Circle Area Formula: How to Calculate a Circle’s Area

The area of a circle is calculated with A = πr², where r is the radius. Enter the radius in the unit you want to use, and this calculator returns the circle’s area in square units, along with its circumference for reference.

Formula

The standard circle area formula is A = πr². In words, multiply pi by the radius multiplied by itself.

• A is the area, measured in square units such as square centimetres (cm²), square metres (m²), square inches (in²), or square feet (ft²).
• π (pi) is approximately 3.14159. It is the constant ratio of a circle’s circumference to its diameter.
• r is the radius: the straight-line distance from the circle’s centre to its edge, measured in a length unit.

The calculator treats the input unit as a generic length unit and reports area in its corresponding square unit. For instance, a radius of 5 centimetres produces an area in square centimetres. Its second result, circumference, is a length, not an area; it is calculated as C = 2πr.

Worked Example

Using 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.

The reference circumference is 2 × π × 5 = 31.4159… units, or 31.42 units rounded to two decimal places. A radius of 5 cm, for example, means an area of 78.54 cm² and a circumference of 31.42 cm.

Radius, Diameter, and When to Use the Formula

The radius and diameter describe related but different measurements. The diameter crosses the circle through its centre from one edge to the other, so it is twice the radius: d = 2r. If a problem gives the diameter, first divide it by two, then use the area formula. Equivalently, substituting r = d/2 gives A = π(d/2)², or A = πd²/4.

Use the area formula when you need the amount of flat surface inside a circular boundary—for example, to compare round tabletops, circular garden beds, or disks. It gives the two-dimensional area, not the distance around the boundary and not the volume of a three-dimensional object.

For a physical project, the calculated area may be only one part of planning. A circular surface may have a rim, a central opening, or an irregular edge, and those features may affect the usable area. A ring-shaped region, for example, is not the area of the full outer circle: subtract the inner circle’s area from the outer circle’s area.

How the Formula Works

Every circle’s circumference divided by its diameter has the same value, π. The area formula follows from the geometry of a circle: the amount of enclosed surface grows in proportion to the square of its radius. That square is why doubling a radius does not merely double the area. It multiplies the area by four.

This relationship is useful for quick comparisons. If one circle has twice the radius of another, its area is four times as large. If its radius is three times as large, its area is nine times as large. Circumference, by contrast, changes in direct proportion to radius: doubling the radius doubles the circumference.

The formula assumes a true circle in a flat plane. It does not account for measurement uncertainty, a wavy boundary, or a surface that curves in three dimensions. In those cases, the answer is an ideal geometric estimate based on the radius supplied.

Units, Precision, and Common Mistakes

Keep the radius in one consistent unit throughout the calculation. If the radius is measured in metres, the area is in square metres. If it is measured in inches, the answer is in square inches. Do not label an area with a length unit: m² and cm² measure area, while m and cm measure length.

Conversions for area are squared conversions. Since 1 metre equals 100 centimetres, 1 m² equals 10,000 cm²—not 100 cm². Similarly, 1 foot equals 12 inches, so 1 ft² equals 144 in². Convert the radius before calculating, or convert the final area using the squared length conversion factor.

• Using diameter as radius: divide a given diameter by two before squaring it. Forgetting this makes the calculated area four times too large.
• Squaring only the radius: calculate r × r, then multiply by π. The expression is πr², not (πr)².
• Rounding too early: retain the full calculator result during intermediate steps and round only the final answer to a sensible precision.
• Confusing area and circumference: area is in square units; circumference is in ordinary length units.

Measurements themselves may be approximate. Because radius is squared, a small radius error can have a more noticeable effect on the area. For ordinary estimates, use a measured radius and report a number of decimal places that matches the quality of that measurement rather than implying excessive precision.

Frequently Asked Questions

What is the formula for the area of a circle?
It is A = πr²: multiply pi by the radius squared.

How do I find a circle’s area from its diameter?
Divide the diameter by two to get the radius, then calculate A = πr². You can also use A = πd²/4.

What is the area of a circle with radius 5?
Its area is π × 5² = 25π, or approximately 78.54 square units. The unit depends on the unit used for the radius.

Why is the area in square units?
The calculation multiplies one length by another: radius × radius. Thus a radius in centimetres produces square centimetres, and a radius in feet produces square feet.

Does doubling the radius double the area?
No. Since the radius is squared, doubling it makes the area four times as large. The circumference, however, doubles.

What is the difference between area and circumference?
Area measures the surface enclosed by the circle and uses square units. Circumference measures the distance around its edge and uses ordinary length units.

Related

• Area of a Circular Sector Formula
• Area to the Right of Z Calculator & Guide
• Area Calculator Google: How to Measure Any Space

in r | Radius | units | 5 | 0 | 100000
out a | Area | square units | pi * r ^ 2 | 2
out c | Circumference | units | 2 * pi * r | 2