Circle Area Calculator
Enter a known measurement below (radius, diameter, or circumference) and this tool will calculate the area instantly.
What is the area of a circle?
The area of a circle is the amount of two-dimensional space enclosed inside the circle’s boundary. If you imagine painting the inside of a round table top, the amount of paintable surface is the area. Area is always measured in square units, such as cm2, m2, or ft2.
Formula used in this calculator
The core formula is:
A = πr2
Where:
- A = area
- π (pi) ≈ 3.14159
- r = radius (distance from center to edge)
If you know the diameter
The diameter is twice the radius, so r = d / 2. Once radius is found, area is still A = πr2.
If you know the circumference
Circumference and radius are related by C = 2πr. Rearranging gives r = C / (2π), then area follows from A = πr2.
How to use this area of a circle calculator
- Select whether you have radius, diameter, or circumference.
- Enter the numeric value.
- Optionally choose a unit for cleaner output.
- Click Calculate Area to see area and related circle measurements.
Worked examples
Example 1: Radius given
If radius = 5 cm, then:
A = π × 52 = 25π ≈ 78.54 cm2
Example 2: Diameter given
If diameter = 12 m, then radius = 6 m. So:
A = π × 62 = 36π ≈ 113.10 m2
Example 3: Circumference given
If circumference = 31.4 in, then radius ≈ 31.4 / (2π) ≈ 5 in. So area is about:
A ≈ π × 52 ≈ 78.54 in2
Common mistakes to avoid
- Using diameter directly in πr2 without dividing by 2 first.
- Forgetting to square the radius.
- Reporting area in linear units (cm) instead of square units (cm2).
- Rounding too early in multi-step calculations.
Where this is useful in real life
Circle area calculations show up everywhere: landscaping circular flower beds, estimating round rugs, cutting lids for containers, calculating cross-sectional pipe flow area, designing circular signs, and solving geometry homework problems.
Quick FAQ
Can the area be negative?
No. A geometric area is never negative. This calculator requires positive input values.
What if I only know radius in one unit and want area in another?
Convert the radius first, then compute area. Because area is squared, unit conversions have a squared effect.
How precise are the results?
The calculator uses JavaScript’s built-in numeric precision and π from Math.PI, which is accurate for practical use in school, engineering estimates, and daily tasks.