Area of a Circle: Formula, Examples & Calculator

This calculator works out the area of a circle from its radius, diameter, or circumference. You enter one known value, and it returns the area in square units, along with the other two linear measurements for reference. The page also explains the formula, shows a step-by-step example, and covers the common mistakes people make when measuring circles.

Formula

The area of a circle is given by the formula:

A = π × r²

where:

• A = area of the circle (square units, e.g., m², ft², cm²)
• π (pi) ≈ 3.14159265…, a mathematical constant
• r = radius of the circle (units of length, e.g., m, ft, cm)

If you know the diameter d (which is twice the radius), the formula becomes A = π × (d/2)². If you know the circumference C, you can find the radius first using r = C / (2π), then apply the area formula.

Worked Example

Using the default values from the calculator above (radius = 5 m):

1. Write down the formula: A = π × r²
2. Substitute the radius: A = π × (5 m)²
3. Square the radius: (5 m)² = 25 m²
4. Multiply by π: A = 3.14159… × 25 m² = 78.5398… m²
5. Round to two decimal places: A ≈ 78.54 m²

The calculator shows 78.54 m² for the area, 31.42 m for the circumference, and 10 m for the diameter, all rounded to two decimals.

When to Use the Circle Area Formula

You need the area of a circle whenever you are covering, filling, or comparing a round surface. Common situations include:

• Finding how much carpet, tile, or paint is needed for a circular room or tabletop.
• Calculating the cross-sectional area of a pipe or wire (to estimate flow or resistance).
• Determining the size of a circular garden bed, pond, or fountain.
• Working out the area of a pizza or cake when comparing sizes.
• Computing the area of a circular section in engineering or construction drawings.

The formula works for any circle, regardless of size, as long as you measure the radius in the same unit you want the area in. If you measure in meters, the area is in square meters; if in feet, the area is in square feet.

How to Read the Result

The first output is the area, which is the total space inside the circle. The other two outputs, circumference and diameter, are provided for convenience—they are not needed to compute the area, but they help you verify your input or convert between measurements.

For example, if you enter a radius of 5 m, the area is 78.54 m². That means you could fit 78.54 square meter tiles inside the circle (ignoring gaps). The circumference (31.42 m) is the distance around the circle, and the diameter (10 m) is the distance across the center.

If you only have the diameter, divide it by 2 to get the radius before using the formula. If you only have the circumference, divide it by 2π to get the radius.

Common Mistakes and How to Avoid Them

Several errors are easy to make when calculating circle area:

• Using the diameter instead of the radius. The formula requires r, not d. If you plug in the diameter without dividing by 2, your area will be four times too large.
• Forgetting to square the radius. A common slip is computing π × r instead of π × r². For r = 5, π × 5 = 15.71, but the correct area is 78.54.
• Mixing units. If the radius is in inches, the area is in square inches. Do not mix feet and inches without converting first.
• Rounding too early. If you round π to 3.14 before multiplying, you get a slightly different answer. For most purposes, using 3.14 is fine, but for precision, keep more digits of π until the final step.
• Confusing circumference and area. Circumference is a length (units like m), area is a square measure (units like m²). They cannot be compared directly.

To avoid these, always write down the formula, substitute the radius (not the diameter), and check that your final units are squared.

Limits of the Formula

The formula A = πr² is exact for a perfect Euclidean circle. In the real world, a “circular” object may not be perfectly round due to manufacturing tolerances, wear, or deformation. For most practical purposes, the difference is negligible, but for high-precision engineering, you may need to measure the actual shape.

Also, the formula assumes the circle is flat and two-dimensional. If you are dealing with a sphere (like a ball) or a cylinder (like a can), you need different formulas for surface area or volume. For a sphere, the surface area is 4πr²; for a cylinder’s side, it is 2πrh.

Finally, the calculator gives results rounded to two decimal places. If you need more precision, you can use the formula directly with a calculator that has a π button.

Frequently Asked Questions

Can I calculate the area from the circumference?

Yes. First find the radius using r = C / (2π), then use A = πr². For example, if the circumference is 31.42 m, the radius is 31.42 / (2 × 3.1416) = 5 m, and the area is 78.54 m².

What if I only know the diameter?

Divide the diameter by 2 to get the radius, then apply the formula. If the diameter is 10 m, the radius is 5 m, and the area is 78.54 m². Alternatively, use the formula A = π × (d/2)² directly.

Why is π used in the formula?

π is the ratio of a circle’s circumference to its diameter, and it is the same for every circle. It appears in the area formula because the area of a circle is proportional to the square of its radius, and the constant of proportionality is exactly π.

How do I convert the area to square feet if I measured in inches?

If you measure the radius in inches, the area is in square inches. To convert to square feet, divide by 144 (since 1 ft = 12 in, so 1 ft² = 144 in²). For example, a radius of 6 inches gives an area of π × 36 ≈ 113.1 in², which is about 0.785 ft².

What is the difference between area and circumference?

Area is the space inside the circle, measured in square units (like m²). Circumference is the distance around the circle, measured in linear units (like m). For a circle with radius 5 m, the area is 78.54 m² and the circumference is 31.42 m.

Does the formula work for an ellipse?

No. An ellipse has a different area formula: A = π × a × b, where a and b are the semi-major and semi-minor axes. The circle formula is a special case where a = b = r.

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in r | Radius | m | 5 | 0
out area | Area | m² | pi * r^2 | 2
out circ | Circumference | m | 2 * pi * r | 2
out diam | Diameter | m | 2 * r | 2