Area of a Circle Calculator: Radius or Diameter to Area
Calculate the area, diameter, radius, and circumference of a circle.
Circle Calculator
Calculate area, circumference, diameter, and radius of a circle
Quick Tips
- • π is approximated as 3.14159
- • Diameter = 2 × radius
- • Area units are squared (e.g., cm², m²)
What is the Area of a Circle?
The area of a circle is the amount of space inside the circle boundary.
It depends only on the radius (r). If you know the diameter (d), you can convert it to radius using r = d/2.
Circle Formulas
Area: A = πr²
Circumference: C = 2πr
Diameter: d = 2r
Radius from diameter: r = d/2
Quick Reference (What Each Formula Gives You)
| You know | You want | Use this |
|---|---|---|
| Radius (r) | Area | A = πr² |
| Radius (r) | Circumference | C = 2πr |
| Radius (r) | Diameter | d = 2r |
| Diameter (d) | Radius | r = d/2 |
| Diameter (d) | Area | A = π(d/2)² |
How to Calculate Circle Area (Step-by-Step)
- 1Start with the radius r. (If you only have diameter d, use r = d/2.)
- 2Square the radius: r²
- 3Multiply by π: A = πr²
- 4Keep units squared (cm², m², in², etc.)
Worked Examples
| Given | Steps | Result (Exact) | Result (Approx) |
|---|---|---|---|
| r = 5 | A = π×5² = 25π | 25π | 78.54 |
| d = 10 | r = 10/2 = 5 → A = 25π | 25π | 78.54 |
| r = 2.5 | A = π×(2.5)² = 6.25π | 6.25π | 19.63 |
Units tip: If radius is in cm, area will be in cm². Circumference stays in cm. Area always uses squared units.
Diagram: Radius, Diameter, and Circumference
Related Shapes: Semicircle and Sector
If you’re working with part of a circle:
- Semicircle area = (πr²) / 2
- Quarter circle area = (πr²) / 4
- Sector area (angle θ in degrees) = (θ/360) × πr²
Area of a Circle FAQs
Can I calculate area using diameter instead of radius?
Yes. Convert diameter to radius using r = d/2, then apply A = πr². Or use A = π(d/2)² directly.
Why is circle area measured in squared units?
Area measures surface size. If length is cm, area becomes cm² because it covers a 2D region.
What value of π does the calculator use?
Most calculators use π ≈ 3.141592653589793 for accurate results.
What if my radius is a decimal?
No issue. The formula still works, and the result will often be a decimal.
How do I find circumference if I know area?
First solve for r from A = πr²: r = √(A/π). Then compute C = 2πr.