area of circle calculator

What is the area of a circle?

The area of a circle is the amount of two-dimensional space inside its boundary. If you imagine painting the inside of a circular table, the painted surface is the table’s circular area. Area is always expressed in square units such as cm², m², or in².

Because circles are curved instead of straight-sided, the formula uses the constant π (pi), approximately 3.14159. This makes circle area one of the most common and useful formulas in geometry, engineering, design, physics, and everyday planning.

Circle area formula

Primary formula

A = πr²

• A = area
• π = pi (about 3.14159)
• r = radius (distance from center to edge)

If you know diameter instead

Diameter is twice the radius, so r = d/2. Substituting into the main formula gives:

A = π(d/2)² = πd²/4

If you know circumference instead

Circumference is related to radius by C = 2πr, so r = C/(2π). Then:

A = π(C/(2π))² = C²/(4π)

How to use this area of circle calculator

• Select whether you know radius, diameter, or circumference.
• Enter the numeric value.
• Select the unit (cm, m, in, ft, etc.).
• Choose decimal precision and click Calculate Area.
• The calculator shows converted radius and final area in square units.

Worked examples

Example 1: Radius is known

Suppose radius is 5 cm. A = πr² = π(5²) = 25π ≈ 78.54 cm².

Example 2: Diameter is known

Diameter is 12 m, so radius is 6 m. A = π(6²) = 36π ≈ 113.10 m².

Example 3: Circumference is known

Circumference is 31.4 in. Radius = C/(2π) ≈ 5 in, then area ≈ 78.54 in².

Common mistakes to avoid

• Using diameter directly in A = πr² without first dividing by 2.
• Forgetting to square the radius.
• Reporting units as cm instead of cm².
• Rounding too early during intermediate steps.
• Entering negative values (lengths should be positive).

Practical uses of circle area

Circle area appears in many real-world tasks:

• Landscaping circular flower beds and patios
• Estimating material for round tabletops or rugs
• Designing pipes, tanks, and circular mechanical parts
• Planning paint coverage on circular signs
• Analyzing cross-sectional areas in science and engineering

Quick FAQ

What is the difference between radius and diameter?

Radius goes from center to edge. Diameter goes from edge to edge through the center. Diameter is always 2 × radius.

Why does the result use square units?

Area measures surface, not length. Surface units are squared (for example, m²).

Can I use fractions or decimals?

Yes. The calculator accepts decimal values. You can convert fractions to decimals first for easiest input.

Final takeaway

The area of a circle is simple once you know which measurement you have. Convert to radius, apply A = πr², and report the answer in square units. Use the calculator above for quick, accurate results whether your starting value is radius, diameter, or circumference.