Calculating Area of a Circle: Formula and Examples

To calculate the area of a circle, square its radius and multiply by pi: A = πr². Enter the radius in the circle area calculator to get the area in square units, along with the circle’s circumference for reference.

Formula

The area formula is A = πr², also written as A = π × r × r.

• A is the area, measured in square units, such as square centimeters (cm²), square inches (in²), or square meters (m²).
• r is the radius: the straight-line distance from the circle’s center to its edge, measured in units such as centimeters, inches, or meters.
• π (pi) is the constant ratio of a circle’s circumference to its diameter, approximately 3.14159265.

The calculator’s first result is area, rounded to two decimal places. Its second result is circumference, the distance around the circle, in the same length units as the radius. Circumference is included as a related measurement; it is not part of the area result.

Worked Example

With the calculator’s default radius of 5 units:

1. Square the radius: 5 × 5 = 25 square units.
2. Multiply by pi: A = π × 25 = 78.5398… square units.
3. Round to two decimal places: the area is 78.54 square units.

For the related circumference result, C = 2πr = 2 × π × 5 = 31.4159… units, or 31.42 units rounded to two decimal places. The calculator keeps the radius as entered and rounds displayed results, rather than rounding pi early in the calculation.

How to Find the Radius

The radius is half the diameter. If you know the diameter, divide it by 2 before using the area formula: A = π(d ÷ 2)², where d is the diameter. For example, a circle with a diameter of 10 cm has a radius of 5 cm and an area of about 78.54 cm².

If you know the circumference instead, rearrange C = 2πr to get r = C ÷ (2π). You can then use that radius in A = πr². Alternatively, substitute directly to obtain A = C² ÷ (4π). Keep the circumference and the resulting area units consistent: a circumference in inches gives an area in square inches.

In some practical settings, the center may not be marked. Measure the circle’s widest straight-line span through the center to estimate its diameter, then halve it. For a physical object that is not perfectly circular, measurements from more than one direction can reveal whether treating it as a circle is a reasonable approximation.

Units and Reading the Result

Area is two-dimensional, so its units are squared. A radius measured in centimeters produces an answer in square centimeters; a radius in feet produces square feet. The formula does not convert units automatically, and the output label “square units” is generic: interpret it using the unit you entered.

Metric and US customary units both work. For instance, use a radius in meters to get m², or a radius in inches to get in². If converting an area, square the length-conversion factor too: 1 ft = 12 in, so 1 ft² = 144 in², not 12 in². Similarly, converting a radius from meters to centimeters before calculating changes the numerical area by a factor of 10,000 because (100 cm)² = 10,000 cm².

Do not mix a radius in one unit with a diameter or circumference in another unless you convert first. A calculator can return a mathematically correct number that is still misleading if the units have been entered inconsistently or interpreted incorrectly.

When the Circle Formula Applies

A = πr² gives the area of a flat, perfect circle. It is useful for estimating the face of a round tabletop, the cross-section of a pipe, a circular garden bed, or a disk. The formula concerns the flat region inside the boundary; it does not calculate the surface area or volume of a three-dimensional object.

For an annulus—the ring-shaped region between two circles with the same center—subtract the inner circle’s area from the outer circle’s area: A = π(R² − r²), where R is the outer radius and r is the inner radius. For a half-circle, divide the full circle’s area by 2. Other sectors, or “slices,” need an additional angle measurement; for an angle θ in degrees, the sector area is (θ ÷ 360)πr².

Real objects may be irregular, tilted, or imperfectly round. In those cases, the circle formula gives an estimate only if a representative radius can be chosen. A map or photograph can also distort apparent shape or scale, so measurements taken from it need an appropriate scale and may require correction for distortion.

Common Mistakes and Accuracy

• Using the diameter as the radius: If the known measurement is the diameter, halve it first. Putting the diameter directly into πr² makes the calculated area four times too large.
• Forgetting to square the radius: The formula is πr², not π × 2r. Squaring means multiplying the radius by itself.
• Reporting square units incorrectly: Area uses units such as cm² or ft², not cm or ft. Length and area describe different kinds of measurement.
• Rounding too soon: Keep extra digits during intermediate steps and round only the final answer. The final precision should also reflect how accurately the radius was measured.

Because radius is squared, small measurement errors can matter. If the radius changes by a fraction, the area changes by roughly twice that fraction for small changes. For example, a radius that is about 1% too large produces an area about 2% too large. This is why a highly precise calculator output should not be mistaken for a highly precise real-world measurement.

Frequently Asked Questions

How do you calculate the area of a circle?
Square the radius and multiply by pi: A = πr². The answer is expressed in square units.

What is the area of a circle with diameter 10?
The radius is 10 ÷ 2 = 5. Its area is π × 5² = 25π, approximately 78.54 square units.

Can I calculate circle area from circumference?
Yes. Use A = C² ÷ (4π), where C is the circumference. Make sure the circumference is in one consistent length unit; the answer will be in that unit squared.

Why is the answer in square units?
The formula multiplies radius by radius, so its units are multiplied too: for example, cm × cm = cm². That reflects the two-dimensional size of the enclosed region.

Is area the same as circumference?
No. Area measures the space inside a circle, while circumference measures the length around its edge. Area is in square units; circumference is in ordinary length units.

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in r | Radius | units | 5 | 0
out area | Area | square units | pi * r ^ 2 | 2
out circumference | Circumference | units | 2 * pi * r | 2