the final answer.
Frequently asked questions
How do I calculate the area of a circle?
Square the radius and multiply by π: A = π × r². A circle with radius 5 cm has an area of about 78.539816 cm².
How do I find circle area from the diameter?
Divide the diameter by two, square that radius, and multiply by π. The equivalent direct formula is A = πd² ÷ 4.
Which units does the area use?
It uses the square of the selected length unit: centimeters become cm², meters become m², and inches become in².
What is the difference between a circle and its circumference?
A circle is the entire region inside the boundary, so it has area. Circumference is the length of the boundary and is calculated as C = 2πr.
How do I get the radius from a diameter?
Divide the diameter by two: r = d ÷ 2. A diameter of 18 cm therefore has a radius of 9 cm.
Updated: 2026-08-16